Proietti, Tommaso (2009): The Multistep BeveridgeNelson Decomposition.

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Abstract
The BeveridgeNelson decomposition defines the trend component in terms of the eventual forecast function, as the value the series would take if it were on its longrun path. The paper introduces the multistep BeveridgeNelson decomposition, which arises when the forecast function is obtained by the direct autoregressive approach, which optimizes the predictive ability of the AR model at forecast horizons greater than one. We compare our proposal with the standard BeveridgeNelson decomposition, for which the forecast function is obtained by iterating the onestepahead predictions via the chain rule. We illustrate that the multistep BeveridgeNelson trend is more efficient than the standard one in the presence of model misspecification and we subsequently assess the predictive validity of the extracted transitory component with respect to future growth.
Item Type:  MPRA Paper 

Original Title:  The Multistep BeveridgeNelson Decomposition 
Language:  English 
Keywords:  Trend and Cycle; Forecasting; Filtering. 
Subjects:  E  Macroeconomics and Monetary Economics > E3  Prices, Business Fluctuations, and Cycles > E32  Business Fluctuations; Cycles E  Macroeconomics and Monetary Economics > E3  Prices, Business Fluctuations, and Cycles > E31  Price Level; Inflation; Deflation C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C52  Model Evaluation, Validation, and Selection C  Mathematical and Quantitative Methods > C2  Single Equation Models; Single Variables > C22  TimeSeries Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models 
Item ID:  15345 
Depositing User:  Tommaso Proietti 
Date Deposited:  23. May 2009 17:42 
Last Modified:  12. Feb 2013 21:49 
References:  Buhlmann, P. (1997). Sieve bootstrap for time series. Bernoulli, 3, 123–148. B¨uhlmann, P. (2002). Bootstraps for time series. Statistical Science, 17, 52–72. Bloomfield, P. (1976). Fourier Analysis of Time Series: An Introduction. New York: Wiley. Bondon, P. (2001). Recursive relations for multistep prediction of a stationary time series. Journal of Time Series Analysis, 22, 309–410. Brockwell, P.J. and Dahlhaus, P. (2003). Generalized LevinsonDurbin and Burg algorithms. Journal of Econometrics, 118, 129149. Brockwell, P.J., Dahlhaus, P. and Trinidade, A. (2005). Modified Burg algorithms for multivariate subset autoregression. Statistica Sinica, 15, 197213. Clements, M.P. and Hendry, D.F. (1996). Multistep estimation for forecasting. Oxford Bulletin of Economics and Statistics, 58, 657–684. Cogley, T. (2002), A simple adaptive measure of core inflation. Journal of Money Credit and Banking, 34, 94113. Chevillon, G. (2007). Direct multistep estimation and forecasting. Journal of Economic Surveys, 21, 746785. Cox, D.R. (1961). Prediction by exponentially weighted moving averages and related methods. Journal of the Royal Statistical Society, Series B, 23, 414–422. Dahlhaus, R. (1988). Small sample effects in time series analysis: a new asymptotic theory and a new estimate. Annals of Statistics, 16, 808841. Doornik, J.A. (2006), Ox. An ObjectOriented Matrix Programming Language, Timberlake Consultants Press, London. Findley, D.F. (1983). On the use of multiple models for multiperiod forecasting. Proceedings of Business and Economic Statistics, American Statistical Association, 528531. Granger, C. W. J. and Jeon, Y. (2006). Dynamics of model overfitting measured in terms of autoregressive roots. Journal of Time Series Analysis, 27, 347365. Granger, C.W. J. and Newbold, P. (1986). Forecasting Economic Time Series. Academic Press. Harvey, A.C. (1989), Forecasting, Structural Time Series and the Kalman Filter, Cambridge University Press, Cambridge, UK. Haywood, G. and Tunnicliffe Wilson, G. (1997), Fitting Time Series Models by Minimizing Multistepahead Errors: a Frequency Domain Approach, Journal of the Royal Statistical Society, Series B, 59, 237–254. Hodrick R.J., and Prescott, E.C. (1997). Postwar U.S. Business Cycles: an Empirical Investigation. Journal of Money, Credit and Banking, 29, 116. Hurvich, C.M. and Tsai C.L. (1997). Selection of a multistep linear predictor for short time series. Statistica Sinica, 7, 395–406. Ing, C.K. (2003). Multistep prediction in autoregressive processes. Econometric Theory, 19, 254279. Ing, C.K. (2004). Selecting optimal multistep predictors for autoregressive process of unknown order. Annals of Statistics, 32, 693722. Kang, H. (1987). The Tapering Estimation of the FirstOrder Autoregressive Parameters. Biometrika, 74, 643–645. Marcellino, M., Stock, J.H. and Watson, M. (2006). A comparison of direct and iterated multistep AR methods for forecasting microeconomic time series. Journal of Econometrics, 135, 499526. Morley, J., (2002), A statespace approach to calculating the BeveridgeNelson decomposition, Economics Letters 75, 123127. Morley, J., (2009), The Two Interpretations of the BeveridgeNelson Decomposition. Working paper, Department of Economics, Washington University. Morley, J.C., Nelson, C.R. and Zivot E. (2003), Why are the BeveridgeNelson and unobserved components decompositions of GDP so different? The Review of Economics and Statistics, 85, 235243. Nelson, C.R. (2008), The BeveridgeNelson decomposition in retrospect and prospect. Journal of Econometrics, 146, 202–206. Oh, K.H., E. Zivot, and Creal, D. (2008) The Relationship between the BeveridgeNelson decomposition and Unobserved Components Models with Correlated Shocks. Journal of Econometrics, 146, 207–219. Percival D., Walden A. (1993). Spectral Analysis for Physical Applications. Cambridge University Press. Priestley, M.B. (1981), Spectral Analysis and Time Series. London, Academic Press. Proietti, T. (1995). The BeveridgeNelson decomposition: Properties and extensions, Statistical Methods and Applications, 4, 101124. Proietti, T. (2006). Trendcycle decompositions with correlated components, Econometric Reviews, 25, 6184. Proietti, T., and Harvey, A.C. (2000). A Beveridge Nelson Smoother. Economics Letters, 67, 139–146. Shaman, P., and Stine, R.A. (1988). The Bias of Autoregressive Coefficient Estimators. Journal of the American Statistical Association, 83, 842–848. Shibata, R. (1980). Asymptotically efficient selection of the order of the model for estimating parameters of a linear process. Annals of Statistics, 8, 147164. Stock, J.H. and Watson, M. (2007). Why Has U.S. Inflation Become Harder to Forecast? Journal of Money, Credit and Banking, Supplement to Vol. 39, No. 1, 13–33. Tiao, G. C., and Xu, D. (1993). Robustness of Maximum Likelihood Estimates for MultiStep Predictions: The Exponential Smoothing Case. Biometrika, 80, 623–641. Tiao, G. C., and Tsay, R. S. (1994). Some advances in nonlinear and adaptive modelling in timeseries, Journal of Forecasting, 13, 109–131. Tjostheim, D. Paulsen J. (1983). Bias of some CommonlyUsed Time Series Estimates, Biometrika, 70, 389–399. Watson, M.W. (1986). Univariate detrending methods with stochastic trends. Journal of Monetary Economics, 18, 4975. Weiss, A.A. (1991). Multistep estimation and forecasting in dynamic models. Journal of Econometrics, 48, 135149. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/15345 