SAMPLE MEANS, SAMPLE AUTOCOVARIANCES, AND LINEAR REGRESSION OF STATIONARY MULTIVARIATE LONG MEMORY PROCESSES

We develop an asymptotic theory for the first two sample moments of a stationary multivariate long memory process under fairly general conditions. In this theory the convergence rates and the limits (the fractional Brownian motion, the Rosenblatt process, etc.) all depend intrinsically on the degree...

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Bibliographic Details
Published in:Econometric theory 2002-02, Vol.18 (1), p.51-78
Main Author: Chung, Ching-Fan
Format: Article
Language:English
Subjects:
Brownian motion
Central limit theorem
Econometrics
Estimators
Least squares method
Linear regression
Martingales
Maximum likelihood estimation
Multivariate analysis
Perceptron convergence procedure
Regression analysis
Sample mean
Samples
Sampling
Sampling bias
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Summary:We develop an asymptotic theory for the first two sample moments of a stationary multivariate long memory process under fairly general conditions. In this theory the convergence rates and the limits (the fractional Brownian motion, the Rosenblatt process, etc.) all depend intrinsically on the degree of long memory in the process. The theory of the sample moments is then applied to the multiple linear regression model. An interesting finding is that, even though all the regressors and the disturbance are stationary and ergodic, the joint long memory in one single regressor and in the disturbance can invalidate the usual asymptotic theory for the ordinary least squares (OLS) estimation. Specifically, the convergence rates of the OLS estimators become slower, the limits are not normal, and the standard t- and F-tests all collapse.
ISSN:0266-4666
1469-4360
DOI:10.1017/S0266466602181047