Proietti, Tommaso (2010): Trend Estimation.

PDF
MPRA_paper_21607.pdf Download (67kB)  Preview 
Abstract
Trend estimation deals with the characterization of the underlying, or long–run, evolution of a time series. Despite being a very pervasive theme in time series analysis since its inception, it still raises a lot of controversies. The difficulties, or better, the challenges, lie in the identification of the sources of the trend dynamics, and in the definition of the time horizon which defines the long run. The prevalent view in the literature considers the trend as a genuinely latent component, i.e. as the component of the evolution of a series that is persistent and cannot be ascribed to observable factors. As a matter of fact, the univariate approaches reviewed here assume that the trend is either a deterministic or random function of time.
Item Type:  MPRA Paper 

Original Title:  Trend Estimation 
Language:  English 
Keywords:  Time series models; unobserved components. 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C10  General C  Mathematical and Quantitative Methods > C2  Single Equation Models; Single Variables > C22  TimeSeries Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models 
Item ID:  21607 
Depositing User:  Tommaso Proietti 
Date Deposited:  25. Mar 2010 06:08 
Last Modified:  12. Feb 2013 21:40 
References:  Anderson, T.W. (1971), The Statistical Analysis of Time Series, Wiley, New York. Engle, R.F. and Granger, C.W.J. (1987). Cointegration and Error Correction: Representation, Estimation, and Testing. Econometrica, 55, 251–276. Forni, M., Hallin, M., Lippi, F., Reichlin L. (2000). The Generalized Dynamic Factor Model: Identification and Estimation. Review of Economics and Statistics 82, 540554. Green P.J. and Silverman, B.V. (1994) Nonparametric Regression and Generalized Linear Models: a Roughness Penalty Approach. Chapman & Hall, London. Harvey, A.C. (1989). Forecasting, Structural Time Series and the Kalman Filter, Cambridge University Press, Cambridge, UK. Henderson, R. (1916). Note on Graduation by Adjusted Average, Transaction of the Actuarial Society of America, 17, 4348. Hillmer, S.C. and Tiao G.C. (1982) An ARIMAmodelbased approach to seasonal adjustment. Journal of the American Statistical Association, 77, 6370. Hodrick, R., and Prescott, E.C. (1997). Postwar U.S. Business Cycle: an Empirical Investigation, Journal of Money, Credit and Banking, 29, 1, 116. Kendall M., Stuart, A., and Ord, J.K. (1983). The Advanced Theory of Statistics, Vol 3. C. Griffin. Leser, C.E.V. (1961). A Simple Method of Trend Construction, Journal of the Royal Statistical Society B, 23, 91107. Loader, C. (1999). Local regression and likelihood. SpringerVerlag, New York Nelson, C.R., and Plosser, C.I. (1982). Trends and random walks in macroeconomic time series: some evidence and implications. Journal of Monetary Economics, 10, 13962. Percival D., Walden A. (1993). Spectral Analysis for Physical Applications. Cambridge University Press. Poirier, D.J. (1973). Piecewise regression using cubic splines, Journal of American Statistical Association, 68, 515524. Rasmussen, C.E. and Williams, C.K.I. (2006). Gaussian Processes for Machine Learning. The MIT Press. Ruppert D., Wand, M.J. and Carroll R.J. (2003). Semiparametric regression, Cambridge University Press. Stock, J. H. and Watson, M.W. (2002b). Forecasting using principal components from a large number of predictors. Journal of the American Statistical Association, 97 11671179. Watson, G.S. (1964). Smooth regression analysis, Shankya Series A, 26, 359372. Wecker, W.E., and Ansley, C.F. (1983). The signal extraction approach to nonlinear regression and spline smoothing. Journal of the American Statistical Association, 78, 8189. Whittaker, E. (1923). On new method of graduation. Proceedings of the Edinburgh Mathematical Society, 41, 63–75. Whittle P. (1983) Prediction and Regulation by Linear Least Squares Methods, Second edition. Basil Blackwell, Oxford. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/21607 