An Asymptotic Expansion for the Distribution of the Likelihood Radio Criterion for a Gaussian Autoregressive Moving Average Process Under a Local Alternative
- 1 April 1985
- journal article
- research article
- Published by Cambridge University Press (CUP) in Econometric Theory
- Vol. 1 (1) , 73-84
- https://doi.org/10.1017/s0266466600011002
Abstract
In this paper, we shall derive the asymptotic expansion for the distribution of the likelihood ratio criterion for a Gaussian autoregressive moving average process under a sequence of local alternative hypotheses converging to the null hypothesis with rate of convergence where n is the sample size. Explicit algebraic formulae are presented for certain special cases, including the ARMA(1,1).Keywords
This publication has 10 references indexed in Scilit:
- On the Second Order Asymptotic Efficiency of Estimators of Gaussian ARMA ProcessesThe Annals of Statistics, 1983
- Some Approximations to the Distribution of Econometric Criteria which are Asymptotically Distributed as Chi-SquaredEconometrica, 1980
- Finite Sample Theory and the Distributions of Alternative Estimators of the Marginal Propensity to ConsumeThe Review of Economic Studies, 1980
- The Commutation Matrix: Some Properties and ApplicationsThe Annals of Statistics, 1979
- A General Theorem in the Theory of Asymptotic Expansions as Approximations to the Finite Sample Distributions of Econometric EstimatorsEconometrica, 1977
- Approximations to Some Finite Sample Distributions Associated with a First-Order Stochastic Difference EquationEconometrica, 1977
- Econometric Estimators and the Edgeworth ApproximationEconometrica, 1976
- The likelihood ratio criterion for a composite hypothesis under a local alternativeBiometrika, 1975
- Gram-Charlier Approximations Applied to t Ratios of k-Class EstimatorsEconometrica, 1975
- Likelihood ratio and associated test criteriaBiometrika, 1971