Green and Fielitz (1977) claimed that many daily stock return series are characterized by long-term dependence.
Aydogan and Booth (1988) concluded that there was no significant evidence for long-term memory in common stock returns.
Lo (1991) found little evidence of long-term memory in historical U.S. stock market returns.
Lobato and Savin (1998) found no evidence of long memory in daily stock returns.
Cheung (1993) found evidence of long memory in foreign exchange rates.
Willinger, Taqqu and Teverovsky (1999) found empirical evidence of long-range dependence in stock price returns, but the evidence was not absolutely conclusive.
Peters (1996) applied R/S analysis and concluded that most of the capital markets are characterized by long memory processes.
Weron and Przybylowicz (2000) found that electricity price returns are strongly mean-reverting.
Using the spectral regression method, Barkoulas, Baum and Travlos (2000) found significant and robust evidence of positive long-term persistence in the Greek stock market.
Mandelbrot (1972) applied R/S analysis to financial returns.
Cajueiro and Tabak (2004) found that the markets of Hong Kong, Singapore and China exhibit long-range dependence.
Beine and Laurent (2003) investigate the major exchange rates and find no evidence of long memory in the conditional mean.
Baum, Barkoulas and Caglayan (1999) reject the hypothesis of long memory in real exchange rates in the post-Bretton Woods era.
Hiemstra and Jones (1997) applied the modified rescaled range test to the return series of 1,952 common stocks and their results indicated that long memory is not a widespread characteristic of those stocks.
Cheung and Lai (2001) found long memory in yen-based real exchange rates.
Sapio (2004) used specral analysis and found long-memory in day-ahead electricity prices.
Oh, Um and Kim (2006) studied the long-term memory in diverse stock market indices and foreign exchange rates using the Detrended Fluctuation Analysis(DFA). For all daily and high-frequency market data studied, no significant long-term memory property was detected in the return series.
Barkoulas and Baum (1996) applied the spectral regression method and found no evidence of long memory in either aggregate or sectoral stock indices, but evidence of long memory in 5, intermediate memory in 3 and no fractal structure in 22 of the 30 Dow Jones Industrials companies. Overall findings did not offer convincing evidence against the martingale model.
Cajueiro and Tabak (2005) state that the presence of long-range dependence in asset returns seems to be a stylized fact. They studied the individual stocks in the Brazilian stock market and found evidence that firm-specific variables can explain, at least partially, the long-range dependence phenomena.
Sadique and Silvapulle (2001) examined the presence of long memory in weekly stock returns of seven countries, namely Japan, Korea, New Zealand, Malaysia, Singapore, the USA and Australia. They found evidence for long-term dependence in four countries: Korea, Malaysia, Singapore and New Zealand.
Cheung and Lai (1993) examined the long memory behaviour in gold returns during the post-Bretton Woods period and found that the long memory behaviour in gold returns is rather unstable. They conclude, ``[w]hen only few observations corresponding to major political events in the Middle East, together with the Hunts event, in late 1979 are omitted, little evidence of long memory can be found.''
Henry (2002) investigated long range dependence in nine international stock index returns. They found evidence of long memory in four of them, the German, Japanese, South Korean and Taiwanese markets, but not for the markets of the UK, USA, Hong Kong, Singapore and Australia.
Goetzmann (1993) considered three centuries of stock market prices. R/S tests provided some evidence that the detrended London Stock Exchange (LSE) and NYSE prices may exhibit long-term memory.
Lux (1996) analyzed German stock market data and found no evidence for (positive or negative) long-term dependence in the returns series.
De Peretti (2003) examined the behaviour of four tests for fractional integration in daily observations of silver prices. He concluded that one must use at least a bilateral bootstrap test to detect long-range dependence in time series, and deduced that silver prices do not exhibit long memory.
Mills (1993) found little evidence of long memory in daily UK stock returns.
Panas (2001) found long-memory in the Athens Stock Exchange.
Moody and Wu (1996) improve Lo’s R/S statistic and conclude that the DEM/USD series is mildly trending on time scales of 10 to 100 ticks.
Tschernig (1995) found evidence for weak long memory in the changes of DM/USD spot rates and the SF/USD spot rates; in contrast, there was no evidence for for long memory in the DM/SF spot rate changes.
Tolvi (2003) found long memory in Finnish stock market return data.
Chow, Pan and Sakano (1996) found evidence that consistently revealed the absence of long-term dependence in 22 international equity market indexes.
Nawrocki (1995) considered the CRSP monthly value-weighted index and the S&P 500 daily index, and found that the Hurst exponent and the Lo modified R/S statistic indicate that there is persistent finite memory.
Using a monthly data set consisting of stock market indices of 16 OECD countries, Tolvi (2003) found statistically significant long memory for three countries: Denmark, Finland and Ireland, which are all small markets.
Nath (2001) found indications of long-term memory in the Indian stock market using R/S analysis, but suggested that a more rigid analysis, such as Lo's modified R/S statistic, should be used.
Moody and Wu (1995) performed rescaled range and Hurst exponent analysis on tick-by-tick interbank foreign exchange rates, and found that they are mean-reverting.
Limam (2003) analyzed stock index returns in 14 markets and concluded that long memory tends to be associated with thin markets.
Bhar (1994) tested for long-term memory in yen/dollar exchange rate using Lo's methodology and found no evidence of long-term memory.
Embrechts, Cader and Deboeck (1994) applied rescaled range analysis to US Fed Fund rates, US Treasury notes, Swiss franc/US dollar exchange rates and the Japanese stock market (TOPIX) and claimed that it shows that most financial markets follow a biased random walk.
Cavalcante and Assaf (2002) found little evidence of long memory in the returns of the Brazilian Stock Market.
Using the spectral regression method, Barkoulas and Baum (1997) found significant evidence of long memory in the 3- and 6-month returns (yield changes) on Eurocurrency deposits denominated by Japanese yen (Euroyen).
Chen (2000) calculated the classical rescaled range statistic of Hurst for seven Asia-Pacific countries' stock indices and concluded that all the index returns have long memory.
Embrechts (1994) claims that the Hurst coefficient for yen/dollar returns indicates a memory effect.
Huang and Yang (1999) apply the modified R/S technique to intraday data and find the phenomenon of long-term memory in both NYSE and NASDAQ indices.
Crato and Ray (2000) found no evidence for long memory in futures' returns.
Grau-Carles (2005) apply four tests for long memory to two major daily stock indices, the Standard & Poor's 500 and the Dow Jones Industrial Average, two samples from each. There was no evidence of long memory in the returns.
Nath and Reddy (2002) used R/S analysis and found long-term long memory in rupee-dollar exchange rate.
Zhuang, Green and Maggioni (2000) investigated British stock returns and found little or no evidence of long-range dependence.
Publications
GREENE, Myron T. and Bruce D. FIELITZ, 1977. Long-term dependence in common stock returns. Journal of Financial Economics, Volume 4, Issue 3, May 1977, Pages 339-349. [Cited by 89] (3.03/year)
Abstract: "The efficient market, martingale model of security price movements requires that the arrival of new information be promptly arbitraged away. A necessary and sufficient condition for the existence of an arbitraged price is that statistical dependence among prices must decrease very rapidly. If persistent statistical dependence is present, the arbitraged price changes do not follow a martingale and should have an infinite variance. Using a technique for detecting long-term dependence, called R/S analysis, 200 daily stock return series are studied; many series are characterized by long-term dependence. Thus, in the presence of long-term dependence, the martingale model does not hold. Also, the distribution of security returns is non-normal stable Paretian as opposed to Gaussian."
CAMPBELL, John Y., Andrew W. LO and A. Craig MacKINLAY, 1997, The Econometrics of Financial Markets. Princeton University Press. [Cited by 135] (300/year)
2.6 Tests For Long-Range Dependence [5 pages]
"In particular, what the earlier literature had assumed was evidence of long-range dependence in US stock returns may well be the result of quickly decaying short-range dependence instead."
DING, Zhuanxin, Clive W. J. GRANGER and Robert F. ENGLE, 2001. A long memory property of stock market returns and a new model, Journal of Empirical Finance, Volume 1, Issue 1, June 1993, Pages 83-106. [Cited by 593] (111.52/year)
Abstract: "A ‘long memory’ property of stock market returns is investigated in this paper. It is found that not only there is substantially more correlation between absolute returns than returns themselves, but the power transformation of the absolute return ¦rt¦d also has quite high autocorrelation for long lags. It is possible to characterize ¦rt¦d to be ‘long memory’ and this property is strongest when d is around 1. This result appears to argue against ARCH type specifications based upon squared returns. But our Monte-Carlo study shows that both ARCH type models based on squared returns and those based on absolute return can produce this property. A new general class of models is proposed which allows the power δ of the heteroskedasticity equation to be estimated from the data."
TAQQU, Murad S., Vadim TEVEROVSKY and Walter WILLINGER, 1995. Estimators for long-range dependence: An empirical study, Fractals, Vol. 3, No. 4 (1995) 785-798. [Cited by 316] (27.93/year)
Abstract: "Various methods for estimating the self-similarity parameter and/or the intensity of long-range dependence in a time series are available. Some are more reliable than others. To discover the ones that work best, we apply the different methods to simulated sequences of fractional Gaussian noise and fractional ARIMA (0, d, 0). We also provide here a theoretical justification for the method of residuals of regression."
LO, Andrew W., 1991. Long-term memory in stock market prices, Econometrica, Vol. 59, No. 5. (Sep., 1991), pp. 1279-1313. [Cited by 433] (25.01/year)
Abstract: "A test for long-run memory that is robust to short-range dependence is developed. It is an extension of the “range over standard deviation” or R/S statistic, for which the relevant asymptotic sampling theory is derived via functional central limit theory. This test is applied to daily and monthly stock returns indexes over several time periods and, contrary to previous findings, there is no evidence of long-range dependence in any of the indexes over any sample period or sub-period once short-range dependence is taken into account. Illustrative Monte Carlo experiments indicate that the modified R/S test has power against at least two specific models of long-run memory, suggesting that stochastic models of short-range dependence may adequately capture the time series behavior of stock returns."
Conclusion: "Using a simple modification of the Hurst-Mandelbrot rescaled range that accounts for short-term dependence, and contrary to previous studies, I find little evidence of long-term memory in historical U.S. stock market returns. If the source of serial correlation is lagged adjustment to new information, the absence of strong dependence in stock returns should not be surprising from an economic standpoint, given the frequency with which financial asset markets clear. Surely financial security prices must be immune to persistent informational asymmetries, especially over longer time spans. Perhaps the fluctuations of aggregate economic output are more likely to display such long-run tendencies, as Kondratiev and Kuznets have suggested, and this long-memory in output may eventually manifest in the return to equity. But if some form of long-range dependence is indeed present in stock returns, it will not be easily detected by any of our current statistical tools, especially in view of the optimality of the R/S statistic in the Mandelbrot and Wallis (1969) sense. Direct estimation of particular models may provide more positive evidence of long-term memory and is currently being pursued by several investigators."
PETERS, E.E., 1991. Chaos and order in the capital markets. Wiley New York. [Cited by 297] (19.39/year)
GUILLAUME, D.M., et al., 1997. From the bird's eye to the microscope: A survey of new stylized facts of the intra-daily foreign exchange markets. Finance and Stochastics. [Cited by 172] (18.46/year)
Abstract: "This paper presents stylized facts concerning the spot intra-daily foreign exchange markets. It first describes intra-daily data and proposes a set of definitions for the variables of interest. Empirical regularities of the foreign exchange intra-daily data are then grouped under three major topics: the distribution of price changes, the process of price formation and the heterogeneous structure of the market. The stylized facts surveyed in this paper shed new light on the market structure that appears composed of heterogeneous agents. It also poses several challenges such as the definition of price and of the time-scale, the concepts of risk and efficiency, the modeling of the markets and the learning process."
ENGEL, C. and J.D. HAMILTON, 1990. Long Swings in the Dollar: Are They in the Data and Do Markets Know It?. The American Economic Review. [Cited by 285] (17.47/year)
Abstract: "The value of the dollar appears to move in one direction for long periods of time. The authors develop a new statistical model of exchange rate dynamics as a sequence of stochastic, segmented time trends. They reject the null hypothesis that exchange rates follow a random walk in favor of their model of long swings. The authors' model also generates better forecasts than a random walk. The specification is a natural framework for assessing the importance of the "peso problem" for the dollar. The authors nonetheless reject uncovered interest parity."
LOBATO, I.N. and N.E. SAVIN, 1998. Real and Spurious Long-Memory Properties of Stock-Market Data. Journal of Business & Economic Statistics, Vol. 16, No. 3. (Jul., 1998), pp. 261-268. [Cited by 139] (16.71/year)
Abstract: "We test for the presence of long memory in daily stock returns and their squares using a robust semiparametric procedure. Spurious results can be produced by nonstationarity and aggregation. We address these problems by analyzing subperiods of returns and using individual stocks. The test results show no evidence of long memory in the returns. By contrast, there is strong evidence in the squared returns."
COMTE, F. and E. RENAULT, 1998. Long memory in continuous-time stochastic volatility models. Mathematical Finance. [Cited by 126] (15.15/year)
Abstract: "This paper studies a classical extension of the Black and Scholes model for option pricing, often known as the Hull and White model. Our specification is that the volatility process is assumed not only to be stochastic, but also to have long-memory features and properties. We study here the implications of this continuous-time long-memory model, both for the volatility process itself as well as for the global asset price process. We also compare our model with some discrete time approximations. Then the issue of option pricing is addressed by looking at theoretical formulas and properties of the implicit volatilities as well as statistical inference tractability. Lastly, we provide a few simulation experiments to illustrate our results."
HURST, H.E., 1951. Long-term storage capacity of reservoirs. Transactions of the American Society of Civil Engineers, Volume 116, Pages 770--799. [Cited by 815] (14.47/year)
CHEUNG, Yin-Wong, 1993. Long memory in foreign-exchange rates, Journal of Business & Economic Statistics, January 1993, Vol. 11, No. 1, pp. 93-101. [Cited by 125] (9.39/year)
Abstract: "Using the Geweke-Porter-Hudak test, we find evidence of long memory in exchange-rate data. This implies that the empirical evidence of unit roots in exchange rates may not be robust to long-memory alternatives. Fractionally integrated autoregressive moving average (ARFIMA) models are estimated by both the time-domain exact maximum likelihood (ML) method and the frequency-domain approximate ML method. Impulse-response functions and forecasts based on these estimated ARFIMA models are evaluated to gain insight into the long-memory characteristics of exchange rates. Some tentative explanations of the long memory found in the exchange rates are discussed."
WILLINGER, Walter, Murad S. TAQQU and Vadim TEVEROVSKY, 1999. Stock market prices and long-range dependence, Finance and Stochastics, Volume 3, Number 1 / January, 1999, 1-13. [Cited by 62] (8.47/year)
Abstract: "Using the CRSP (Center for Research in Security Prices) daily stock return data, we revisit the question of whether or not actual stock market prices exhibit long-range dependence. Our study is based on an empirical investigation reported in Teverovsky, Taqqu and Willinger [33] of the modified rescaled adjusted range or R/S statistic that was proposed by Lo [17] as a test for long-range dependence with good robustness properties under “extra” short-range dependence. Our main conclusion is that because the modified R/S statistic shows a strong preference for accepting the null hypothesis of no long-range dependence, irrespective of whether long-range dependence is present in the data or not, Lo’s acceptance of the hypothesis for the CRSP data (i.e., no long-range dependence in stock market prices) is less conclusive than is usually regarded in the econometrics literature. In fact, upon further analysis of the data, we find empirical evidence of long-range dependence in stock price returns, but because the corresponding degree of long-range dependence (measured via the Hurst parameter H) is typically very low (i.e., H-values around 0.60), the evidence is not absolutely conclusive."
LILLO, Fabrizio and J. Doyne FARMER, 2004. The long memory of the efficient market, Studies in Nonlinear Dynamics and Econometrics, Volume 8, Issue 3, Article 1. [Cited by 25] (7.54/year)
Abstract: "For the London Stock Exchange we demonstrate that the signs of orders obey a long-memory process. The autocorrelation function decays roughly as a power law with an exponent of 0.6, corresponding to a Hurst exponent H = 0.7. This implies that the signs of future orders are quite predictable from the signs of past orders; all else being equal, this would suggest a very strong market inefficiency. We demonstrate, however, that fluctuations in order signs are compensated for by anti-correlated fluctuations in transaction size and liquidity, which are also long-memory processes that act to make the returns whiter. We show that some institutions display long-range memory and others don’t."
SIMONSEN, Ingve, Alex HANSEN and Olav Magnar NES, 1998. Determination of the Hurst exponent by use of wavelet transforms, Physical Review E, Volume 58, Number 3, Pages 2779-2787, September 1998. [Cited by 50] (6.01/year)
Abstract: "We propose a method for (global) Hurst exponent determination based on wavelets. Using this method, we analyze synthetic data with predefined Hurst exponents, fracture surfaces, and data from economy. The results are compared to those obtained with Fourier spectral analysis. When many samples are available, the wavelet and Fourier methods are comparable in accuracy. However, when one or only a few samples are available, the wavelet method outperforms the Fourier method by a large margin."
GIRAITIS, Liudas, Piotr KOKOSZKA and Remigijus LEIPUS, 2001. Testing for Long Memory in the Presence of a General Trend, Journal of Applied Probability, Vol. 38, No. 4. (Dec., 2001), pp. 1033-1054. [Cited by 29] (5.46/year)
Abstract: "The paper studies the impact of a broadly understood trend, which includes a change point in mean and monotonic trends studied by Bhattacharya et al. (1983), on the asymptotic behaviour of a class of tests designed to detect long memory in a stationary sequence. Our results pertain to a family of tests which are similar to Lo’s (1991) modified R/S test. We show that both long memory and nonstationarity (presence of trend or change points) can lead to rejection of the null hypothesis of short memory, so that further testing is needed to discriminate between long memory and some forms of nonstationarity. We provide quantitative description of trends which do or do not fool the R/S-type long memory tests. We show, in particular, that a shift in mean of a magnitude larger than N -1/2, where N is the sample size, affects the asymptotic size of the tests, whereas smaller shifts do not do so."
WERON, R. and B. PRZYBYLOWICZ, 2000. Hurst analysis of electricity price dynamics. Physica A: Statistical Mechanics and its Applications, Volume 283, Issues 3-4, 15 August 2000, Pages 462-468. [Cited by 26] (4.12/year)
Abstract: "The price of electricity is extremely volatile, because electric power cannot be economically stored, end user demand is largely weather dependent, and the reliability of the grid is paramount. However, underlying the process of price returns is a strong mean-reverting mechanism. We study this feature of electricity returns by means of Hurst R/S analysis."
Final remarks: "We have analyzed two data sets containing information about electricity prices in California and Central Europe. In both cases, the returns have been found to be mean-reverting processes. However, due to the calculation method of the SWEP index or, maybe, the di erence between the exchange spot market in California and the Swiss–German OTC spot market, the latter data set revealed a weaker anti-persistence."
BARKOULAS, John T., Christopher F. BAUM and Nickolaos TRAVLOS, 2000. Long memory in the Greek stock market, Applied Financial Economics, Volume 10, Number 2, 1 April 2000, pp. 177-184. [Cited by 25] (3.96/year)
Abstract: "Tests are made of the stochastic long memory in the Greek stock market, an emerging capital market. The fractional differencing parameter is estimated using the spectral regression method. Contrary to findings for major capital markets, significant and robust evidence of positive long-term persistence is found in the Greek stock market. As compared to benchmark linear models, the estimated fractional models provide improved out-of-sample forecasting accuracy for the Greek stock returns series over longer forecasting horizons."
CAJUEIRO, Daniel O. and Benjamin M. TABAK, 2004. Evidence of long range dependence in Asian equity markets: the role of liquidity and market …. Physica A: Statistical Mechanics and its Applications, Volume 342, Issues 3-4, 1 November 2004, Pages 656-664. [Cited by 8] (3.45/year)
Abstract: "In this paper, the efficient market hypothesis is tested for China, Hong Kong and Singapore by means of the long memory dependence approach. We find evidence suggesting that Hong Kong is the most efficient market followed by Chinese A type shares and Singapore and finally by Chinese B type shares, which suggests that liquidity and capital restrictions may play a role in explaining results of market efficiency tests."
Conclusions: "In this paper, we investigate the long-range dependence phenomena in three Asian markets, namely Hong Kong, Singapore and China, and find evidence that these markets present long range-dependence. We also build a ranking from lowest to highest inefficiency and find that liquidity and market capitalization may play a role in understanding results coming out from tests for long range dependence. These results suggest that more research is needed on testing for long range dependence for different markets and on increasing our understanding of the possible causes and origins of long range dependencies. Theoretical models that address these issues should be particularly welcome."
BEINE, Michel and Sébastien LAURENT, 2003. Central Bank Interventions and Jumps in Double Long Memory Models of Daily Exchange Rates, Journal of Empirical Finance, Volume 10, Issue 5, December 2003, Pages 641-660. [Cited by 10] (3.02/year)
Abstract: "In this paper, we estimate ARFIMA–FIGARCH models for the major exchange rates (against the US dollar) which have been subject to direct central bank interventions in the last decades. We show that the normality assumption is not adequate due to the occurrence of volatility outliers and its rejection is related to these interventions. Consequently, we rely on a normal mixture distribution that allows for endogenously determined jumps in the process governing the exchange rate dynamics. This distribution performs rather well and is found to be important for the estimation of the persistence of volatility shocks. Introducing a time-varying jump probability associated to central bank interventions, we find that the central bank interventions, conducted in either a coordinated or unilateral way, induce a jump in the process and tend to increase exchange rate volatility."
BAUM, Christopher F., John T. BARKOULAS and Mustafa CAGLAYAN, 1999. Long memory or structural breaks: can either explain nonstationary real exchange rates under the current float?Journal of International Financial Markets, Institutions and Money, Volume 9, Issue 4, November 1999, Pages 359-376. [Cited by 20] (2.73/year)
Abstract: "This paper considers two potential rationales for the apparent absence of mean reversion in real exchange rates in the post-Bretton Woods era. We allow for (i) fractional integration and (ii) a double mean shift in the real exchange rate process. These methods, applied to CPI-based rates for 17 countries and WPI-based rates for 12 countries, demonstrate that the unit-root hypothesis is robust against both fractional alternatives and structural breaks. This evidence suggests rejection of the doctrine of absolute long-run purchasing power parity during the post-Bretton Woods era."
MONTANARI, A., 2003. Long-range dependence in hydrology. Theory and Applications of Long-Range Dependence, edited by: …. [Cited by 9] (2.71/year)
GIRAITIS, L., et al., 2000. Semiparametric estimation of the intensity of long memory in conditional heteroskedasticity, Statistical Inference for Stochastic Processes, Volume 3, Numbers 1-2 / January, 2000, Pages 113-128. [Cited by 17] (2.69/year)
The paper is concerned with the estimation of the long memory parameter in a conditionally heteroskedastic model proposed by Giraitis et al. (1999b). We consider estimation methods based on the partial sums of the squared observations, which are similar in spirit to the classical R / S analysis, as well as spectral domain approximate maximum likelihood estimators. We review relevant theoretical results and present an empirical simulation study.
HIEMSTRA, Craig and Jonathan D. JONES, 1997. Another look at long memory in common stock returns, Journal of Empirical Finance, Volume 4, Issue 4, December 1997, Pages 373-401. [Cited by 25] (2.65/year)
Abstract: "We apply the modified rescaled range test to the return series of 1,952 common stocks. The results indicate that long memory is not a widespread characteristic of these stocks. But logit models of the event of a test rejection reveal that rejections are linked to firms with large risk-adjusted average returns. The maximal moment of a return distribution is also found to influence the event of a rejection, but not in a way suggestive of moment-condition failure. Evidence suggestive of survivorship bias is also uncovered. We conclude that there is some evidence consistent with persistent long memory in the returns of a small proportion of stocks."
CHEUNG, Yin-Wong and Kon S. LAI, 2001. Long Memory and Nonlinear Mean Reversion in Japanese Yen-Based Real Exchange Rates, Journal of International Money and Finance, Volume 20, Issue 1, February 2001, Pages 115-132. [Cited by 14] (2.63/year)
Abstract: "The extraordinary difficulty in uncovering parity reversion in yen-based real exchange rates has often been ascribed to a missing trend variable. This study identifies an alternative explanation and shows that the puzzling behavior of real yen rates may stem from long-memory dynamics, which undermine unit-root tests in their ability to detect mean reversion. The long-memory findings are consistent with the long swings in yen exchange rates during the current float. Further analysis also reveals evidence of non-monotonic reversion toward parity."
SAPIO, Sandro, 2004. Market design, bidding rules, and long memory in electricity prices, Revue d’Economie Industrielle 107: 151-170. [Cited by 6] (2.59/year)
Abstract: "In uniform price, sealed-bid, day-ahead electricity auctions, the market price is set at the intersection between aggregate demand and supply functions constructed by a market operator. Each day, just one agent - the marginal generator - owns the market-clearing plant. Moreover, day-ahead auctions are embedded in multi-segment systems, wherein diverse protocols coexist and change over time.
This complex environment leads to adoption of simple, adaptive bidding rules. Specifically, such a market design enables the emergence of two different types of routines, depending on whether the agent is a likely marginal or inframarginal generator. However, because of the uniform price mechanism, only the bidding behavior of the former can be reflected into market prices.
Depending on the specific way marginal generators process past information to set their bids - 'hyperbolic' or 'exponential' - electricity prices are likely to display long- or short-memory. Using an analogy with the hyperbolic discounting - a quite robust behavioral bias in humans - a long-memory view of electricity prices can be supported. This insight is confirmed by spectral analysis of daily data from NordPool and CalPX markets, in sharp contrast with most previous empirical studies.
This paper underlines the importance of institutional settings in determining the relationship between individual behavior and market outcomes, and proposes an interesting mapping of bidding rules and models of information processing into the time series properties of market prices."
DUBRULLE, B., F. GRANER and D. SORNETTE (editors), 1997. Scale Invariance and Beyond. Scale Invariance and Beyond. Proceedings of the Les Houches …. [Cited by 24] (2.58/year)
OH, GabJin, Cheol-Jun UM and Seunghwann KIM, 2006. Long-term Memory and Volatility Clustering in Daily and High-frequency Price Changes. Arxiv preprint physics/0601174. [Cited by 1] (2.45/year)
Abstract: "We study the long-term memory in diverse stock market indices and foreign exchange rates using the Detrended Fluctuation Analysis(DFA). For all daily and high-frequency market data studied, no significant long-term memory property is detected in the return series, while a strong long-term memory property is found in the volatility time series. The possible causes of the long-term memory property are investigated using the return data filtered by the AR(1) model, reflecting the short-term memory property, and the GARCH(1,1) model, reflecting the volatility clustering property, respectively. Notably, we found that the memory effect in the AR(1) filtered return and volatility time series remains unchanged, while the long-term memory property either disappeared or diminished significantly in the volatility series of the GARCH(1,1) filtered data. We also found that in the high-frequency data the long-term memory property may be generated by the volatility clustering as well as higher autocorrelation. Our results imply that the long-term memory property of the volatility time series can be attributed to the volatility clustering observed in the financial time series."
BARKOULAS, John T. and Christopher F. BAUM, 1996. Long term dependence in stock returns, Economics Letters, Volume 53, Issue 3, December 1996, Pages 253-259. [Cited by 25] (2.42/year)
Abstract: "We test for long-term dependence in US stock returns, analyzing composite and sectoral stock indices and firms’ returns series to evaluate aggregation effects. Fractal dynamics are not detected in stock indices but are present in some firms’ returns series."
CAJUEIRO, Daniel O. and Benjamin M. TABAK, 2005. Possible causes of long-range dependence in the Brazilian stock market. Physica A: Statistical Mechanics and its Applications, Volume 345, Issues 3-4, 15 January 2005, Pages 635-645. [Cited by 3] (2.28/year)
Abstract: "While the presence of long-range dependence in the asset returns seems to be a stylized fact, the issue of arguing the possible causes of this phenomena is totally obscure. Trying to shed light in this problem, we investigate the possible sources of the long-range dependence phenomena in the Brazilian Stock Market. For this purpose, we employ a sample which comprises stocks traded in the Brazilian financial market (BOVESPA Index). The Hurst exponent here is considered as our measure of long-range dependence and it is evaluated by six different methods. We have found evidence of statistically significant rank correlation between specific variables of the Brazilian firms which subscribe stocks and the long-range dependence phenomena present in these stocks."
SADIQUE, Shibley and Param SILVAPULLE, 2001. Long-term memory in stock market returns: international evidence. International Journal of Finance & Economics, Volume 6, Issue 1, January 2001, Pages 59-67. [Cited by 12] (2.26/year)
Abstract: "A lot of recent work has addressed the issue of the presence of long memory components in stock prices because of the controversial implications of such a finding for market efficiency and for martingale models of asset prices used in financial economics and technical trading rules used for forecasting. This paper examines the presence of long memory in the stock returns of seven countries, namely Japan, Korea, New Zealand, Malaysia, Singapore, the USA and Australia. The classical and modified rescaled range tests, the semiparametric test proposed by Geweke and Porter-Hudak, the frequency domain score test proposed by Robinson and its time-domain counterpart derived by Silvapulle, are applied to these returns in order to detect the long memory property. Evidence suggests that the Korean, Malaysian, Singapore and New Zealand stock returns are long-term dependent, indicating that these two markets are not efficient. The results of this study should be useful to regulators, practitioners and derivative market participants, whose success precariously depends on the ability to forecast stock price movements."
CHEUNG, Yin-Wong and Kon S. LAI, 1993. Do Gold Market Returns Have Long Memory?The Financial Review, Volume 28, Issue 2, May 1993, Pp. 181-202. [Cited by 29] (2.18/year)
Abstract: "This study examines the long memory behavior in gold returns during the post-Bretton Woods period using a new rescaled range technique. Unlike the conventional rescaled range analysis, the new rescaled range analysis is robust to short-term dependence and conditional heteroscedasticity found in the gold data. Statistical results suggest that the long memory behavior in gold returns is rather unstable. When only few observations corresponding to major political events in the Middle East, together with the Hunts event, in late 1979 are omitted, little evidence of long memory can be found."
HENRY, Ólan T. , 2002. Long memory in stock returns: Some international evidence, Applied Financial Economics, Volume 12, Number 10, 1 October 2002, pp. 725-729. [Cited by 9] (2.08/year)
Abstract: "Recent empirical studies suggest that long horizon stock returns are forecastable. While this phenomenon is usually attributed to time varying expected returns, or speculative fads, it may also be due to long memory in the returns series. Long range dependence is investigated using parametric and semiparametric estimators in a sample of nine international stock index returns. The results provide evidence of long memory in the German, Japanese, South Korean and Taiwanese markets."
GOETZMANN, William N., 1993. Patterns in Three Centuries of Stock Market Prices. The Journal of Business, Vol. 66, No. 2. (Apr., 1993), pp. 249-270. [Cited by 25] (1.88/year)
Abstract: "This article applies autoregression and rescaled range statistics to very long stock market series to test the hypothesis that long-term temporal dependencies are present in financial data. For the annual capital appreciation returns to the London Stock Exchange, evidence of persistence in raw returns greater than 5 years and of mean reversion in deviations from rolling 20-year averages is found. Similar patterns are observed for the New York Stock Exchange; however, they are not significant at traditional confidence levels."
LUX, Thomas, 1996. Long-term stochastic dependence in financial prices: evidence from the German stock market, Applied Economics Letters, Volume 3, Number 11, 1 November 1996, pp. 701-706. [Cited by 18] (1.74/year)
Abstract: "A number of authors have argued that financial prices may exhibit hidden long-term dependence. We consider this claim analysing German stock market data. Applying three different concepts for the identification of long memory effects, virtually no evidence of such behaviour is found for stock market returns. Another recent assertion says that long term memory may not be pertinent to stock returns but rather to the conditional volatility of financial market prices. As it turns out, this claim is very much supported by our investigation of German stock market data. Furthermore, the long memory property is more pronounced in absolute values of returns than in the squares of returns (both used as proxies for volatility). The methods employed are: the time-honoured procedure of estimating the Hurst exponent for the scaling behaviour of the range of cumulative departures from the mean of a time series, the modified range analysis."
de PERETTI, Christian, 2003. Bilateral Bootstrap Tests for Long Memory: An Application to the Silver Market, Computational Economics, Volume 22, Numbers 2-3 / October, 2003, Pages 187-212. [Cited by 5] (1.51/year)
Abstract: "Many time series in diverse fields of application may exhibit long-memory. The class of fractionally integrated (FI) processes can be used to try to model this strong data dependence. Asymptotic tests for FI include the re-scaled range statistic test and its modified form, the frequency-domain regression-based procedure, the modified Higuchi’s test and Jensen’s test. De Peretti and Marimoutou (2002) finds that proper finite-sample inferences are not possible using these techniques without correcting for size distortions. Some attempt this correction through ‘bootstrapping’, but this method is not perfect and needs more study and improvements. In this paper, I examine and compare the finite-sample properties of parametric and nonparametric bootstrap tests by using graphical techniques of Davidson and MacKinnon (1998a) for showing whether they properly correct the distortions while retaining their power relative to the corresponding asymptotic tests. One of the tests uses a double bootstrap that provide better true power and size properties. I use a bilateral P value that permits the true power of the tests to grow when the size distortions are asymmetric. We then apply these procedures to a real time series to investigate its long memory properties."
ROSE, O., 1996. Estimation of the Hurst Parameter of Long-Range Dependent Time Series. Research Report. [Cited by 14] (1.36/year)
Abstract: "This paper is a condensed introduction to self-similarity, self-similar processes, and the estimation of the Hurst parameter in the context of time series analysis. It gives an overview of the literature on this subject and provides some assistance in implementing Hurst parameter estimators and carrying out experiments with empirical time series."
PANAS, Epaminondas, 2001. Estimating fractal dimension using stable distributions and exploring long memory through ARFIMA models in Athens Stock Exchange, Applied Financial Economics, Volume 11, Number 4 / August 1, Pages 395-402. [Cited by 7] (1.32/year)
Abstract: "It is argued that the study of the correct specification of returns distributions has attractive implications in financial economics. This study estimates Levy–stable (fractal) distributions that can accurately account for skewness, kurtosis, and fat tails. The Levy–stable family distributions are parametrized by the Levy index (α), 0 < α ≤ 2, and include the normal distribution as a special case (α = 2). The Levy index, α, is the fractal dimension of the probability space. The unique feature of Levy–stable family distributions is the existence of a relationship between the fractal dimension of the probability space andthe fractal dimensionof the time series. This relationshipis simply expressed in terms of Hurst exponent (H), i.e. α = 1/H. In addition, Hurst exponent is related to long-memory effects. Thus, estimating the Levy index allows us to determine long-memory effects. The immediate practical implication of the present work is that on the one hand we estimate the shape of returns distributions and on the other hand we investigate the fractal dimensions. Overall, then, the Levy–stable family distributions methodology appears to be useful for analysing the returns distribution, for understanding the fractal dimension of returns and for providing the researcher with direct insights into the long-memory effects of stock returns. A second approach to test the long memory hypothesis is attempted in this paper. This test involves an estimation of the ARFIMA models. A comparative analysis of the two approaches indicates the existence of long-memory in the Athens Stock Exchange. The results of this study are based on a sample of stocks from the Athens Stock Exchange using daily data."
MOODY, John and Lizhong WU, 1996. Improved estimates for the rescaled range and Hurst exponents, In: Neural Networks in Financial Engineering: Proceedings of the Third International Conference on Neural Networks in the Capital Markets London, England 11-13 October 95, pages 537-553. [Cited by 12] (1.16/year)
Abstract: "Rescaled Range R/S analysis and Hurst Exponents are widely used as measures of long-term memory structures in stochastic processes. Our empirical studies show, however, that these statistics can incorrectly indicate departures from random walk behavior on short and intermediate time scales when very short-term correlations are present. A modification of rescaled range estimation (R/S~ analysis) intended to correct bias due to short-term dependencies was proposed by Lo (1991). We show, however, that Lo’s R/Sbar statistic is itself biased and introduces other problems, including distortion of the Hurst exponents. We propose a new statistic R/S* that corrects for mean bias in the range R, but does not suffer from the short term biases of R/S or Lo’s R/S~. We support our conclusions with experiments on simulated random walk and AR(1) processes and experiments using high frequency interbank DEM / USD exchange rate quotes. We conclude that the DEM / USD series is mildly trending on time scales of 10 to 100 ticks, and that the mean reversion suggested on these time scales by R/S or R/S~ analysis is spurious."
TSCHERNIG, Rolf, 1995. Long memory in foreign exchange rates revisited. Journal of International Financial Markets, Institutions & Money, Volume 5, Issues 2/3, Pages 53-78. [Cited by 13] (1.15/year)
Abstract: "There has been recent evidence for long memory in the changes of foreign exchange spot rates that is captured by the fractionally integrated ARMA model. This paper extends these investigations in several directions. First, the estimation procedure allows for GARCH errors. Second, in addition to the total period from 1973 to 1990 three subperiods are analyzed. Third, for the US-Dollar spot rates of the Deutsche Mark and the Swiss Franc ARFIMA model selection and estimation results for various observation frequencies are compared to ARFIMA specifications and their parameter values that are obtained from temporal aggregation. As a result the evidence for weak long memory in the changes of US-Dollar exchange rates is confirmed. However, long memory appears to be a property attached to the US currency since the analysis of the Deutsche Mark/Swiss Franc spot rate changes does not reveal any long memory."
GIORDANO, S., et al., 1997. A Wavelet-based approach to the estimation of the Hurst Parameter for self-similar data. Digital Signal Processing Proceedings, 1997. DSP 97., 1997 13th International Conference on [Cited by 10] (1.07/year)
Abstract: "In this paper we analyse a wavelet based method for the estimation of the Hurst parameter of synthetically-generated self-similar traces, widely used in a great variety of applications, ranging from computer graphics to parsimonious traffic modelling in broadband networks. The aim of this work is to point out the efficiency of multiresolution schemes in the analysis of fractal processes, characterized by similar statistical features over different time scales. To this end we generated a huge amount of data using the random midpoint displacement (RMD) algorithm, a well-known fast technique for the generation of fractional Gaussian noise (fGn) traces. We then evaluated the Hurst parameter of such sequences in the wavelet domain and compared the results with those obtained with more traditional methods, based on the estimation of the fractal dimensional (Higuchi method) and the moments of the aggregated series."
TOLVI, Jussi, 2003. Long Memory in a Small Stock Market, Economics Bulletin, Vol. 7 no. 3 pp. 1-13. [Cited by 3] (0.90/year)
Abstract: "The presence of long memory in Finnish stock market return data is tested using nonparametric methods. The data set has daily returns on six indices and forty companies. Depending on the testing method used, statistically significant long memory is detected in 24% to 67% of the series. This is considerably more than what is usually found in data of this kind."
Conclusions: "The presence of long memory in Finnish stock market returns was examined in this article. Two testing methods were used, and however the results are interpreted, there would appear to be a considerable number of series with statistically significant long memory. Clear evidence for long memory was found in the returns of all six indices, and in nearly two thirds of the 40 individual stocks by the LM testing method. Fewer series were found to have long memory in the GPH estimation results, but this may be due to the lower power of the method, compared to the LM test.
It seems therefore, that the hypothesis of more frequent presence of long memory in small markets is supported by the results. More evidence for return long memory can be found in this data set, than what has earlier been found in, for example, the U.S. stock markets. Some evidence was also found for the hypothesis that the presence of long memory in the returns of individual stocks is correlated with the sample moments. In this data set kurtosis is positively correlated with the presence of long memory, whereas mean and standard deviation seem to be negatively correlated."
CHOW, K. Victor, Ming-Shium PAN and Ryoichi SAKANO, 1996. On the long-term or short-term dependence in stock prices: Evidence from international stock markets, Review of Quantitative Finance and Accounting, Volume 6, Number 2 / March, 1996, pages 181-194. [Cited by 7] (0.68/year)
Abstract: "This study examines the short- and long-term dependence in the United States and 21 international equity market indexes. Two heteroscedastic-robust testing methods, the modified rescaled range analysis and the rescaled variance ratio test, are employed to test for the existence of dependence. The evidence consistently reveals the absence of long-term dependence in these 22 stock returns indexes. The random walk hypothesis for most, but not all, stock returns indexes is not rejected. When the random walk hypothesis is rejected, the evidence supporting the rejection is weak and the stochastic dependence occurs mainly in short-horizon, rather then long-horizon holding period returns."
NAWROCKI, David, 1995. R/S Analysis and Long Term Dependence in Stock Market Indices, Managerial Finance, Vol. 21, No. 7, 1995, 78-91. [Cited by 7] (0.62/year)
Abstract: "Recent studies indicating long term dependence in stock market indices have found a mean reversion process. However, studies using rescaled range (R/S) analysis have not found evidence of a mean reversion or ergodic process. Instead, evidence from these studies indicate either long term persistence in a nonperiodic cycle or short run Markovian dependence with no long term persistence. The purpose of this paper is to study the issue of long term dependence using rescaled range analysis. The empirical results obtained in this study support the persistent dependence/nonperiodic cycle results and suggest that the dependence arises from the general economic cycle."
TOLVI, Jussi, 2003. Long memory and outliers in stock market returns. Applied Financial Economics, Volume 13, Number 7, July 2003, pp. 495-502. [Cited by 2] (0.60/year)
Abstract: "Long memory in the form of fractional integration is analysed in stock market returns. Special emphasis is placed on taking into account the potential bias caused by neglected outliers in the data. It is first shown by a simulation experiment that outliers will bias the estimated fractional integration parameter towards zero. In a monthly data set, consisting of stock market indices of 16 OECD countries, statistically significant long memory is found for three countries. In one of these long memory is only found when outliers are first taken into account."
NATH, Golaka C., 2001. Long Memory and Indian Stock Market-An Empirical Evidence. UTIICM Conference Paper. [Cited by 3] (0.56/year)
Abstract: "This paper makes a serious attempt to explore whether there exists a need to study the use of non-linear models to test the existence of long memory in an emerging market like India. It starts by discussing how various authors are challenging the efficient market hypothesis. This has led to the use of non-linear dynamic systems for modeling movement in stock prices. In order to confirm whether the efficient market hypothesis is applicable to the Indian Stock Market, the study has used the NSE NIFTY returns for the last decade and tested them for normality. Finally, two important tests have been performed using these data: the Variance ratio test and the Rescaled Range (R/S) Analysis to test for persistence in the NIFTY daily returns."
LECOURT, C., 2000. Dependance de Court et Long Terme des Rendements de Taux de Change. Economie et Prevision, 5, 127-137. [Cited by 3] (0.47/year)
HORV?TH, L., 2001. Change-Point Detection in Long-Memory Processes. Journal of Multivariate Analysis. [Cited by 2] (0.38/year)
Abstract: "We discuss some methods to test for possible changes in the parameters of a long-memory sequence. We obtain the limit distributions of the test statistics under the no-change null hypothesis. The consistency of the tests is also investigated."
MOODY, John and Lizhong WU, 1995. Price behavior and Hurst exponents of tick-by-tick interbank foreign exchange rates, Proceedings of the IEEE/IAFE 1995 Computational Intelligence for Financial Engineering, pages 26-30. [Cited by 4] (0.35/year)
Abstract: "Our previous analysis of tick-by-tick interbank Foreign Exchange (FX) rates has suggested that the market is not efficient on short time scales. We find that the price changes show mean-reverting rather than random-walk behavior [4]. The results of rescaled range and Hurst exponent analysis presented in the first part of this paper further confirms the mean-reverting attribute in the FX data. In the second part of this paper, we report the highly significant correlations between Bid/Ask spreads, volatility and forecastability that we have found in the FX data. These interactions show that higher volatility results in higher forecast error and increased risk for market makers, and that to compensate for this increase in risk, market makers increase their Bid/Ask spreads."
LIMAM, Imed, 2003. Is long memory a property of thin stock markets? International evidence using Arab countries. Review of Middle East Economics and Finance, Volume 1, Number 3 / December 2003, pages 251-266. [Cited by 1] (0.30/year)
Abstract: "The paper analyzes the long memory property of stock index returns in 14 markets with diverse levels of development. While the sample includes the developed stock markets of Japan, UK and USA, it also includes, in addition to the emerging markets of Brazil, India and Mexico, those of eight Arab countries as benchmarks of thin markets with the aim of investigating the link between fractional integration dynamics in stock returns and the level of stock market development. Using parametric and semi-parametric estimation procedures, the results show that the property of long-range dependence in stock index returns tend to be associated with relatively thin stock markets. Evidence from the Arab countries seems to suggest that long-memory might also be linked to the peculiar characteristics and the environment within which each stock market operates."
BHAR, R., 1994. Testing for long-term memory in yen/dollar exchange rate. Asia-Pacific Financial Markets, Volume 1, Number 2 / September, 1994, Pages 101-109. [Cited by 3] (0.24/year)
Abstract: "This paper examines evidence of long-term memory in the yen/dollar price change as well as in the daily estimate of volatility of the exchange rate series. The methodology used is due to Lo (1989) which is robust to the presence of heteroscedasticity and is applied to a ten year data set. The result shows no evidence of long-term memory in the price change series indicating efficient pricing by the market participants. The volatility series, however, shows evidence of long-term memory which may have implications for traders dealing with long lived assets."
EMBRECHTS, M., M. CADER and G.J. DEBOECK, 1994. Nonlinear Dimensions of Foreign Exchange, Stock, and Bond Markets. Trading on the Edge-Neural, Genetic, and Fuzzy Systems for &h. [Cited by 3] (0.24/year)
CAVALCANTE, Jorge and Ata ASSAF, 2002. Long Range Dependence in the Returns and Volatility of the Brazilian Stock Market Manuscript. Rio de Janeiro. [Cited by 1] (0.23/year)
Abstract: "This study provides empirical evidence of the long-range dependence in the returns and volatility of Brazilian Stock Market (BSM). We test for long memory in the daily returns and volatility series. The measures of long-term persistence employed are the modified rescaled range (R/S) statistic proposed by Lo (1991), the rescaled variance V/S statistic proposed by Giraitis et al. (2003), and the semiparametric estimator of Robinson (1995). Further analysis is conducted via FIGARCH model of Baillie et al. (1996). Significant long memory is conclusively demonstrated in the volatility measures, while there is a little evidence of long memory in the returns themselves. This evidence disputes the hypothesis of market efficiency and therefore implies fractal structure in the emerging stock market of Brazil. We conclude, that stock market dynamics in the biggest emerging market, even with its different institutions and information flows than the developed market, present similar return-generating process to the preponderance of studies employing other data. Our results should be useful to regulators, practitioners and derivative market participants, whose success depends on the ability to forecast stock price movements."
BARKOULAS, John T. and Christopher F. BAUM, 1997. Long Memory and Forecasting in Euroyen Deposit Rates, Asia-Pacific Financial Markets, Volume 4, Number 3 / January, 1997, pages 189-201. Also: Financial Engineering and the Japanese Markets, 1997, 4:189-201. [Cited by 2] (0.21/year)
Abstract: "We test for long memory in 3- and 6-month daily returns series on Eurocurrency deposits denominated in Japanese yen (Euroyen). The fractional differencing parameter is estimated using the spectral regression method. The conflicting evidence obtained from the application of tests against a unit root as well as tests against stationarity provides the motivation for testing for fractional roots. Significant evidence of positive long-range dependence is found in the Euroyen returns series. The estimated fractional models result in dramatic out-of-sample forecasting improvements over longer horizons compared to benchmark linear models, thus providing strong evidence against the martingale model."
HAMPTON, J., 1996. Rescaled Range Analysis: Approaches for the Financial Practitioner, Part 3. NeuroVe$ t, Vol. 4, No. 4, pp. 27-30. [Cited by 2] (0.19/year)
PANDEY, V., T. KOHERS and G. KOHERS, 1995. Chaotic Determinism in the Stock Returns of the Major PAcific Rim Equity MArkets and the US. Eastern Finance Association Meeting in Hilton Head, Carolina, U.S.A. [Cited by 2] (0.18/year)
CHEN, Shu-Heng, 2000. Lecture 7: Rescale Range Analysis and the Hurst Exponent Financial Economics (I), Department of Economics, National Chengchi University. [Cited by 1] (0.16/year)
Abstract: "Hurst exponent is one of the most frequently used statistics to describe the the weakly stationary stochastic process which has long memory. In this lecture, the classical rescaled range statistic of Hurst is computed for seven Asia-Pacific countries’ stock indices. It is confirmed that all index return have long memory."
EMBRECHTS, M., 1994. Basic concepts of nonlinear dynamics and chaos theory. GJ Deboeck, Trading on the edge. [Cited by 2] (0.16/year)
HUANG, Bwo-Nung and Chin W. YANG, 1999. An Examination of Long-term Memory Using the Intraday Stock Returns. [Cited by 1] (0.14/year)
Abstract: "In this paper, we show that by applying the modified R/S technique to the intraday data, there exists the phenomenon of long-term memory in both NYSE and NASDAQ indices. The policy implication is that an abnormal profit is entirely possible for certain time intervals during a trading day. The efficient market hypothesis may actually coexist with a global structure to comprise a fractal market hypothesis. In addition, via a univariate ARMA model, we can make more accurate forecasts on the stock returns in the time period when a long-term memory is found."
TEVEROVSKY, Vadim, Murad S. TAQQU and Walter WILLINGER, 1999. A critical look at Lo’s modified R/S statistic. Journal of Statistical Planning and Inference, Volume 80, Issues 1-2, 1 August 1999, Pages 211-227. [Cited by 1] (0.14/year)
Abstract: "We report on an empirical investigation of the modified rescaled adjusted range or R/S statistic that was proposed by Lo, 1991. Econometrica 59, 1279–1313, as a test for long-range dependence with good robustness properties under ‘extra’ short-range dependence. In contrast to the classical R/S statistic that uses the standard deviation S to normalize the rescaled range R, Lo’s modified R/S-statistic Vq is normalized by a modified standard deviation Sq which takes into account the covariances of the first q lags, so as to discount the influence of the short-range dependence structure that might be present in the data. Depending on the value of the resulting test-statistic Vq, the null hypothesis of no long-range dependence is either rejected or accepted. By performing Monte-Carlo simulations with ‘truly’ long-range- and short-range dependent time series, we study the behavior of Vq, as a function of q, and uncover a number of serious drawbacks to using Lo’s method in practice. For example, we show that as the truncation lag q increases, the test statistic Vq has a strong bias toward accepting the null hypothesis (i.e., no long-range dependence), even in ideal situations of ‘purely’ long-range dependent data."
ROBINSON, P.M., 1998. Comment on “Real and Spurious Long-Memory Properties of Stock-Market Data”, by IG Lobato and NE …. Journal of Business & Economic Statistics. [Cited by 1] (0.12/year)
CRATO, Nuno and Bonnie K. RAY, 2000. Memory in Returns and Volatilities of Commodity Futures’ Contracts. The Journal of Futures Markets, Volume 20, Issue 6, Pages 525-543. [not cited] (0/year)
Abstract: "Various authors claim to have found evidence of stochastic long-memory behavior in futures’ contract returns using the Hurst statistic. This paper reexamines futures’ returns for evidence of persistent behavior using a biased-corrected version of the Hurst statistic, a nonparametric spectral test, and a spectral-regression estimate of the long-memory parameter. Results based on these new methods provide no evidence for persistent behavior in futures’ returns. However, they provide overwhelming evidence of long-memory behavior for the volatility of futures’ returns. This finding adds to the emerging literature on persistent volatility in financial markets and suggests the use of new methods of forecasting volatility, assessing risk, and optimizing portfolios in futures’ markets."
GRAU-CARLES, Pilar, 2005. Tests of Long Memory: A Bootstrap Approach. Computational Economics, Volume 25, Numbers 1-2 / February, 2005, Pages 103-113. [not cited] (0/year)
Abstract: "Many time series in diverse fields have been found to exhibit long memory. This paper analyzes the behaviour of some of the most used tests of long memory: the R/S analysis, the modified R/S, the Geweke and Porter-Hudak (GPH) test and the detrended fluctuation analysis (DFA). Some of these tests exhibit size distortions in small samples. It is well known that the bootstrap procedure may correct this fact. Here I examine the size and power of those tests for finite samples and different distributions, such as the normal, uniform, and lognormal. In the short-memory processes such as AR, MA and ARCH and long memory ones such as ARFIMA, p-values are calculated using the post-blackening moving-block bootstrap. The Monte Carlo study suggests that the bootstrap critical values perform better. The results are applied to financial return time series."
ZHUANG, Yaqin, Christopher J. GREEN and Paolo MAGGIONI, The Great Rebound, The Great Crash, and Persistence in British Stock Prices. Economic Research Paper No. 00/11, Loughborough University. [not cited] (0/year)
Abstract: "In this paper, we investigate the persistence of British stock returns over the period 1962-98 using the Variance Ratio (VR) test to check for short-range dependence and the Modified Rescaled Range (MRS) test to check for long-range dependence. A central contribution of the paper is that we investigate the role of the great rebound in stock prices in January 1975 and the crash of October 1987. These shocks, which together represent less than 1% of the data fundamentally alter the time series properties of the data, with extreme skewness, excess kurtosis, and ARCH present in the unadjusted data, but absent from much of the shock-purged data. The VR and MRS tests reveal relatively little evidence of persistence in the original data. However, the VR tests exhibit systematic and significant reversals of sign as between the original and the shock-purged data. It appears that stock prices in Britain persistently stayed away from the mean, and then reverted back towards it in just two exceptionally large jumps. The results reinforce the need for researchers to take extra care in analysing British stock market data in the post-war period."
HAMPTON, J. (1996a), "Rescaled Range Analysis: Approaches for the Financial Practitioner, Part 1," NeuroVe$t Journal, Vol. 4, No. 1, pp. 23-28.
HAMPTON, J. (1996b), "Rescaled Range Analysis: Approaches for the Financial Practitioner, Part 2," NeuroVe$t Journal, Vol. 4, No. 3, pp. 23-29.
TENORIO, Manoel F., Carlos E. PEDREIRA and Nitzi M. ROEHL, The Cotton Time Series: A Study of the Competition Series Behavior and Statistics, Nonlinear Financial Forecasting - Proceedings of the First INFFC, edited by Randall B. Caldwell [not listed]
