Direct and iterated multistep AR methods for difference stationary processes
AbstractThe paper focuses on the comparison of the direct and iterated AR predictors when Xt is a difference stationary process. In particular, it provides some useful results for comparing the efficiency of the two predictors and for extracting the trend from macroeconomic time series using the two methods. The main results are based on an encompassing representation for the two predictors which enables to derive their properties quite easily under a maintained model. The paper provides an analytic expression for the mean square forecast error of the two predictors and derives useful recursive formulae for computing the direct and iterated coefficients. From the empirical standpoint, we propose estimators of the AR coefficients based on the tapered Yule-Walker estimates; we also provide a test of equal forecast accuracy which is very simple to implement and whose critical values can be obtained with the bootstrap method. Since multistep prediction is tightly bound up with the estimation of the long run component in a time series, we turn to the role of the direct method for trend estimation and derive the corresponding multistep Beveridge-Nelson decomposition.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 10859.
Date of creation: 01 Oct 2008
Date of revision:
Beveridge-Nelson decomposition; Multistep estimation; Tapered Yule-Walker estimates; Forecast combination;
Other versions of this item:
- Proietti, Tommaso, 2011. "Direct and iterated multistep AR methods for difference stationary processes," International Journal of Forecasting, Elsevier, vol. 27(2), pages 266-280, April.
- Proietti, Tommaso, 2011. "Direct and iterated multistep AR methods for difference stationary processes," International Journal of Forecasting, Elsevier, vol. 27(2), pages 266-280.
- C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
- E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
- C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
- E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-10-07 (All new papers)
- NEP-ECM-2008-10-07 (Econometrics)
- NEP-ETS-2008-10-07 (Econometric Time Series)
- NEP-FOR-2008-10-07 (Forecasting)
- NEP-MAC-2008-10-07 (Macroeconomics)
- NEP-ORE-2008-10-07 (Operations Research)
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