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December, 1982 Testing for Nonstationary Parameter Specifications in Seasonal Time Series Models
David P. Hasza, Wayne A. Fuller
Ann. Statist. 10(4): 1209-1216 (December, 1982). DOI: 10.1214/aos/1176345985

Abstract

Let $Y_t$ be an autoregressive process satisfying $Y_t = \alpha_1 Y_{t - 1} + \alpha_2 Y_{t - d} + \alpha_3 Y_{t - d - 1} + e_t$, where $\{e_t\}^\infty_{t = 0}$ is a sequence of $\operatorname{iid}(0, \sigma^2)$ random variables and $d \geq 2$. Such processes have been used as parametric models for seasonal time series. Typical values of $d$ are 2, 4, and 12 corresponding to time series observed semi-annually, quarterly, and monthly, respectively. If $\alpha_1 = 1, \alpha_2 = 1, \alpha_3 = - 1$ then $\Delta_1\Delta_d Y_t = e_t$, where $\Delta_r Y_t$ denotes $Y_t - Y_{t - r}$. If $(\alpha_1, \alpha_2, \alpha_3) = (1, 1, - 1)$ the process is nonstationary and the theory for stationary autoregressive processes does not apply. A methodology for testing the hypothesis $(\alpha_1, \alpha_2, \alpha_3) = (1, 1, - 1)$ is presented and percentiles for test statistics are obtained. Extensions are presented for multiplicative processes, for higher order processes, and for processes containing deterministic trend and seasonal components.

Citation

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David P. Hasza. Wayne A. Fuller. "Testing for Nonstationary Parameter Specifications in Seasonal Time Series Models." Ann. Statist. 10 (4) 1209 - 1216, December, 1982. https://doi.org/10.1214/aos/1176345985

Information

Published: December, 1982
First available in Project Euclid: 12 April 2007

zbMATH: 0505.62074
MathSciNet: MR673655
Digital Object Identifier: 10.1214/aos/1176345985

Subjects:
Primary: 62M10
Secondary: 62J05

Rights: Copyright © 1982 Institute of Mathematical Statistics

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Vol.10 • No. 4 • December, 1982
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