Median-unbiased Estimation and Exact Inference Methods for First-order Autoregressive Models with Conditional Heteroscedasticity of Unknown Form

Consider the first-order autoregressive model y_t = phiy_t - 1 + ϵ_t, t = 1, H , T, with arbitrary initial non-zero value y_0. Assuming that the error terms ϵ_t are independently distributed according to median-zero distributions [Zielinski (1999)Journal of Time Series Analysis, Vol. 20, p. 477] shows that the estimator conjectured by Hurwicz (1950)Statistical Inference in Dynamic Economic Models. New York, NY: Wiley - the median of the consecutive ratios y_t/y_t - 1- is an exactly median-unbiased estimator of the autoregressive parameter phi. This paper shows that the Hurwicz estimator remains median-unbiased under more general distributional assumptions, without assuming statistical independence. In particular, no restrictions are placed on the degree of heterogeneity and dependence of the conditional variance process. A computationally efficient method is also proposed to build exact confidence intervals for the autoregressive parameter which are valid in finite samples for any value of phi on the real line. Copyright 2005 Blackwell Publishing Ltd.