Proietti, Tommaso (2008): Direct and iterated multistep AR methods for difference stationary processes.
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Abstract
The 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 YuleWalker 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 BeveridgeNelson decomposition.
Item Type:  MPRA Paper 

Original Title:  Direct and iterated multistep AR methods for difference stationary processes 
Language:  English 
Keywords:  BeveridgeNelson decomposition; Multistep estimation; Tapered YuleWalker estimates; Forecast combination 
Subjects:  C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C51  Model Construction and Estimation E  Macroeconomics and Monetary Economics > E3  Prices, Business Fluctuations, and Cycles > E32  Business Fluctuations ; Cycles C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C53  Forecasting and Prediction Methods ; Simulation Methods E  Macroeconomics and Monetary Economics > E3  Prices, Business Fluctuations, and Cycles > E31  Price Level ; Inflation ; Deflation C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables > C22  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes 
Item ID:  10859 
Depositing User:  Tommaso Proietti 
Date Deposited:  01. Oct 2008 08:41 
Last Modified:  16. Feb 2013 08:08 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/10859 
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