MEDIAN-UNBIASED ESTIMATION AND EXACT INFERENCE METHODS FOR FIRST-ORDER AUTOREGRESSIVE MODELS WITH CONDITIONAL HETEROSCEDASTICITY OF UNKNOWN FORM

摘要

Consider the first-order autoregressive model y_t = φy_(t-1) + ε_t, t = 1,..., 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 φ. 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 φ on the real line.