Testing a sub-hypothesis in linear regression models with long memory covariates and errors

Abstract

Testing a sub-hypothesis in linear regression models with long memory covariates and errors Applications of Mathematics, Vol. 53 (2008) Abstract. This paper considers the problem of testing a sub-hypothesis in homoscedastic linear regression models when the covariate and error processes form independent long memory moving averages. The asymptotic null distribution of the likelihood ratio type test based on Whittle quadratic forms is shown to be a chi-square distribution. Additionally, the estimators of the slope parameters obtained by minimizing the Whittle dispersion is seen to be n 1/2 -consistent for all values of the long memory parameters of the design and error processes.

Testing of a sub-hypothesis in linear regression models with long memory errors and deterministic design

“…The proof repeats the corresponding argument in the random design case given in Koul and Surgailis (2008) …”

“…Rao (1973). Koul and Surgailis (2008) observed that if {X t } is a vector of zero mean stationary moving average processes independent of the error process then under H 0 , Q n → D 8 2 2 p−k . The primary reason why this weak limit of Q n is different from the one obtained in the present case is the limiting behavior of Z n .…”

“…This limiting null distribution of Q n is different from what is available in the case of random design. Koul and Surgailis (2008) proved that if the design process {X t , t ∈ Z} is random having short or long memory, mean zero and is independent of { t , t ∈ Z}, then Q n tends weakly to a chi-square r.v. The conditions on f in Koul and Surgailis (2008) are similar as given below.…”