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Asymptotic expansions of the distributions of some test statistics for Gaussian ARMA processes

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  • Taniguchi, Masanobu

Abstract

Let {Xt} be a Gaussian ARMA process with spectral density f[theta]([lambda]), where [theta] is an unknown parameter. The problem considered is that of testing a simple hypothesis H:[theta] = [theta]0 against the alternative A:[theta] [not equal to] [theta]0. For this problem we propose a class of tests , which contains the likelihood ratio (LR), Wald (W), modified Wald (MW) and Rao (R) tests as special cases. Then we derive the [chi]2 type asymptotic expansion of the distribution of T [set membership, variant] up to order n-1, where n is the sample size. Also we derive the [chi]2 type asymptotic expansion of the distribution of T under the sequence of alternatives An: [theta] = [theta]0 + [var epsilon]/[radical sign]n, [epsilon] > 0. Then we compare the local powers of the LR, W, MW, and R tests on the basis of their asymptotic expansions.

Suggested Citation

  • Taniguchi, Masanobu, 1988. "Asymptotic expansions of the distributions of some test statistics for Gaussian ARMA processes," Journal of Multivariate Analysis, Elsevier, vol. 27(2), pages 494-511, November.
    • Handle: RePEc:eee:jmvana:v:27:y:1988:i:2:p:494-511
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    Cited by:

    1. Bernardo M. Lagos & Pedro A. Morettin, 2004. "Improvement of the Likelihood Ratio Test Statistic in ARMA Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(1), pages 83-101, January.
    2. Robinson, Peter M. & Rossi, Francesca, 2015. "Refinements in maximum likelihood inference on spatial autocorrelation in panel data," Journal of Econometrics, Elsevier, vol. 189(2), pages 447-456.
    3. Firmin Doko Tchatoka, 2015. "On bootstrap validity for specification tests with weak instruments," Econometrics Journal, Royal Economic Society, vol. 18(1), pages 137-146, February.
    4. Kakizawa, Yoshihide, 2012. "Generalized Cordeiro–Ferrari Bartlett-type adjustment," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 2008-2016.
    5. Noud P.A. van Giersbergen, 2013. "Bartlett correction in the stable second‐order autoregressive model with intercept and trend," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 67(4), pages 482-498, November.
    6. Kakizawa, Yoshihide, 2010. "Comparison of Bartlett-type adjusted tests in the multiparameter case," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1638-1655, August.
    7. Kakizawa, Yoshihide, 2012. "Improved chi-squared tests for a composite hypothesis," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 141-161.

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