J. Japan Statist. Soc., Vol. 37 (No. 1), pp. 1-28, 2007

A Modified Box-Cox Transformation in the Multivariate ARMA Model

Takahiro Terasaka and Yuzo Hosoya

Abstract. The Box-Cox transformation has been used as a simple method of transforming dependent variable in ordinary-linear regression circumstances for improving the Gaussian-likelihood fit and making the disturbance terms of a model reasonably homoscedastic. The paper introduces a new version of the Box-Cox transformation and investigates how it works in terms of asymptotic performance and application, focusing in particular on inference on stationary multivariate ARMA models. The paper proposes a computational estimation procedure which extends the three-step Hannan and Rissanen method so as to accommodate the transformation and, for the purpose of parameter testing, the paper proposes a Monte-Carlo Wald test. The allied algorithm is applied to a bivariate series of the Tokyo stock-price index (Topix) and the call rate.

Key words and phrases: Box-Cox transformation, limit theorems, Monte-CarloWald test, multivariate ARMA model, ratio data, transformation-linear process.

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