Long Memory in Nonlinear Processes

Deo, Rohit S.; Hsieh, Meng-Chen; Hurvich, Clifford M.; Soulier, Philippe

doi:10.1007/0-387-36062-x_10

Cited by 14 publications

(12 citation statements)

References 58 publications

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“…Variations on these processes, which retain their main features, are possible; see Deo et al (2006) for a detailed account. Given the econometric motivation of the error duration and renewal-reward processes given by Parke (1999) and Liu (2000), and since it would be difficult to present a completely unified presentation and proof of our results, we consider in this paper only these two processes.…”

Section: Differences Between the Two Modelsmentioning

confidence: 99%

Asymptotics for duration-driven long range dependent processes

Hsieh

Hurvich

Soulier

2007

Journal of Econometrics

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We consider processes with second order long range dependence resulting from heavy tailed durations. We refer to this phenomenon as duration-driven long range dependence (DDLRD), as opposed to the more widely studied linear long range dependence based on fractional differencing of an i.i.d. process. We consider in detail two specific processes having DDLRD, originally presented in Taqqu and Levy [1986. Using renewal processes to generate long-range dependence and high variability. Dependence in Probability and Statistics. Birkhauser, Boston, pp. 73-89], and Parke [1999. What is fractional integration? Review of Economics and Statistics 81, 632-638]. For these processes, we obtain the limiting distribution of suitably standardized discrete Fourier transforms (DFTs) and sample autocovariances. At low frequencies, the standardized DFTs converge to a stable law, as do the standardized sample autocovariances at fixed lags. Finite collections of standardized sample autocovariances at a fixed set of lags converge to a degenerate distribution. The standardized DFTs at high frequencies converge to a Gaussian law. Our asymptotic results are strikingly similar for the two DDLRD processes studied. We calibrate our asymptotic results with a simulation study which also investigates the properties of the semiparametric log periodogram regression estimator of the memory parameter. r 2006 Published by Elsevier B.V. JEL classification: C14; C22

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Section: Differences Between the Two Modelsmentioning

confidence: 99%

Asymptotics for duration-driven long range dependent processes

Hsieh

Hurvich

Soulier

2007

Journal of Econometrics

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“…We model the time series { X j , j ≥ 1} as

\begin{matrix} alignleft \\ align-1 X_{j} = σ (Y_{j}) ε_{j}, σ (Y_{j}) = \exp (Y_{j}), & align-2 \end{matrix}

where { ε j , j ≥ 1} is an independent identically distributed sequence of random variables with mean 0, and { Y j , j ≥ 1} is a Gaussian process. Given the additional assumption of LRD variables { σ ( Y j ), j ≥ 1}, this model was introduced as LMSV model in Breidt et al () and therefore is often referred to as such; see Harvey (), Ray and Tsay (), Hurvich and Soulier (), and Deo et al ().…”

Section: Simulationsmentioning

confidence: 99%

“…where { j , j ≥ 1} is an independent identically distributed sequence of random variables with mean 0, and {Y j , j ≥ 1} is a Gaussian process. Given the additional assumption of LRD variables { (Y j ), j ≥ 1}, this model was introduced as LMSV model in Breidt et al (1998) and therefore is often referred to as such; see Harvey (2007), Ray and Tsay (2000), Hurvich and Soulier (2009), and Deo et al (2006). According to the previous considerations, we simulate Pareto distributed sequences…”

Section: Simulationsmentioning

confidence: 99%

“…Initially, the LMSV model had been introduced by Breidt et al (1998) and, independently, by Harvey (2007). An overview of stochastic volatility models with LRD and their basic properties is given in Deo et al (2006) and in Hurvich and Soulier (2009). A test for distinguishing weakly dependent stochastic volatility time series with a trend from LMSV time series, possibly with a trend, has recently been developed in Jach and Kokoszka (2017).…”

Section: Introductionmentioning

confidence: 99%

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Testing for Change in Long‐Memory Stochastic Volatility Time Series

Betken

Kulik

2019

Journal Time Series Analysis

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In this article, change‐point problems for long‐memory stochastic volatility (LMSV) models are considered. A general testing problem which includes various alternative hypotheses is discussed. Under the hypothesis of stationarity the limiting behavior of CUSUM‐ and Wilcoxon‐type test statistics is derived. In this context, a limit theorem for the two‐parameter empirical process of LMSV time series is proved. In particular, it is shown that the asymptotic distribution of CUSUM test statistics may not be affected by long memory, unlike Wilcoxon test statistics which are typically influenced by long‐range dependence. To avoid the estimation of nuisance parameters in applications, the usage of self‐normalized test statistics is proposed. The theoretical results are accompanied by an analysis of Standard & Poor's 500 daily closing indices with respect to structural changes and by simulation studies which characterize the finite sample behavior of the considered testing procedures when testing for changes in mean and in variance.

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“…If σ(x) = exp(x), then the model is referred to in the econometrics literature as Long Memory in Stochastic Volatility (LMSV) and was introduced in [4]. For an overview of stochastic volatility models with long memory we refer to [7].…”

Section: Introductionmentioning

confidence: 99%

The tail empirical process for long memory stochastic volatility sequences

Kulik

Soulier

2011

Stochastic Processes and their Applications

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This paper describes the limiting behaviour of tail empirical processes associated with long memory stochastic volatility models. We show that such a process has dichotomous behaviour, according to an interplay between the Hurst parameter and the tail index. On the other hand, the tail empirical process with random levels never suffers from long memory. This is very desirable from a practical point of view, since such a process may be used to construct the Hill estimator of the tail index. To prove our results we need to establish new results for regularly varying distributions, which may be of independent interest.

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Long Memory in Nonlinear Processes

Cited by 14 publications

References 58 publications

Asymptotics for duration-driven long range dependent processes

Asymptotics for duration-driven long range dependent processes

Testing for Change in Long‐Memory Stochastic Volatility Time Series

The tail empirical process for long memory stochastic volatility sequences

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