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Seasonal Moving‐average Unit Root Tests in the Presence of a Linear Trend

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  • Wing‐kuen Tam
  • Gregory Reinsel

Abstract

To distinguish stochastic from deterministic seasonality, test procedures are developed for a unit root in the integrated seasonal moving‐average (SMA) model when an underlying deterministic trend is present. Locally best invariant unbiase (LBIU) and point optimal invariant tests are considered. Their asymptotic distributions are developed and are found to differ from those for the no‐linear‐trend case. The limiting distribution of the LBIU statistic is expressed as a functional of Brownian motions. The procedures are extended to more general seasonal autoregressive moving‐average (ARMA) models, and to the inclusion of exogenous regressors. Finite‐sample distributions are also derived for the SMA(1) model. Simulations suggest that these distributions provide accurate approximations for more general ARMA models. A numerical example is included to illustrate the tests.

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  • Wing‐kuen Tam & Gregory Reinsel, 1998. "Seasonal Moving‐average Unit Root Tests in the Presence of a Linear Trend," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(5), pages 609-625, September.
    • Handle: RePEc:bla:jtsera:v:19:y:1998:i:5:p:609-625
    DOI: 10.1111/1467-9892.00112
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    1. repec:kap:iaecre:v:11:y:2005:i:3:p:257-266 is not listed on IDEAS
    2. Mynbaev, Kairat, 2003. "Asymptotic properties of OLS estimates in autoregressions with bounded or slowly growing deterministic trends," MPRA Paper 18448, University Library of Munich, Germany, revised 2005.
    3. Luis Gil-Alana, 2005. "Unit and Fractional Roots at the Long Run and the Seasonal Frequencies in Macroeconomic Time Series," International Advances in Economic Research, Springer;International Atlantic Economic Society, vol. 11(3), pages 257-266, August.

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