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Econometrics
Financial Economics
Applied Econometrics

Econometrics
Financial Economics
Applied Econometrics

2004 (Oral) Econometrics and Industrial Organization
2003(Written) Microeconomics and Macroeconomic Theory

Economic Forecasting With End of Sample Tests

Professor Peter C.B. Phillips
Professor Donald W.K. Andrews
Professor Ray C. Fair

May 2006

Ph.D., Economics, Yale University, expected May 2006
M.Phil., Department of Economics, Yale University, May 2005
M.A., Department of Economics, Yale University, December 2003
Bachelor of Economics (Hons) University of New South Wales, October 2002
Bachelor of Laws (Equivalent to a J.D.) University of New South Wales, October 2002

Fulbright Scholarship 2002
Yale University Graduate Fellowship, 2002–2006
Cowles Foundation Award, 2002–2006
Cowles Summer Prize, 2005
University Medal in Economics, University of New South Wales, 2002
Economics Society of Australia — NSW Branch for first place in the Honors Class, 2000
Statistical Society of NSW Branch Award, 2000

Yale University
  Instructor
     Introduction to Finance, Summer 2005
  Teaching Assistant
     Financial Markets, Fall 2004
     Financial theory, Spring, 2005
  Math and Science Tutor — Yale College, September 2005–Present

University of New South Wales
  Teaching Assistant
     Quantitative Methods A, 2000–2002
     Quantitative Methods B, 2000–2001

Independent Pricing and Regulatory Tribunal (IPART), Sydney, Australia 1999–2001 (Part time)
   Whilst at IPART, I worked on projects helping to determine the regulated tariffs for gas, as well as cross industry projects, including transfer pricing, option pricing and demand management.
Blake Dawson Waldron Lawyers, Sydney, Australia 2001–2002 (Part Time)
   I worked in both the antitrust and tax divisions of the firm.

Mentor for Hillhouse Scholar program 2004–2005

Professor Peter C.B. Phillips
Department of Economics
Yale University
PO Box 208281
New Haven, CT 06520-8281
Phone: (203) 432-3695
Fax: (203) 432-6167
E-mail: peter.phillips@yale.edu

Professor Ray C. Fair
Department of Economics
Yale University
PO Box 208281
New Haven, CT 06520-8281
Phone: (203) 432-3695
Fax: (203) 432-6167
E-mail: ray.fair@yale.edu

This dissertation looks at ways to improve forecasting performance, focusing on the effects of changes in the mean at the end of the sample. For long-term forecasting, the forecasts from a simple autoregressive (AR) model tend towards the long-run mean as the forecast horizon increases. It is therefore important to estimate this parameter accurately. In doing so, it becomes relevant to be able to distinguish between mere random disturbances as opposed to shifts in the underlying series. This dissertation determines a way to test for shifts in specific parameters of a model, and then uses this information to improve forecasting performance. The first two chapters outline this new end of sample testing procedure, the Two-Step Test, and look at its application to forecasting in autoregressive models. The last chapter extends this new testing method to vector autoregressive (VAR) models and vector error correction models (VECM). The Two Step Test is the first test which can detect changes in specific parameters at the end of the sample and detect changes in the cointegrating means directly.

I. A two-step procedure for testing specific parameter changes at the end of a sample

When using AR models, forecasts tend towards the long-run mean of the series. To best estimate this model, observed changes near the end of sample need to be characterized as changes in the underlying mean or as random disturbances under some form of structural break model. Most structural break tests assume a large number of observations, but in end-of-sample testing, there are only a limited number of observations available. Andrews (2003) developed an end-of-sample test that looks for any changes in the series. If it is assumed ex ante that changes are discernable through the mean, then the Andrews test is applicable. However, this assumption is too strong. The Two Step Test is developed to detect changes in specific parameters of the model by means of an additional step. Critical values of the test are determined using the Andrews subsampling method. When applied to a simple AR (1) model, the Two-Step Test performs well in detecting changes and is robust to changes in the other parameters.

The mean of an AR model is a nonlinear combination of all the coefficients, and a transformation proposed by Bewley (1979) allows for the direct estimation of the mean via the intercept in the transformed model. The two-step testing procedure is applied to the Bewley transformed model to test for changes in the long-run mean. Again, the Two-Step Test is found to perform well in detecting changes in the mean. The use of this new test is not restricted to testing for changes in the mean for forecasting but also has wide policy applications. It would be a useful tool in governmental strategic planning and policy development because it will allow for more accurate predictions of future macroeconomic variables. This would be particularly relevant for inflation targeting.

II. Mean correction using end-of-sample testing

The second chapter in this dissertation uses the two-step procedure outlined above to improve forecast performance. As forecasts tend towards the long run mean, the mean needs to be estimated accurately to ensure precision in forecasting. The two-step procedure applied to a Bewley transformed model can test for changes in the long run mean. If changes are observed, this information can be incorporated to improve forecasts. Clements and Hendry (1996, 1998) posit that shifts in the deterministic factors can have significant effects on the forecasts, and propose using intercept corrections to place the forecasts "back on track". This method only works well if there have been shifts in the intercept. This paper proposes a new mean correction method which pre tests the end of sample for changes in the mean and adjusts the model by the estimate of the change in mean, if the pre test is rejected. The problems faced by Clements and Hendry are thus avoided. In simulations, it provides smaller mean squared forecast errors compared to the intercept correction method. This method is then applied to macroeconomic data to look at the performance of the forecasts in a practical application.

The first two chapters contribute to the current literature by providing the first end of sample test that can look for changes in specific parameters of the model. This will be useful not only in forecasting applications, but also in general policy work where it is particularly important to know if specific parameters have changed. The mean correction approach improves on the current literature by providing a better solution (in terms of mean squared error) to the problem of deterministic shifts in data.

III. End-of-sample testing and forecasting in VAR and VEC models

The third chapter extends the results from the above two papers to the VAR and VEC models. The extension to the VAR model is a straight forward extension of the AR model to a system of equations. With a system of equations, it becomes even more important to be able to detect and correct for changes in each specific series, as now, the mean is a nonlinear combination of all the parameters in the model. The Two Step method allows for the detection of a particular series within the VAR. It then corrects that series only, thereby eliminating the contamination that would result from just correcting one of the parameters in the VAR model.

Direct application of the above approach to the VECM will not work to distinguish between breaks in the cointegrating means and the means of the common trends. In order to get a direct estimation of the means, the model is written in triangular form. The Bewley transformation is then applied to this triangular representation, thus enabling the direct estimation of the cointegrating and common trend means. The Two-Step Test was applied to this newly transformed model, and if a break is found, the mean correction method is used to correct the forecasts. This test is again invariant to changes in the other parameters of the model, and when combined with the mean correction method, it improves forecasting performance.

The Two-Step Test is the first test that can directly detect changes in the mean of the cointegrating equations and common trends in VECMs. It also provides a complete methodology on how to adjust the forecasts when these shifts arise.