True Versus Spurious Long Memory: Some Theoretical Results and a Monte Carlo Comparison

A common feature of financial time series is their strong persistence. Yet, long memory may just be the spurious effect of either structural breaks or slow switching regimes. We explore the effects of spurious long memory on the elasticity of the stock market price with respect to volatility and show how cross-sectional aggregation may generate spurious persistence in the data. We undertake an extensive Monte Carlo study to compare the performance of five tests, constructed under the null of true long memory versus the alternative of spurious long memory due to level shifts or breaks.     

Comparison of non-parametric and semi-parametric tests in detecting long memory

The first two stages in modelling times series are hypothesis testing and estimation. For long memory time series, the second stage was studied in the paper published in [M. Boutahar et al., Estimation methods of the long memory parameter: monte Carlo analysis and application, J. Appl. Statist. 34(3), pp. 261–301.] in which we have presented some estimation methods of the long memory parameter. The present paper is intended for the first stage, and hence completes the former, by exploring some tests for detecting long memory in time series. We consider two kinds of tests: the non-parametric class and the semi-parametric one. We precise the limiting distribution of the non-parametric tests under the null of short memory and we show that they are consistent against the alternative of long memory. We perform also some Monte Carlo simulations to analyse the size distortion and the power of all proposed tests. We conclude that for large sample size, the two classes are equivalent but for small sample size the non-parametric class is better than the semi-parametric one.     

A new simple test against spurious long memory using temporal aggregation

We have developed a new test against spurious long memory based on the invariance of long memory parameter to aggregation. By using the local Whittle estimator, the statistic takes the supremum among combinations of paired aggregated series. Simulations show that the test performs good in finite sample sizes, and is able to distinguish long memory from spurious processes with excellent power. Moreover, the empirical application gives further evidence that the observed long memory in German stock returns is spurious.     

Long memory and changepoint models: a spectral classification procedure

Time series within fields such as finance and economics are often modelled using long memory processes. Alternative studies on the same data can suggest that series may actually contain a ‘changepoint’ (a point within the time series where the data generating process has changed). These models have been shown to have elements of similarity, such as within their spectrum. Without prior knowledge this leads to an ambiguity between these two models, meaning it is difficult to assess which model is most appropriate. We demonstrate that considering this problem in a time-varying environment using the time-varying spectrum removes this ambiguity. Using the wavelet spectrum, we then use a classification approach to determine the most appropriate model (long memory or changepoint). Simulation results are presented across a number of models followed by an application to stock cross-correlations and US inflation. The results indicate that the proposed classification outperforms an existing hypothesis testing approach on a number of models and performs comparatively across others.     

基于分整特性视角的我国股市长记忆性识别

金融时间序列的长记忆性检验常采用标度分析法，但结果往往不令人满意。从分整特性的新视角，利用KPSS检验和LW检验对我国股市收益及其波动的记忆性特征进行了深入研究。研究结果表明，我国股市的波动序列中存在显著的长记忆性。而收益序列本身无明显的长记忆性。这与成熟股票市场有关长记忆性的研究结论基本一致．与新兴股票市场的研究结论有所不同。此项结论对股市的长期投资者具有重要的决策意义。     

Long memory versus structural breaks: An overview

We discuss the increasing literature on misspecifying structural breaks or more general trends as long-range dependence. We consider tests on structural breaks in the long-memory regression model as well as the behaviour of estimators of the memory parameter when structural breaks or trends are in the data but long memory is not. Methods for distinguishing both of these phenomena are proposed. The financial support of Volkswagenstiftung is gratefully acknowledged.     

Linear and segmented trends in sea surface temperature data

This paper deals with the analysis of the MET Office Hadley Centre's sea surface temperature data set (HadSST3) by using long-range dependence techniques. We incorporate linear and segmented trends using fractional integration, and thus permitting long memory behavior in the detrended series. The results indicate the existence of warming trends in the three series examined (Northern and Southern Hemispheres along with global temperatures), with orders of integration which are in the range (0.5, 1) and thus implying nonstationary long memory and mean reverting behavior. This is innovative compared with other works that assume short memory behavior in the detrended series. Allowing for segmented trends two features are observed: increasing values in the degree of dependence of the series across time and significant warming trends from 1940 onwards.     

A nonparametric statistical procedure for the detection of marine pollution

This paper is devoted to the estimation of the derivative of the regression function in fixed-design nonparametric regression. We establish the almost sure convergence as well as the asymptotic normality of our estimate. We also provide concentration inequalities which are useful for small sample sizes. Numerical experiments on simulated data show that our nonparametric statistical procedure performs very well. We also illustrate our approach on high-frequency environmental data for the study of marine pollution.     

Estimation of the degree of dependence in the temperatures in the northern hemisphere using semi-parametric techniques

We are concerned in this article with the estimation of the degree of dependence between the observations of the monthly temperatures in the northern hemisphere from 1854 to 1989 by means of using fractionally integrated semi-parametric techniques. We use several estimation procedures proposed by P. M. Robinson in a number of papers, and the results indicate that the order of integration of the series is around 0.37, implying that the time series is stationary but with long memory behaviour. Separating the data in two subsamples (1854-1921 and 1922-89), the results show that there has been an increase in the degree of dependence across time by about 0.05-0.10, the order of integration oscillating around 0.3 (0.35) for the time period 1854-1921, and around 0.35 (0.40) for the period 1922-89.     

中国通货膨胀率的非线性动态行为研究——来自MS—ARFIMA模型的新证据

使用允许长记忆参数d服从区制转换的MS—ARFIMA模型对中国月度通货膨胀路径的动态行为进行新的实证研究,结果显示：中国通货膨胀不仅均值水平和不确定性存在着“低通胀”区制和“高通胀”区制,而且更为重要的是,通货膨胀序列的平稳性也表现出显著的区制转换动态。“低通胀”区制下,长记忆参数d1=0．361,说明通货膨胀是协方差平稳序列,“高通胀”区制下,长记忆参数d2=1．145,说明通货膨胀是非平稳序列。这一新的研究结论意味着中国通货膨胀冲击的持久性效应也存在相应的区制转移变化。这要求央行在管控通货膨胀过程中,既要考虑均值和不确定性的区制变化,又要兼顾平稳性和持久性的区制变化。     

Behaviour of skewness, kurtosis and normality tests in long memory data

We establish the limiting distributions for empirical estimators of the coefficient of skewness, kurtosis, and the Jarque–Bera normality test statistic for long memory linear processes. We show that these estimators, contrary to the case of short memory, are neither ${\sqrt{n}}We establish the limiting distributions for empirical estimators of the coefficient of skewness, kurtosis, and the Jarque–Bera normality test statistic for long memory linear processes. We show that these estimators, contrary to the case of short memory, are neither ?n{\sqrt{n}}-consistent nor asymptotically normal. The normalizations needed to obtain the limiting distributions depend on the long memory parameter d. A direct consequence is that if data are long memory then testing normality with the Jarque–Bera test by using the chi-squared critical values is not valid. Therefore, statistical inference based on skewness, kurtosis, and the Jarque–Bera normality test, needs a rescaling of the corresponding statistics and computing new critical values of their nonstandard limiting distributions.     

Estimating Long and Short Run Effects in Static Panel Models

Abstract

This paper assesses the biases of four different estimators with respect to the short run and the long run parameters if a static panel model is used, although the data generating process is a dynamic error components model. We analytically derive the associated biases and provide a discussion of the determinants thereof. Our analytical and numerical results as well as Monte Carlo simulations illustrate that the asymptotic bias of both the within and the between parameter with respect to the short run and long run impact can be substantial, depending on the memory of the data generating process, the length of the time series and the importance of the cross-sectional variation in the explanatory variables.     

A non linear wavelet based estimator for long memory processes

Two wavelet based estimators are considered in this paper for the two parameters that characterize long range dependence processes. The first one is linear and is based on the statistical properties of the coefficients of a discrete wavelet transform of long range dependence processes. The estimator consists in measuring the slope (related to the long memory parameter) and the intercept (related to the variance of the process) of a linear regression after a discrete wavelet transform is performed (Veitch and Abry, 1999). In this paper its properties are reviewed, and analytic evidence is produced that the linear estimator is applicable only when the second parameter is unknown. To overcome this limitation a non linear wavelet based estimator - that takes into account that the intercept depends on the long memory parameter - is proposed here for the cases in which the second parameter is known or the only parameter of interest is the long memory parameter. Under the same hypothesis assumed for the linear estimator, the non linear estimator is shown to be asymptotically more efficient for the long memory parameter. Numerical simulations show that, even for small data sets, the bias is very small and the variance close to optimal. An application to ATM based Internet traffic is presented.Financial support from the Italian Ministry of University and Scientific Research (MIUR), also in the context of the COFIN 2002 ALINWEB (Algorithms for the Internet and the Web) Project, is gratefully acknowledged.     

Why Aggregate Long Memory Time Series?

This article shows that, for large samples, temporally aggregating a true long memory time series (in order to get an improved estimator) may make little or no sense, as the practitioner can get virtually the same estimates as those from the aggregated series by choosing the appropriate bandwidths on the original one, provided some fairly general conditions apply. Besides, the practitioner has a wider choice of bandwidths than she has of aggregating levels. However, these results apply only to two specific and commonly used estimators, and do not apply to the aggregation procedure undertaken to compute the realized volatility. Also, aggregating a time series in order to test true versus spurious long memory (as in Ohanissian et al., 2008) is a relevant issue, particularly regarding stochastic and/or realized volatility, as many nonlinear processes display spurious long memory where the above result does not apply.     

Long memory in intertrade durations,counts and realized volatility of NYSE stocks

We study the persistence of intertrade durations, counts (number of transactions in equally spaced intervals of clock time), squared returns and realized volatility in 10 stocks trading on the New York Stock Exchange. A semiparametric analysis reveals the presence of long memory in all of these series, with potentially the same memory parameter. We introduce a parametric latent-variable long-memory stochastic duration (LMSD) model which is shown to better fit the data than the autoregressive conditional duration model (ACD) in a variety of ways. The empirical evidence we present here is in agreement with theoretical results on the propagation of memory from durations to counts and realized volatility presented in Deo et al. (2009).     

Modelling political popularity: a correction

Summary. The paper supplies a missing step in the aggregation argument that was used in our 1997 paper in this journal. We show that monthly poll data representing the average of a sample of voter preferences, evolving in different ways in the face of new information, should follow a fractionally integrated process.     

Estimating Long and Short Run Effects in Static Panel Models

This paper assesses the biases of four different estimators with respect to the short run and the long run parameters if a static panel model is used, although the data generating process is a dynamic error components model. We analytically derive the associated biases and provide a discussion of the determinants thereof. Our analytical and numerical results as well as Monte Carlo simulations illustrate that the asymptotic bias of both the within and the between parameter with respect to the short run and long run impact can be substantial, depending on the memory of the data generating process, the length of the time series and the importance of the cross-sectional variation in the explanatory variables.     

含控制因子的R/S分析的H参数估计及应用

R/S分析法是揭示金融时间序列长记忆性的主要方法之一。针对经典R/S与修正R/S分析法之不足,对R/S分析法进行改进,设计含控制因子的R/S统计量,并应用蒙特卡洛模拟说明改进的方法比经典R/S与修正R/S分析法在估计H指数上的有效性。运用新方法对上证综合指数和深圳成分指数收益率序列的长记忆性与两市的平均非周期循环长度进行实证分析,研究表明：沪、深股市的收益率序列都具有长记忆性,但是沪市的收益率序列不存在明显的平均非周期循环长度,而深市的收益率序列则存在一个大约308天的平均非周期循环长度。     

Markov regime switching in mean and in fractional integration parameter

We propose a specific general Markov-regime switching estimation both in the long memory parameter d and the mean of a time series. We employ Viterbi algorithm that combines the Viterbi procedures in two state Markov-switching parameter estimation. It is well-known that existence of mean break and long memory in time series can be easily confused with each other in most cases. Thus, we aim at observing the deviation and interaction of mean and d estimates for different cases. A Monte Carlo experiment reveals that the finite sample performance of the proposed algorithm for a simple mixture model of Markov-switching mean and d changes with respect to the fractional integrating parameters and the mean values for the two regimes.     

Some simulations and applications of forecasting long-memory time-series models

In this paper, we show some results of forecasting based on the ARFIMA(p,d,q) and ARIMA(p,d,q) models. We show, by simulation, that the technique of forecasting of the ARIMA(p,d,q) model can also be used when d is fractional, i.e., for the ARFIMA(p,d,q) model. We also conduct a simulation study to compare the two estimators of d obtained through regression methods. They are used in the hypothesis test to decide whether or not the series has long memory property and are compared on the basis of their k-step ahead forecast errors. The properties of long-memory models are also investigated using an actual set of data.