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129
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 17 (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.
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 16 (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...
Inference and Forecasting for Fractional Autoregressive Integrated Moving Average Models, with an application to US and UK inflation
 Institute, Erasmus University Rotterdam
, 1999
"... We discuss computational aspects of likelihoodbased specication, estimation, inference, and forecasting of possibly nonstationary series with long memory. We use the arfima(p; d; q) model with deterministic regressors and we compare sampling characteristics of approximate and exact rstorder asy ..."
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Cited by 13 (2 self)
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We discuss computational aspects of likelihoodbased specication, estimation, inference, and forecasting of possibly nonstationary series with long memory. We use the arfima(p; d; q) model with deterministic regressors and we compare sampling characteristics of approximate and exact rstorder asymptotic methods. We extend the analysis using a higherorder asymptotic method, suggested by Cox and Reid (1987). Ecient computation and simulation allow us to apply parametric bootstrap inference as well. We investigate the relevance of the dierences between the methods for the timeseries analysis of monthly core consumer price ination in the US and quarterly overall consumer price ination in the UK. We concentrate on (stationarity) tests for the order of integration and on inference for outofsample forecasts of the price level. * Econometric Institute, Erasmus University Rotterdam, The Netherlands. ** Nueld College, New Road, Oxford OX1 1NF, UK. 1 Introduction In this pap...
Estimation and interpretation of 1/f a noise in Human Cognition
, 2004
"... Recent analyses of serial correlations in cognitive tasks have provided preliminary evidence of the presence of a particular form of longrange serial dependence known as 1/f noise. It has been argued that longrange dependence has been largely ignored in mainstream cognitive psychology even though ..."
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Cited by 11 (2 self)
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Recent analyses of serial correlations in cognitive tasks have provided preliminary evidence of the presence of a particular form of longrange serial dependence known as 1/f noise. It has been argued that longrange dependence has been largely ignored in mainstream cognitive psychology even though it accounts for a substantial proportion of variability in behavior (see, e.g., Gilden, 1997, 2001). In this article, we discuss the defining characteristics of longrange dependence and argue that claims about its presence need to be evaluated by testing against the alternative hypothesis of shortrange dependence. For the data from three experiments, we accomplish such tests with autoregressive fractionally integrated movingaverage time series modeling. We find that longrange serial dependence in these experiments can be explained by any of several mechanisms, including mixtures of a small number of shortrange processes.
Maximum Likelihood Estimators for ARMA and ARFIMA Models: A Monte Carlo Study
, 1999
"... We analyze by simulation the properties of two time domain and two frequency domain estimators for low order autoregressive fractionally integrated moving average Gaussian models, ARFIMA (p; d; q). The estimators considered are the exact maximum likelihood for demeaned data, EML, the associated modi ..."
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Cited by 10 (0 self)
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We analyze by simulation the properties of two time domain and two frequency domain estimators for low order autoregressive fractionally integrated moving average Gaussian models, ARFIMA (p; d; q). The estimators considered are the exact maximum likelihood for demeaned data, EML, the associated modified profile likelihood, MPL, and the Whittle estimator with, WLT, and without tapered data, WL. Length of the series is 100. The estimators are compared in terms of pileup effect, mean square error, bias, and empirical confidence level. The tapered version of the Whittle likelihood turns out to be a reliable estimator for ARMA and ARFIMA models. Its small losses in performance in case of "wellbehaved" models are compensated sufficiently in more "difficult" models. The modified profile likelihood is an alternative to the WLT but is computationally more demanding. It is either equivalent to the EML or more favorable than the EML. For fractionally integrated models, particularly, it dominate...
Bayesian analysis of autoregressive fractionally integrated moving average processes
 Journal of Time Series Analysis
"... Abstract. For the autoregressive fractionally integrated moving average (ARFIMA) processes which characterize both long memory and short memory behavior in time series, we formulate Bayesian inference using Markov chain Monte Carlo methods. We derive a form for the joint posterior distribution of th ..."
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Cited by 10 (0 self)
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Abstract. For the autoregressive fractionally integrated moving average (ARFIMA) processes which characterize both long memory and short memory behavior in time series, we formulate Bayesian inference using Markov chain Monte Carlo methods. We derive a form for the joint posterior distribution of the parameters that is computationally feasible for repetitive evaluation within a modified Gibbs sampling algorithm that we employ. We illustrate our approach through two examples.
Inference and Forecasting for ARFIMA Models With an Application to US and UK Inflation
, 2004
"... Practical aspects of likelihoodbased inference and forecasting of series with long memory are considered, based on the arfima(p; d; q) model with deterministic regressors. Sampling characteristics of approximate and exact firstorder asymptotic methods are compared. The analysis is extended using m ..."
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Cited by 9 (2 self)
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Practical aspects of likelihoodbased inference and forecasting of series with long memory are considered, based on the arfima(p; d; q) model with deterministic regressors. Sampling characteristics of approximate and exact firstorder asymptotic methods are compared. The analysis is extended using modified profile likelihood analysis, which is a higherorder asymptotic method suggested by Cox and Reid (1987). The relevance of the differences between the methods is investigated for models and forecasts of monthly core consumer price inflation in the US and quarterly overall consumer price inflation in the UK.
LIMIT THEOREMS FOR BIVARIATE APPELL POLYNOMIALS  Part. I: CENTRAL LIMIT THEOREMS
, 1997
"... Consider the stationary linear process X t = P 1 u=\Gamma1 a(t\Gammau) u , t 2 Z, where f u g is an i.i.d. finite variance sequence. The spectral density of fX t g may diverge at the origin (longrange dependence) or at any other frequency. Consider now the quadratic form QN = P N t;s=1 b(t \Gamm ..."
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Cited by 9 (2 self)
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Consider the stationary linear process X t = P 1 u=\Gamma1 a(t\Gammau) u , t 2 Z, where f u g is an i.i.d. finite variance sequence. The spectral density of fX t g may diverge at the origin (longrange dependence) or at any other frequency. Consider now the quadratic form QN = P N t;s=1 b(t \Gamma s)Pm;n (X t ; X s ), where Pn;m (X t ; X s ) denotes a nonlinear function (Appell polynomial). We provide general conditions on the kernels b and a for N \Gamma1=2 QN to converge to a Gaussian distribution. We show that this convergence holds if b and a are not too badly behaved. However, the good behavior of one kernel may compensate for the bad behavior of the other. The conditions are formulated in the spectral domain.
Efficiency improvements in inference on stationary and nonstationary fractional time series
 ANNALS OF STATISTICS
, 2005
"... We consider a time series model involving a fractional stochastic component, whose integration order can lie in the stationary/invertible or nonstationary regions and be unknown, and an additive deterministic component consisting of a generalized polynomial. The model can thus incorporate competing ..."
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Cited by 8 (6 self)
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We consider a time series model involving a fractional stochastic component, whose integration order can lie in the stationary/invertible or nonstationary regions and be unknown, and an additive deterministic component consisting of a generalized polynomial. The model can thus incorporate competing descriptions of trending behavior. The stationary input to the stochastic component has parametric autocorrelation, but innovation with distribution of unknown form. The model is thus semiparametric, and we develop estimates of the parametric component which are asymptotically normal and achieve an Mestimation efficiency bound, equal to that found in work using an adaptive LAM/LAN approach. A major technical feature which we treat is the effect of truncating the autoregressive representation in order to form innovation proxies. This is relevant also when the innovation density is parameterized, and we provide a result for that case also. Our semiparametric estimates employ nonparametric series estimation, which avoids some complications and conditions in kernel approaches featured in much work on adaptive estimation of time series models; our work thus also contributes to methods and theory for nonfractional time series models, such as autoregressive moving averages. A Monte Carlo study of finite sample performance of the semiparametric estimates is included.