Econometric Modelling and Forecasting

David F. Hendry

Economics Department, OxfordUniversity

Course outline

The course concerns the theory and practice of econometric modelling and forecasting in a non-stationary and evolving world, when the model and mechanism differ. The main model class is a vector autoregression in integrated-cointegrated variables leading to an equilibrium-correction system, but intermittently subject to structural breaks. The framework, its basic concepts and main implications are based on the theory of reduction. Only subsets of variables can be analyzed, so their data generation process is the target for modelling. Models with no losses on reduction are congruent; those that explain rival models are encompassing. The main reductions correspond to key econometrics concepts (causality, exogeneity, invariance, etc.), and are the null hypotheses of model-evaluation tests, sustained by a taxonomy of evaluation information.Congruent and encompassing sub-models can, therefore, be justified: how should they be selected?

A new approach to empirical model discovery extending general-to-specific (Gets) modelling is described. Gets mimics reduction by simplifying a congruent general model to a minimal dominant representation. The initial general model must allow for many variables, long lags, multiple breaks, possible data contamination, and non-linearities but all these extensions can be created automatically. However, the selection algorithm must be able to handle more variables than observations. Computer automation of selection algorithms has allowed operational studies of alternative strategies, and revealed high success rates for Autometrics. We consider its performance across different states of nature, highlighting the extent to which such model selection is efficient and non-distortionary. Embedding theory models; collinearity; impulse-indicator saturation (IIS) and its generalization to more candidate variables than observations; and tests for, and modelling of, non-linearity and exogeneity are described. Viable congruent and encompassing sub-models can be successfully selected. Nevertheless, forecasting is different.

When the processes being modelled are not time invariant, many of the famous theorems of economic forecasting no longer hold; rather their converses often do: e.g., non-causal devices may outperform causal. Six aspects of unpredictability in forecasting compound the four additional mistakes most likely in empirical models. A generalized taxonomy of forecast errors is developed, allowing for structural change in the forecast period, the model to be mis-specified over the sample period, and selected from sample evidence, the parameters of the model to be estimated (possibly inconsistently) from the data, which might be measured with error, the forecasts to commence from incorrect initial conditions, and innovation errors to cumulate over the forecast horizon. The taxonomy reveals the central role of unanticipated location shifts, and helps explain the outcomes of forecasting competitions, as well as the emphasis on IIS in model selection. Other potential sources of forecast failure seem less relevant. Regime-shift non-stationarity can be removed by co-breaking (the cancellation of breaks across linear combinations of variables). Corrections to reduce forecast-error biases (intercept and forecast-error corrections) help robustify forecasts in the face of location shifts. Forecast pooling and rapid updating are noted, but the recommended procedure is to difference the modelselected by Gets. Autometrics can also be used to improve the quality of estimates of forecast-origin data.

Computer sessions commence with introductions to OxMetrics and PcGiveas basic modelling tools, including cointegration and system procedures. Applications of Autometrics, Monte Carlo simulation using PcNaive, and empirical forecasting using PcGive all illustrate the theory.

Readings: Papers

Econometric Modelling

Campos, Julia, Neil R. Ericsson and David F. Hendry, 2005, “Editors' Introduction” to General to Specific Modeling (Cheltenham: Edward Elgar), pp. 1–81.

Hendry, David F., 2009, “The Methodology of Empirical Econometric Modeling: Applied Econometrics Through the Looking-Glass’’ Chapter 1 in Mills, T.C. and Patterson, K.D. (eds), Palgrave Handbook of Econometrics, Volume 2: Applied Econometrics. (Basingstoke: Palgrave MacMillan).

Hendry, David F. and Hans-Martin Krolzig, 2005, “The Properties of Automatic Gets Modelling,”Economic Journal, 115, C32–C61.

Hoover, Kevin D. and Steven J. Perez, 1999, “Data Mining Reconsidered: Encompassing and the General-to-Specific Approach to Specification Search,” Econometrics Journal, Vol. 2, pp. 167–91.

Doornik, Jurgen A., 2009,“Autometrics’’, in Castle, J.L. and Shephard, N. (eds), The Methodology and Practice of Econometrics. (Oxford: OxfordUniversity Press).

Castle, Jennifer L. and David F. Hendry, 2009,“Evaluating Automatic Model Selection”, Economics Department, Oxford.

Castle, Jennifer L., Jurgen A. Doornik and David F. Hendry, 2009,“Model Selection when there are Multiple Breaks”, Economics Department, Oxford.

Hendry, David F. and Grayham E. Mizon,, 2010, “Econometric Modelling of Changing Time Series”, Economics Department, Oxford.

Hendry, David F. and Carlos Santos, 2010, “An Automatic Test of Super Exogeneity”, Economics Department, Oxford.

Castle, Jennifer L. and David F. Hendry, 2010,“Automatic Selection for Non-linear Models”, Economics Department, Oxford.

Forecasting

Clements, Michael P. and David F. Hendry, 2003, “An Overview of Economic Forecasting,” in Companion to Economic Forecasting, ed. by Clements and Hendry (Oxford: Blackwells),pp.1–18.

Clements, Michael P. and David F. Hendry, 2005, “Overview to Information and Model Transformations in Economic Forecasting,” Oxford Bulletin of Economics and Statistics,67, 713–753.

Hendry, David F., 2006, “Robustifying Forecasts from Equilibrium-Correction Models”, Journal of Econometrics, 135, 399–426.

Castle, Jennifer L., and Fawcett, Nicholas W.P. and Hendry, David F., 2009, “Forecasting with Equilibrium-correctionModels during Structural Breaks”

Clements, Michael P. and David F. Hendry, 2010, “Forecasting from Mis-specified Models in the Presence of Unanticipated Location Shifts”

Castle, Jennifer L., and Fawcett, Nicholas W.P. and Hendry, David F., 2009, “Nowcasting is not just Contemporaneous Forecasting”, National Institute Economic Review, 210, 71–89

Readings: Books

Doornik, Jurgen A. and David F. Hendry 2007, Empirical Econometric Modelling using PcGiveI (London: Timberlake Consultants Press).

Hendry, David F. and Bent Nielsen, 2007, Econometric Modeling: A Likelihood Approach (Princeton, PrincetonUniversity Press).

Doornik, Jurgen A. and David F. Hendry, 2007, Interactive Monte Carlo Experimentation in Econometrics using PcNaive (London: Timberlake Consultants Press).

Hendry, David F. and Neil R. Ericsson, eds., 2001, Understanding Economic Forecasts (Cambridge, Massachusetts: MIT Press).

Clements, Michael P. and David F. Hendry, 1998, Forecasting Stationary Economic Time Series (Cambridge: CambridgeUniversity Press).

Clements, Michael P. and David F. Hendry 1999, Forecasting Non-Stationary Economic Time Series (Cambridge, Massachusetts: MIT Press).