On Consistency in Time Series Analysis

P. M. Robinson

doi:10.1214/aos/1176344080

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Home > Journals > Ann. Statist. > Volume 6 > Issue 1 > Article

January, 1978 On Consistency in Time Series Analysis

P. M. Robinson

Ann. Statist. 6(1): 215-223 (January, 1978). DOI: 10.1214/aos/1176344080

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Abstract

A number of statistics that arise in time series analysis can be represented as the sum of a partial realization of a possibly serially dependent and nonstationary discrete-parameter stochastic process. The almost sure and $L_p, p > 1$, convergence of such statistics is investigated, under various moment conditions. The results are applied to the least squares estimates of multiple regressions.