Econometrica: Jul, 1979, Volume 47, Issue 4

Asymptotic Estimation and Hypothesis Testing Results for Vector Linear Time Series Models

https://doi.org/0012-9682(197907)47:4<1005:AEAHTR>2.0.CO;2-Y
p. 1005-1030

R. Kohn

For a general vector linear time series model we prove the strong consistency and asymptotic normality of parameter estimates obtained by maximizing a particular time domain approximation to a Gaussian likelihood, although we do not assume that the observations are necessarily normally distributed. To solve the normal equations we set up a constrained Gauss-Newton iteration and obtain the properties of the iterates when the sample size is large. In particular we show that the iterates are efficient when the iteration begins with a @?N-consistent estimator. We obtain similar results to the above for a frequency domain approximation to a Gaussian likelihood. We use the asymptotic estimation theory to obtain the asymptotic distribution of several familiar test statistics for testing nonlinear equality constraints.