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posted on 12.08.2005by David I. Harvey, Dick van Dijk
This paper presents a response surface analysis for the distributions of the popular
tests for seasonal unit roots in quarterly observed time series variables
developed by Hylleberg et al. (1990). Approximate asymptotic distributions
are obtained, and response surface coefficients for 1%-, 5%- and 10%-level
critical values are reported, permitting simple computation of accurate critical
values for any sample size and lag order. Five test statistics are considered,
along with five different specifications of the deterministic component in the
test regression; allowance is also made for the lag order to be determined endogenously,
using commonly applied selection methods. Dependence of the
critical values and the probability density functions on the sample size and
lag order is also investigated.