Econometrica Vol. 47 No. 4 1979
Asymptotic Estimation and Hypothesis Testing Results for Vector Linear Time Series Models
Abstract
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 VN- 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.
- DOI
- 10.2307/1914144
- Volume
- 47
- Issue
- 4
- Pages
- 1005
- Sources
- openalex crossref bibtex:phds-export.bib