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79
On the Detection and Estimation of Long Memory in Stochastic Volatility
, 1995
"... Recent studies have suggested that stock markets' volatility has a type of longrange dependence that is not appropriately described by the usual Generalized Autoregressive Conditional Heteroskedastic (GARCH) and Exponential GARCH (EGARCH) models. In this paper, different models for describing this ..."
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Cited by 123 (6 self)
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Recent studies have suggested that stock markets' volatility has a type of longrange dependence that is not appropriately described by the usual Generalized Autoregressive Conditional Heteroskedastic (GARCH) and Exponential GARCH (EGARCH) models. In this paper, different models for describing this longrange dependence are examined and the properties of a LongMemory Stochastic Volatility (LMSV) model, constructed by incorporating an Autoregressive Fractionally Integrated Moving Average (ARFIMA) process in a stochastic volatility scheme, are discussed. Strongly consistent estimators for the parameters of this LMSV model are obtained by maximizing the spectral likelihood. The distribution of the estimators is analyzed by means of a Monte Carlo study. The LMSV is applied to daily stock market returns providing an improved description of the volatility behavior. In order to assess the empirical relevance of this approach, tests for longmemory volatility are described and applied to an e...
Functionalcoefficient Regression Models for Nonlinear Time Series
 Journal of the American Statistical Association
, 1998
"... We apply the local linear regression technique for estimation of functionalcoefficient regression models for time series data. The models include threshold autoregressive models (Tong 1990) and functionalcoefficient autoregressive models (Chen and Tsay 1993) as special cases but with the added adv ..."
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Cited by 42 (10 self)
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We apply the local linear regression technique for estimation of functionalcoefficient regression models for time series data. The models include threshold autoregressive models (Tong 1990) and functionalcoefficient autoregressive models (Chen and Tsay 1993) as special cases but with the added advantages such as depicting finer structure of the underlying dynamics and better postsample forecasting performance. We have also proposed a new bootstrap test for the goodness of fit of models and a bandwidth selector based on newly defined crossvalidatory estimation for the expected forecasting errors. The proposed methodology is dataanalytic and is of appreciable flexibility to analyze complex and multivariate nonlinear structures without suffering from the "curse of dimensionality". The asymptotic properties of the proposed estimators are investigated under the ffmixing condition. Both simulated and real data examples are used for illustration. Key Words: ffmixing; Asymptotic normali...
LogPeriodogram Regression Of Time Series With Long Range Dependence
 ANNALS OF STATISTICS
, 1999
"... This paper discusses the use of fractional exponential models (Robinson (1990), Beran (1994)) to model the spectral density f(x) of a covariance stationary process when f(x) may be decomposed as f(x) = x \Gamma2d f (x), where f (x) is bounded and bounded away from zero. A form of logperiodogram ..."
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Cited by 31 (0 self)
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This paper discusses the use of fractional exponential models (Robinson (1990), Beran (1994)) to model the spectral density f(x) of a covariance stationary process when f(x) may be decomposed as f(x) = x \Gamma2d f (x), where f (x) is bounded and bounded away from zero. A form of logperiodogram regression technique is presented both in the parametric context (i.e. f (x) is a finite order exponential model in the sense of Bloomfield (1973)) and the semiparametric context (f (x) is regarded as a nuisance parameter). Assuming gaussianity and additional conditions on the regularity of f (x) which seem mild, asymptotic normality of the parameter estimates in the parametric and the semiparametric context is established. As a byproduct, some improvements over the results presented by Robinson (1994) have been obtained for the large sample distribution of logperiodogram ordinates for Gaussian processes.
Estimation of the Hurst Parameter of LongRange Dependent Time Series
, 1996
"... This paper is a condensed introduction to selfsimilarity, selfsimilar 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 carr ..."
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Cited by 28 (1 self)
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This paper is a condensed introduction to selfsimilarity, selfsimilar 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. 1 Introduction The subject of selfsimilarity and the estimation of statistical parameters of time series in the presence of longrange dependence are becoming more and more common in several fields of science. Up to now there are only a few text books available, e.g. in [2], which give a comprehensive overview of the techniques and estimators. The intention of this paper is not to close this gap but to provide some basic information about selfsimilarity, selfsimilar processes, and estimators of the socalled Hurst parameter H. It gives a rather condensed introduction to selfsimilarity and contains a number of referenced papers which can ...
LongRange Dependence and Data Network Traffic
, 2001
"... This is an overview of a relatively recent application of longrange dependence (LRD) to the area of communication networks, in particular to problems concerned with the dynamic nature of packet flows in highspeed data networks such as the Internet. We demonstrate that this new application area off ..."
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Cited by 23 (1 self)
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This is an overview of a relatively recent application of longrange dependence (LRD) to the area of communication networks, in particular to problems concerned with the dynamic nature of packet flows in highspeed data networks such as the Internet. We demonstrate that this new application area offers unique opportunities for significantly advancing our understanding of LRD and related phenomena. These advances are made possible by moving beyond the conventional approaches associated with the widespread "blackbox" perspective of traditional time series analysis and exploiting instead the physical mechanisms that exist in the networking context and that are intimately tied to the observed characteristics of measured network traffic. In order to describe this complexity we provide a basic understanding of the design, architecture and operations of data networks, including a description of the TCP/IP protocols used in today's Internet. LRD is observed in the large scale behavior of the data traffic and we provide a physical explanation for its presence. LRD tends to be caused by user and application characteristics and has little to do with the network itself. The network affects mostly small time scales, and this is why a rudimentary understanding of the main protocols is important. We illustrate why multifractals may be relevant for describing some aspects of the highly irregular traffic behavior over small time scales. We distinguish between a timedomain and waveletdomain approach to analyzing the small time scale dynamics and discuss why the waveletdomain approach appears to be better suited than the timedomain approach for identifying features in measured traffic (e.g., relatively regular traffic patterns over certain time scales) that have a direct networking interpretation (e....
On the spectral density of the wavelet coefficients of long memory time series with application to the logregression estimation of the memory parameter
, 2006
"... Abstract. In the recent years, methods to estimate the memory parameter using wavelet analysis have gained popularity in many areas of science. Despite its widespread use, a rigorous semiparametric asymptotic theory, comparable to the one developed for Fourier methods, is still missing. In this con ..."
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Cited by 18 (8 self)
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Abstract. In the recent years, methods to estimate the memory parameter using wavelet analysis have gained popularity in many areas of science. Despite its widespread use, a rigorous semiparametric asymptotic theory, comparable to the one developed for Fourier methods, is still missing. In this contribution, we adapt the classical semiparametric framework introduced by Robinson and his coauthors for estimating the memory parameter of a (possibly) nonstationary process. As an application, we obtain minimax upper bounds for the logscale regression estimator of the memory parameter for a Gaussian process and we derive an explicit expression of its variance.
SemiParametric Graphical Estimation Techniques for LongMemory Data.
, 1996
"... This paper reviews several periodogrambased methods for estimating the longmemory parameter H in time series and suggests a way to robustify them. The high frequencies tend to bias the estimates. Using only low frequencies eliminates the bias but increases the variance. We hence suggest plotting t ..."
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Cited by 15 (4 self)
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This paper reviews several periodogrambased methods for estimating the longmemory parameter H in time series and suggests a way to robustify them. The high frequencies tend to bias the estimates. Using only low frequencies eliminates the bias but increases the variance. We hence suggest plotting the estimates of H as a function of a parameter which balances bias versus variance and, if the plot flattens in a central region, to use the flat part for estimating H. We apply this technique to the periodogram regression method, the Whittle approximation to maximum likelihood and to the local Whittle method. We investigate its effectiveness on several simulated fractional ARIMA series and also apply it to estimate the longmemory parameter H in computer network traffic. 1 Introduction Time series with long memory have been considered in many fields including hydrology, biology and computer networks. Unfortunately, estimating the long memory (longrange dependence) parameter H in a given d...
Bayesian Analysis of Long Memory and Persistence using ARFIMA Models
 FORTHCOMING IN THE JOURNAL OF ECONOMETRICS
, 1995
"... This paper provides a Bayesian analysis of Autoregressive Fractionally Integrated Moving Average (ARFIMA) models. We discuss in detail inference on impulse responses, and show how Bayesian methods can be used to (i) test ARFIMA models against ARIMA alternatives, and (ii) take model uncertainty into ..."
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Cited by 13 (1 self)
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This paper provides a Bayesian analysis of Autoregressive Fractionally Integrated Moving Average (ARFIMA) models. We discuss in detail inference on impulse responses, and show how Bayesian methods can be used to (i) test ARFIMA models against ARIMA alternatives, and (ii) take model uncertainty into account when making inferences on quantities of interest. Our methods are then used to investigate the persistence properties of real U.S. GNP.
2006) "Residual logperiodogram inference for long run relationships
 Journal of Econometrics
, 2010
"... We assume that some consistent estimatorbβ of an equilibrium relation between nonstationary series integrated of order d ∈ (0.5, 1.5) is used to compute residuals ût = yt −bβxt (or differences thereof). We propose to apply the semiparametric logperiodogram regression to the (differenced) residuals ..."
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Cited by 13 (2 self)
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We assume that some consistent estimatorbβ of an equilibrium relation between nonstationary series integrated of order d ∈ (0.5, 1.5) is used to compute residuals ût = yt −bβxt (or differences thereof). We propose to apply the semiparametric logperiodogram regression to the (differenced) residuals in order to estimate or test the degree of persistence δ of the equilibrium deviation ut. Providedbβ converges fast enough, we describe simple semiparametric conditions around zero frequency that guarantee consistent estimation of δ. At the same time limiting normality is derived, which allows to construct approximate confidence intervals to test hypotheses on δ. This requires that d − δ> 0.5 for superconsistentbβ, so the residuals can be good proxies of true cointegrating errors. Our assumptions allow for stationary deviations with long memory, 0 ≤ δ < 0.5, as well as for nonstationary but transitory equilibrium errors, 0.5 < δ < 1. In particular, if xt contains several series we consider the joint estimation of d and δ. Wald statistics to test for parameter restrictions of the system have a limiting χ 2 distribution. We also analyze the benefits of a pooled version of the estimate. The empirical applicability of our general cointegration test is investigated by means of Monte Carlo experiments and illustrated with a study of exchange rate dynamics. JEL Classification: C14, C22.