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Direct and iterated multistep AR methods for difference stationary processes

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  • Proietti, Tommaso

Abstract

The paper focuses on a comparison between the direct and iterated AR predictors for difference stationary processes. In particular, it provides new methods for comparing the efficiency of the two predictors. The methods are based on an encompassing representation for the two predictors, which enables us to derive their properties quite easily under a maintained model. The paper provides an analytical expression for the mean square forecast error of the two predictors and derives useful recursive formulae for computing the direct and iterated coefficients. From an 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 are obtained using the bootstrap method.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:intfor:v:27:y::i:2:p:266-280
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    Cited by:

    1. Braione, Manuela, 2016. "A time-varying long run HEAVY model," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 36-44.
    2. Chevillon, Guillaume, 2016. "Multistep forecasting in the presence of location shifts," International Journal of Forecasting, Elsevier, vol. 32(1), pages 121-137.
    3. Chevillon, Guillaume, 2009. "Multi-step forecasting in emerging economies: An investigation of the South African GDP," International Journal of Forecasting, Elsevier, vol. 25(3), pages 602-628, July.
    4. McElroy, Tucker & Wildi, Marc, 2013. "Multi-step-ahead estimation of time series models," International Journal of Forecasting, Elsevier, vol. 29(3), pages 378-394.
    5. Pablo M. Pincheira & Carlos A. Medel, 2015. "Forecasting Inflation with a Simple and Accurate Benchmark: The Case of the US and a Set of Inflation Targeting Countries," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 65(1), pages 2-29, January.

    More about this item

    Keywords

    Multistep estimation Tapered Yule-Walker estimates Forecast evaluation;

    JEL classification:

    • 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; Diffusion Processes

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