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Second order expansion of t-statistic in autoregressive models

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Published by Massachusetts Institute of Technology, Dept. of Economics in Cambridge, MA .
Written in English


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About the Edition

The purpose of this paper is to receive a second order expansion of the t-statistic in AR(1) model in local to unity asymptotic approach. I show that Hansen"s (1998) method for confidence set construction achieves a second order improvement in local to unity asymptotic approach compared with Stock"s (1991) and Andrews" (1993) methods. Keywords: autoregressive process, confidence set, local to unity asymptotics, uniform convergence.

Edition Notes

StatementAnna Mikusheva
SeriesWorking paper series / Massachusetts Institute of Technology, Dept. of Economics -- working paper 07-26, Working paper (Massachusetts Institute of Technology. Dept. of Economics) -- no. 07-26.
ContributionsMassachusetts Institute of Technology. Dept. of Economics
The Physical Object
Pagination20 leaves ;
Number of Pages20
ID Numbers
Open LibraryOL24869641M
OCLC/WorldCa644562317

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Definition. The notation () indicates an autoregressive model of order AR(p) model is defined as = + ∑ = − + where, , are the parameters of the model, is a constant, and is white can be equivalently written using the backshift operator B as = + ∑ = + so that, moving the summation term to the left side and using polynomial notation, we have. SECOND ORDER EXPANSION OF THE T-STATISTIC IN AR(1) MODELS ANNA MIKUSHEVA MIT The purpose of this paper is to differentiate between several asymptotically valid methods for confidence set construction for the autoregressive coefficient in AR(1) models. We show that the nonparametric grid bootstrap procedure suggested by. Second order expansion of t-statistic in autoregressive models By Anna Mikusheva Download PDF (1 MB)Author: Anna Mikusheva. We establish a second order expansion of the t-statistic in an AR(1) model in the local-to-unity asymptotic approach, which differs drastically from the usual Edgeworth-type expansions by approximating the statistic around a nonstandard and nonpivotal limit.

Downloadable! The purpose of this paper is to differentiate between several asymptotically valid methods for confidence set construction for the autoregressive coefficient in AR(1) models. We show that the nonparametric grid bootstrap procedure suggested by Hansen (, Review of Economics and Statist –) achieves a second order refinement in the local-to-unity asymptotic. expansionofthet-statistic. Section4 shows thatthe probabilistic expansion from the previoussectionleadstoa distributional n 5establishes a similar. Second order autoregressive [AR(2)] model has been adopted in the likelihood function to calibrate the soil and water assessment tool (SWAT) model for the .   For data which appears cyclical, the fundamental component of these models is the second order autoregressive, or AR(2) model (1) With e taken as a white noise series, and the coefficients ~1' ~2 being of the form 2 ~1 = 2rcos2TIh, ~2 _r (2) where 0 model rep­resents a stationary process with a single spectral peak.

Similarly, a second-order autoregressive process, denoted AR(2), takes the form. and a p-order autoregressive process, AR(p), takes the form. Property 1: The mean of the y i in a stationary AR(p) process is. Proof: click here. Property 2: The variance of the . NAGARCH. Nonlinear Asymmetric GARCH(1,1) (NAGARCH) is a model with the specification: = + (− − −) + −, where ≥, ≥, > and (+) +. The AIC criterion asymptotically overestimates the order with positive probability, whereas the BIC and HQ criteria estimate the order consis-tently under fairly general conditions if the true order pis less than or equal to pmax. For more information on the use of model selection criteria in VAR models see L¨utkepohl () chapter four. Modelling Non-normal First-order Autoregressive Time Series C. H. SIM University of Malaya, Mala ysia ABSTRACT We shall first review some non-normal stationary first-order autoregressive models. The models are constructed with a given marginal distribution (logistic, hyperbolic secant, exponential, Laplace, or gamma) and the.