Large-Sample Properties of Parameter Estimates for Strongly Dependent Stationary Gaussian Time Series

We show that it is possible to adapt to nonparametric disturbance autocorrelation in time series regression in the presence of long memory in both regressors and disturbances by using a smoothed nonparametric spectrum estimate in frequency-domain generalized least squares. When the collective memory in regressors and disturbances is sufficiently strong, ordinary least squares is not only asymptotically inefficient but asymptotically non-normal and has a slow rate of convergence, whereas generalized least squares is asymptotically normal and Gauss-Markov efficient with standard convergence rate. Despite the anomalous behaviour of nonparametric spectrum estimates near a spectral pole, we are able to justify a standard construction of frequency-domain generalized least squares, earlier considered in case of short memory disturbances. A small Monte Carlo study of finite sample performance is included.

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“…The conclusion now follows because Fox and Taqqu (1986). Thus, the first two terms of the last displayed expression are…”

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confidence: 68%

Adapting to Unknown Disturbance Autocorrelation in Regression with Long Memory

Hidalgo

Robinson

2002

Econometrica

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“…Assumption 4 is a smoothness condition imposing di¤erentiability of the spectral density near the origin, analogous to those imposed on the spectral density at any frequency in parametric frameworks, see for example Fox & Taqqu (1986). The condition is satis…ed, e.g., by fractional ARIMA models.…”

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confidence: 99%

Fully modified narrow‐band least squares estimation of weak fractional cointegration

Nielsen

Frederiksen²

2011

The Econometrics Journal

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract We consider estimation of the cointegrating relation in the weak fractional cointegration model, where the strength of the cointegrating relation (di¤erence in memory parameters) is less than one-half. A special case is the stationary fractional cointegration model, which has found important application recently, especially in …nancial economics. Previous research on this model has considered a semiparametric narrow-band least squares (NBLS) estimator in the frequency domain, but in the stationary case its asymptotic distribution has been derived only under a condition of non-coherence between regressors and errors at the zero frequency. We show that in the absence of this condition, the NBLS estimator is asymptotically biased, and also that the bias can be consistently estimated. Consequently, we introduce a fully modi…ed NBLS estimator which eliminates the bias, and indeed enjoys a faster rate of convergence than NBLS in general. We also show that local Whittle estimation of the integration order of the errors can be conducted consistently based on NBLS residuals, but the estimator has the same asymptotic distribution as if the errors were observed only under the condition of non-coherence. Furthermore, compared to much previous research, the development of the asymptotic distribution theory is based on a di¤erent spectral density representation, which is relevant for multivariate fractionally integrated processes, and the use of this representation is shown to result in lower asymptotic bias and variance of the narrow-band estimators. We present simulation evidence and a series of empirical illustrations to demonstrate the feasibility and empirical relevance of our methodology. Terms of use: Documents in

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“…The Whittle estimator takes a somewhat roundabout route to estimating the Hurst parameter H, although the final procedure is reasonably simple [267,67]. Initially one must specify a mathematical model of a time series that exhibits long-range dependence.…”

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confidence: 99%

Workload Modeling for Computer Systems Performance Evaluation

Feitelson

2015

191

131

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Reliable performance evaluations require the use of representative workloads. This is no easy task since modern computer systems and their workloads are complex, with many interrelated attributes and complicated structures. Experts often use sophisticated mathematics to analyze and describe workload models, making these models difficult for practitioners to grasp. This book aims to close this gap by emphasizing the intuition and the reasoning behind the definitions and derivations related to the workload models. It provides numerous examples from real production systems, with hundreds of graphs. Using this book, readers will be able to analyze collected workload data and clean it if necessary, derive statistical models that include skewed marginal distributions and correlations, and consider the need for generative models and feedback from the system. The descriptive statistics techniques covered are also useful for other domains.

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Large-Sample Properties of Parameter Estimates for Strongly Dependent Stationary Gaussian Time Series

Cited by 758 publications

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Adapting to Unknown Disturbance Autocorrelation in Regression with Long Memory

Adapting to Unknown Disturbance Autocorrelation in Regression with Long Memory

Fully modified narrow‐band least squares estimation of weak fractional cointegration

Workload Modeling for Computer Systems Performance Evaluation

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