Minimum distance estimation and goodness-of-fit tests in first-order autoregression. (English) Zbl 0607.62101

Koul, Hira L.

Ann. Stat. 14, 1194-1213 (1986).

Consider the first-order autoregressive model \(X_ i=\rho X_{i- 1}+\epsilon_ i\), where the \(\{\epsilon_ i\}\) are i.i.d. according to a df F, symmetric about zero. The paper considers a minimum distance estimator of \(\rho\), within a certain class determined by a finite measure on the Borel line. In this class an asymptotically efficient estimator is exhibited. The paper also discusses goodness-of-fit tests of symmetry and for a specified error distribution.

Reviewer: P.A.Morettin

MSC:

62M10	Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G05	Nonparametric estimation
62G10	Nonparametric hypothesis testing
62G20	Asymptotic properties of nonparametric inference

Keywords:

least-squares estimator; Cramér-von Mises type statistic; weighted empirical residual process; stationary; ergodic; influence curve; first- order autoregressive model; minimum distance estimator; asymptotically efficient estimator; goodness-of-fit tests of symmetry