`Weak` trends for inference and forecasting in finite samples
AbstractThis paper studies the small sample properties of processes which exhibit both a stochastic and a deterministic trend. Whereas for estimation, inference and forecasting purposes the latter asymptotically dominates the former, it is not so when only a finite number of observations is available and large non-linearities in the parameters of the process result. To analyze this dependence, we resort to local-asymptotics and present the concept of a `weak` trend whose coefficient is of order O(T-1/2), so that the deterministic trend is O(T1/2) and the process Op(T1/2). In this framework, parameter estimates, unit-root test statistics and forecast errors are functions of `drifting` Ornstein-Uhlenbeck processes. We derive a comparison of direct and iterated multi-step estimation and forecasting of a - potentially misspecified - random walk with drift, and show that we explain well the non-linearities exhibited in finite samples. Another main benefit of direct multi-step estimation stems from some different behaviors of the `multi-step` unit-root and slope tests under the weak and strong (constant coefficient) trend frameworks which could lead to testing which framework is more relevant. A Monte Carlo analysis validates the local-asymptotics approximation to the distributions of finite sample biases and test statistics.
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Bibliographic InfoPaper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 210.
Date of creation: 01 Dec 2004
Date of revision:
Stochastic Trend; Deterministic Trend; Local Asymptotics; Multi-step Forecasting;
Other versions of this item:
- Guillaume Chevillon, 2004. ""Weak" trends for inference and forecasting in finite samples," Documents de Travail de l'OFCE 2004-12, Observatoire Francais des Conjonctures Economiques (OFCE).
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
- C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
- C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
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- Banerjee, A & Hendry, D-F & Mizon, G-E, 1996.
"The Econometric Analysis of Economic Policy,"
Economics Working Papers
eco96/34, European University Institute.
- Diebold & Senhadji, .
"Deterministic vs. Stochastic Trend in U.S. GNP, Yet Again,"
_054, University of Pennsylvania.
- Francis X. Diebold & Abdelhak S. Senhadji, 1996. "Deterministic vs. Stochastic Trend in U.S. GNP, Yet Again," NBER Working Papers 5481, National Bureau of Economic Research, Inc.
- Peter C.B. Phillips, 2004.
"Challenges of Trending Time Series Econometrics,"
Cowles Foundation Discussion Papers
1472, Cowles Foundation for Research in Economics, Yale University.
- Peter C. B. Phillips, 1998. "New Tools for Understanding Spurious Regressions," Econometrica, Econometric Society, vol. 66(6), pages 1299-1326, November.
- Phillips, Peter C B, 1988.
"Regression Theory for Near-Integrated Time Series,"
Econometric Society, vol. 56(5), pages 1021-43, September.
- Chevillon, Guillaume & Hendry, David F., 2005.
"Non-parametric direct multi-step estimation for forecasting economic processes,"
International Journal of Forecasting,
Elsevier, vol. 21(2), pages 201-218.
- Guillaume Chevillon & David F. Hendry, 2004. "Non-Parametric Direct Multi-step Estimation for Forecasting Economic Processes," Economics Papers 2004-W12, Economics Group, Nuffield College, University of Oxford.
- David Hendry & Guillaume Chevillon, 2004. "Non-Parametric Direct Multi-step Estimation for Forecasting Economic Processes," Economics Series Working Papers 196, University of Oxford, Department of Economics.
- Phillips, P C B, 1987.
"Time Series Regression with a Unit Root,"
Econometric Society, vol. 55(2), pages 277-301, March.
- Peter C.B. Phillips, 1985. "Time Series Regression with a Unit Root," Cowles Foundation Discussion Papers 740R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1986.
- Tom Doan, . "PPUNIT: RATS procedure to perform Phillips-Perron Unit Root test," Statistical Software Components RTS00160, Boston College Department of Economics.
- Douglas Staiger & James H. Stock, 1994.
"Instrumental Variables Regression with Weak Instruments,"
NBER Technical Working Papers
0151, National Bureau of Economic Research, Inc.
- Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
- Sampson, Michael, 1991. "The Effect of Parameter Uncertainty on Forecast Variances and Confidence Intervals for Unit Root and Trend Stationary Time-Series Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(1), pages 67-76, Jan.-Marc.
- Clements, M.P. & Hendry, D.P., 1998.
"Forecasting with Difference-Stationary and Trend-Stationary Models,"
The Warwick Economics Research Paper Series (TWERPS)
516, University of Warwick, Department of Economics.
- Michael P. Clements & David F.Hendry, 2001. "Forecasting with difference-stationary and trend-stationary models," Econometrics Journal, Royal Economic Society, vol. 4(1), pages S1-S19.
- David Hendry & Michael P. Clements, 2000. "Forecasting with Difference-Stationary and Trend-Stationary Models," Economics Series Working Papers 5, University of Oxford, Department of Economics.
- Kemp, Gordon C.R., 1999. "The Behavior Of Forecast Errors From A Nearly Integrated Ar(1) Model As Both Sample Size And Forecast Horizon Become Large," Econometric Theory, Cambridge University Press, vol. 15(02), pages 238-256, April.
- Guillaume Chevillon, 2004.
"A Comparison of Multi-step GDP Forecasts for South Africa,"
Economics Series Working Papers
212, University of Oxford, Department of Economics.
- Guillaume Chevillon, 2004. "A Comparison of Multi-step GDP Forecasts for South Africa," Documents de Travail de l'OFCE 2004-13, Observatoire Francais des Conjonctures Economiques (OFCE).
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