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Subsampling Intervals in Autoregressive Models with Linear Time Trend
Author(s) -
Romano Joseph P.,
Wolf Michael
Publication year - 2001
Publication title -
econometrica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 16.7
H-Index - 199
eISSN - 1468-0262
pISSN - 0012-9682
DOI - 10.1111/1468-0262.00242
Subject(s) - autoregressive model , mathematics , unit root , estimator , martingale (probability theory) , martingale difference sequence , star model , series (stratigraphy) , asymptotic distribution , rate of convergence , econometrics , setar , confidence interval , sequence (biology) , statistics , time series , autoregressive integrated moving average , computer science , paleontology , computer network , channel (broadcasting) , genetics , biology
A new method is proposed for constructing confidence intervals in autoregressive models with linear time trend. Interest focuses on the sum of the autoregressive coefficients because this parameter provides a useful scalar measure of the long‐run persistence properties of an economic time series. Since the type of the limiting distribution of the corresponding OLS estimator, as well as the rate of its convergence, depend in a discontinuous fashion upon whether the true parameter is less than one or equal to one (that is, trend‐stationary case or unit root case), the construction of confidence intervals is notoriously difficult. The crux of our method is to recompute the OLS estimator on smaller blocks of the observed data, according to the general subsampling idea of Politis and Romano (1994a), although some extensions of the standard theory are needed. The method is more general than previous approaches in that it works for arbitrary parameter values, but also because it allows the innovations to be a martingale difference sequence rather than i.i.d. Some simulation studies examine the finite sample performance.