Spurious Regressions in Time Series with Long Memory

Gaowen Wang and Nan-Wei Han

Communications in Statistics - Theory and Methods, 2015, vol. 44, issue 4, 837-854

Abstract: This article studies the asymptotic properties of least squares estimators and related test statistics in some spurious regression models that are generated by stationary or nonstationary fractionally integrated processes. We show that even when the fractionally integrated processes are long-range dependent, the asymptotic distributions of the least squares statistics, after appropriately rescaling and normalizing, are functionals of standard Brownian motions rather than of fractional Brownian motions. Some Monte Carlo simulations are provided to indirectly illustrate the performance of the asymptotic results for finite samples.

Date: 2015
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DOI: 10.1080/03610926.2012.753088

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