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The variance ratio and trend stationary model as extensions of a constrained autoregressive model
Author(s) -
Zilca Shlomo
Publication year - 2010
Publication title -
journal of forecasting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.543
H-Index - 59
eISSN - 1099-131X
pISSN - 0277-6693
DOI - 10.1002/for.1137
Subject(s) - autoregressive model , star model , setar , nonlinear autoregressive exogenous model , series (stratigraphy) , econometrics , variance (accounting) , autoregressive integrated moving average , weighting , stationary process , autoregressive–moving average model , time series , mathematics , computer science , statistics , economics , medicine , paleontology , accounting , radiology , biology
This paper shows that a constrained autoregressive model that assigns linearly decreasing weights to past observations of a stationary time series has important links to the variance ratio methodology and trend stationary model. It is demonstrated that the proposed autoregressive model is asymptotically related to the variance ratio through the weighting schedules that these two tools use. It is also demonstrated that under a trend stationary time series process the proposed autoregressive model approaches a trend stationary model when the memory of the autoregressive model is increased. These links create a theoretical foundation for tests that confront the random walk model simultaneously against a trend stationary and a variety of short‐ and long‐memory autoregressive alternatives. Copyright © 2009 John Wiley & Sons, Ltd.