Premium
Median‐unbiased Estimation and Exact Inference Methods for First‐order Autoregressive Models with Conditional Heteroscedasticity of Unknown Form
Author(s) -
Luger Richard
Publication year - 2006
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2005.00456.x
Subject(s) - mathematics , autoregressive model , heteroscedasticity , estimator , statistics , star model , series (stratigraphy) , minimum variance unbiased estimator , bias of an estimator , best linear unbiased prediction , inference , econometrics , time series , autoregressive integrated moving average , computer science , selection (genetic algorithm) , paleontology , artificial intelligence , biology
. Consider the first‐order autoregressive model y t = φ y t −1 + ɛ t , t = 1,…, T , with arbitrary initial non‐zero value y 0 . Assuming that the error terms ɛ t are independently distributed according to median‐zero distributions [Zieliński (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.