A.W. Lo. Long--term memory in stock market prices. Economatria, (59):1276--1313, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....financial data has been observed since Greene and Fielitz [20] and Mandelbrot [29] and [28] Using R S analysis, Greene and Fielitz studied 200 daily stock returns of securities listed on the New York Stock Exchange and they found significant long range dependence. Contrary to their findings, Lo [25] using a modified R S statistic, which is developed to compensate for the presence of short range dependence finds no evidence of long range dependence. However Teverovsky et al. 45] and Willinger et al. 46] identified a number of problems associated with Lo s method. In particular they showed ....

LO, A. W. (1991): Long-term Memory in Stock Market Prices, Econometrica, 59, 1279-1313.

....that may be caused by the events in Iran and the Hunt brothers attempted corner of the silver market in November and December 1979. In a later paper, Aydogan and Booth [3] warn that R S analysis is biased by nonstationary means. Because of short term dependence effects on the R S statistic, Lo [27] develops an R S statistic that corrects for short term autocovariance. However, Cheung [11] tests the Lo [27] statistic using Monte Carlo simulation and finds that it is very sensitive to nonstationary means, while at the same time it is robust to nonnormal distributions and nonstationary ....

....and December 1979. In a later paper, Aydogan and Booth [3] warn that R S analysis is biased by nonstationary means. Because of short term dependence effects on the R S statistic, Lo [27] develops an R S statistic that corrects for short term autocovariance. However, Cheung [11] tests the Lo [27] statistic using Monte Carlo simulation and finds that it is very sensitive to nonstationary means, while at the same time it is robust to nonnormal distributions and nonstationary variance (conditional heteroskedasticity) Given this result, Cheung and Lai [12] restudy gold prices. Using a ....

[Article contains additional citation context not shown here]

Lo, Andrew W. "Long-Term Memory in Stock Market Prices," Econometrica, 1991, v59(5), 1279-1313.

....to income shocks, which is more in line with the rationale of the PIH. 57] presents a similar resolution of the Deaton Paradox with postulated values of d, and tests whether these paradox resolving values of d are consistent with observed income processes. However, he uses a test based on the [76] modified R S statistic which has no clear optimality properties (see [100] and seems to have undesirable small sample properties (see [117] k Such a specification for income also accounts for the rejection of convergence in [10] based on cointegration tests, as, in case income is I(d) d 1, ....

....P t is the price of the asset. 84] first suggested the possibility that asset prices could exhibit LRD. Using the classical R S analysis, 52] uncovered significant statistical evidence of LRD in daily returns on securities listed at the New York Stock Exchange. These results were challenged by[76] who proposed a modified R S statistic, robustifying for possible additional short memory dynamics by taking into account the first q lags of the autocovariance of the observables. He concluded that there is no such clear evidence of LRD in the levels of asset returns. 117] however, show that ....

Lo, A. (1991): "Long term memory in stockmarket prices," Econometrica, 59, 1279--1313.

....equal to 0.5. Sowell (1992b) found that rst di erenced US real GNP quarterly data for 1947 1989 can be characterized by an ARFIMA (3, 0.59, 2) model. Other researchers also used fractionally integrated models in their studies of asset pricing models (Ding et al. 1993) stock returns (Lo, 1991), exchange rates (Diebold et al. 1991; Cheung, 1993; Baillie and Bollerslev, 1994) interest rates (Shea, 1991; Backus and Zin, 1993; Crato and Rothman, 1994) and in#ation rates (Hassler and Wolters, 1995; Baillie et al. 1996) Baillie (1996) provides an excellent survey of the literature in ....

Lo, A.W., 1991. Long term memory in stock market prices. Econometrica 59, 1279}1313.

....critical values In this paragraph the asymptotic distributions of the test statistics under the null hypothesis are derived and the corresponding critical values are estimated numerically. By applying a special version of Donsker s invariance principle and a continuous mapping theorem, see e.g. Lo (1991) and references therein, in the cadlag space D[0;1] the following asymptotics hold: R (T ) w sup s2[0;1] fB (s)g inf s2[0;1] fB (s)g K 1 (T ) w sup s2[0;1] fjB (s)jg K 1 (T ) w sup s2[0;1] B (s) Z 1 0 B (r) dr U (T ) w sup s2[0;1] B (s) Z 1 0 B (r) dr L (T ....

Lo, A.W. (1991). Long-term memory in stock market prices. Econometrica 59, 1279-1313.

....horizon increased, with some 25 45 of the variation of 3 5 year returns being predictable from past returns. A variety of procedures have been developed to test for predictability over different time horizons. Two of the most popular are Lo and MacKinley s (1988) variance ratio (VR) test and Lo s (1991) modified rescaled range (MRS) test. The former is primarily a test for short range papers calt lm grgc 1.doc 2 dependence and the latter a test for long range dependence. Informally, short range dependence occurs in a time series when there is some relationship between realizations at different ....

....exists when the dependence between realizations remains non negligible as the time span increases. Examples of short range dependence include most classes of ARMA model which are integer differenced to achieve stationarity. Long range dependence occurs in fractionally differenced processes. See Lo (1991) and the references cited therein for further details. When first applied to American data, the VR test typically rejected the random walk hypothesis in favour of positive autocorrelations at short horizons (under one year) and negative autocorrelation at longer horizons, both for stock market ....

[Article contains additional citation context not shown here]

Lo, A.W. (1991), "Long-term memory in stock market prices", Econometrica, Vol. 59, No. 5, pp. 1279-1314.

....memory and long memory behavior, which may be modeled by the class of autoregressive fractionally integrated moving average (ARF IMA) processes. Applications of these processes to model 1 time series include work by Diebold and Rudebusch (1989) Geweke and Porter Hudak (1983) Hosking (1984) Lo (1989) and Sowell (1992) A time series fz t g is generated by an autoregressive fractionally integrated moving average (ARFIMA) process (Granger and Joyeaux, 1980 and Hosking, 1981) if OE(B) 1 0B) d z t = B) t ; 1) where OE(B) 1 0 OE 1 B 0 1 1 1 0 OE p B p and (B) 1 0 1 B 0 1 1 1 q B ....

Lo, A. (1989) Long-term memory in stock market prices. Working paper 3014-89 EFA (Alfred P. Sloan School of Management, MIT, Cambridge, Massachusetts).

....analyzing the long term properties of stock returns. Greene and Fielitz (1977) used the R S statistic (Hurst (1951) to test for long term dependence in the daily returns of 200 individual stocks on the NYSE from December 23, 1963 to November 29, 1968 and claim to have found significant evidence. Lo (1991) criticized these results on the grounds that this evidence was due to short term correlation. He proposed a modified version of the R S statistic to test robustly for long term dependence, and found no evidence in favor of long run dependence of the monthly and daily returns on CRSP stock ....

....273 and 82 days, respectively. No evidence of long memory is found in the returns, but there is strong evidence of long memory in the squares. This evidence is even stronger for the absolute value of the returns and hence we concentrate on the squares. These results are in agreement with Lo (1991) and Ding et al. 1993) There are several ways in which the LM test for long memory can produce spurious results. First, the squared returns process could posses a shift in the mean. To show how this can happen consider the following set up. Let y t , t=1,2, N, be a zero mean stochastic ....

Lo, A.W. (1991), "Long Term Memory in Stock Market Prices", Econometrica, 59, 1279-1313.

....could improve the predictability of the prices: it states that correlations between price changes die out very slowly, in a sense made precise below, so that the actual movements in the market are stochastically influenced by the recent to the most remote past. More recent work on R S analysis (Lo, 1991) has demonstrated that this statistic is 2 biased when short range correlation is present in a series, calling into question earlier claims of persistence in futures returns. Using new statistical tools, many authors (Fung and Lo, 1993; Cheung and Lai, 1993; Crato, 1994) have found that ....

....R S analysis to reevaluate the memory of futures returns. Studying a large new data set, they claim to have found persistent long memory in a significant group of futures contracts. This paper reexamines the memory of futures returns using a modified version of the R S statistic developed by Lo (1991), as well as a test based on the estimator of the long memory parameter due to Geweke and Porter Hudak (1983) henceforth GPH. Our results indicate no long memory behavior in futures returns. However, a similar analysis applied to the volatility of the returns finds overwhelming evidence of ....

[Article contains additional citation context not shown here]

Lo, A. W. (1991): "Long-term memory in stock market prices", Econometrica 59, 1279-- 1313.

....October, 1999 The second author gratefully acknowledges the financial support of the National Science Foundation. 1. INTRODUCTION This paper considers two tests of the null hypothesis of short memory, the KPSS test of Kwiatkowski et al. 1992) and the modified rescaled range (MR S) test of Lo (1991). The KPSS test was designed as a test of stationarity against the alternative of a unit root. However, the asymptotic distribution theory in KPSS actually assumes short memory, and Lee and Schmidt (1996) have shown that the test has power against stationary and nonstationary long memory ....

....Cauchy case puts a much higher fraction of observations above the standard critical value. 7. CONCLUDING REMARKS In this paper we have compared the sensitivity to thick tailed errors of two tests of the null of short memory, namely the KPSS test of Kwiatkowski et al. 1992) and the MR S test of Lo (1991). Our intuition suggested that the MR S test might not be very robust, because it is based on the maximum and minimum of the cumulated series, and maxima and minima are potentially very sensitive to tail thickness. We conclude that our intuition was correct. The KPSS test appears to be more robust ....

Lo, A. (1991), "Long-Term Memory in Stock Market Prices," Econometrica, 59, 1279-1313.

....could improve the predictability of the prices: it states that correlations between price changes die out very slowly, in a sense made precise below, so that the actual movements in the market are stochastically influenced by the recent to the most remote past. More recent work on R S analysis (Lo, 1991) has demonstrated that this statistic is biased when short range correlation is present in a series, calling into question earlier claims of persistence in futures returns. Using new statistical tools, many authors (Fung and Lo, 1993; Cheung 2 and Lai, 1993; Crato,1994) have found that financial ....

....regression method of Geweke and Porter Hudak (1983) henceforth GPH, to estimate the parameter characterizing long memory and again claim to find evidence of long memory behavior. In this paper, we reexamine the memory of futures returns using a modified version of the R S statistic developed by Lo (1991), as well as a test based on the GPH estimator of the long memory parameter. Our results indicate no long memory behavior in futures returns. However, a similar analysis applied to the volatility of the returns finds overwhelming evidence of persistence in volatility. This finding is consistent ....

[Article contains additional citation context not shown here]

Lo, Andrew W. (1991). "Long-term memory in stock market prices", Econometrica 59, 1279--1313.

....of the definitions adopted by Nelson (1990) i.e. persistence in probability, in L p norm or almost surely. Besides, the analogy is apparent between the clustering of volatilities of financial returns and what Mandelbrot (1973) described as the Joseph effect . And, effectively, Whistler (1990) Lo (1991), Ding, Granger, and Engle (1993) and Lee and Robinson (1996) are among the first to show how well the long memory representation performs empirically. A general fractionally integrated GARCH model is obtained as a special case of specification 2.5 with the OE(z) polynomial defined as OE(z) 1 ....

Lo, A. (1991): "Long term memory in stock market prices," Econometrica, 59, 1279--1313.

....Indeed, using the R S analysis, Booth, Kaen, and Koveos (1982) present evidence for long memory in daily changes of the US Dollar spot rates of the British Pound, the French Franc, and the Deutsche Mark for the period from July 1, 1973 until June 30, 1979. Using the modified R S test suggested by Lo (1991) that is robust to short range dependence, Cheung (1993) confirms their findings for weekly exchange rate changes for a longer period that also includes the 80 s. Exploiting long memory for prediction, however, requires some kind of long memorymodel. As an attractive parameterization Granger and ....

Lo, Andrew W.. "Long-term memory in stock market prices.", Econometrica, 59 (September 1991): 1279 -- 1314.

....these statistics can incorrectly indicate departures from random walk behavior on short and intermediate time scales when very shortterm 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= S 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 ....

.... number of observations in the time series, Mandelbrot Wallis 1969, Wallis Matalas 1970, Feder 1988, Ambrose, Ancel Griffiths 1993, Moody Wu 1995a, Muller, Dacorogna Pictet 1995) and (2) the rescaled range is sensitive to short term dependence (McLeod Hipel 1978, Hipel McLeod 1978, Lo 1991). The second shortcoming will sometimes lead to completely incorrect results. Lo (1991) analyzed the mean bias in the range statistic R due to short term dependencies in the time series, and proposed a modified rescaling factor S that is intended to remove or reduce these effects. We have found, ....

[Article contains additional citation context not shown here]

Lo, A. W. (1991), `Long term memory in stock market prices', Econometrica 59, 1279--1313.

.... [339, 340] An area of application where self similarity and long range dependence continue to play 4 Willinger, Taqqu and Erramilli a significant role and where many results of practical relevance for traffic engineering have been discovered is economics or, more precisely, financial economics [15,17,31,50,51,54,75,83,167,168,273,284,297,342,383]. The paper [14] provides an overview. For an early application of the self similarity concept and related topics to communications systems, see the seminal paper by Mandelbrot [283] Enlightening philosophical discussions centering around the issues of traditional mathematical modeling (based on ....

....on chaos, probability and statistics, see [29, 46, 47] An overview of statistical inference methods for self similar models and random processes with long range dependence can be found in [22, 24] the papers [392 394] listing additional techniques. More specifically, R S analysis is discussed in [18, 24, 26, 28, 130, 200, 258, 272, 273, 286, 288, 290 292, 302, 310, 394] (see also [10,131] variance time analysis in [24,26,77,258,310,331,394,399] and for spectral domain methods using periodograms, see [24,26,48,84,140,149,157, 159,183,203,204,206,249,253,353,357 366,393,407, 418] Examples of new statistical techniques in this area include [3, 7, 20,21,25,27, ....

A. W. Lo. Long-term memory in stock market prices. Econometrica, 59:1279--1313, 1991.

....to 1 2. If persistent long memory is present, then J(n; q) converges to a value larger than 1 2 (see, e.g. Mandelbrot and Taqqu 1979) Long Memory in Stochastic Volatility 9 If a process satisfies a set of regularity conditions, including the existence of moments of order 4 ffi, with ffi 0, Lo (1991) shows that under the short memory null the statistic V = n Gamma1=2 Q(n; q) converges weakly to the range of the Brownian bridge on the unit interval. The distribution function for this range, say F V , is F V (v) 1 X k= Gamma1 (1 Gamma 4v 2 k 2 )e Gamma2v 2 k 2 : If a ....

....memory. However, no distribution theory is available in this case. In the absence of clear rules for the choice of q, we experimented with a few values. First, we used q = 0, corresponding to the classical estimate. Second, we used q = q , chosen by Andrews (1991) data dependent formula as in Lo (1991, p. 1302) Finally, we tried q = 200 in an attempt to yield statistics which are more robust against short memory effects. 3.2 Finite sample performance of the long memory tests In this section we consider the finite sample performance of the spectral regression test and the R S analysis under ....

Lo, A.W. (1991). Long-term memory in stock market prices. Econometrica 59, 1279-1313.

No context found.

A.W. Lo. Long--term memory in stock market prices. Economatria, (59):1276--1313, 1991.

No context found.

A. W. Lo. Long-term memory in stock market prices. Econometrica, 59:1279--1313, 1991.

No context found.

Andrew W. Lo. Long-term memory in stock market prices. Econometrica, 59:1279--1313, 1991.

No context found.

A.W. Lo. Long--term memory in stock market prices. Economatria, (59):1276--1313, 1991.

No context found.

A. Lo, Long term memory in stock market prices, Econometrica 59 (1991) 1279--1313.

No context found.

Lo, A.W. (1991) "Long Term Memory in Stock Market Prices," Econometrica, 59, 1279 -- 1313.

No context found.

LO, A.W. (1991): \Long-Term Memory in Stock Market Prices", Econometrica, ##, 12791313.

No context found.

-775. Lo, A. (1991). Long-term memory in stock market prices. Econometrica, 59,

No context found.

Lo, Andrew (1989), Long-Term Memory in Stock Market Prices, Economet18 rica 59, 1279--1313.

First 50 documents

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC