Cointegration Analysis: An International Enterprise..

Cointegration analysis is truly an international enterprise, with researchers from most continents and major countries participating. You will, of course, recognize that the very word is Danish, in the same sense as menu is English. The history of the concept and related notions, as this is central to understanding its present position in the econometrician’s toolkit is recalled. Then the idea is illustrated with an example of how we conceive of cointegration in the context of an issue such as inflation, which has been the centre of much economic policy and even more theoretical and empirical analysis.

Unpredictability and the Foundations of Economic Forecasting

We revisit the concept of unpredictability to explore its implications for forecasting strategies in a non-stationary world subject to structural breaks, where model and mechanism differ. Six aspects of the role of unpredictability are distinguished, compounding the four additional mistakes most likely in estimated forecasting models. Structural breaks, rather than limited information, are the key problem, exacerbated by conflicting requirements on forecast-error corrections. We consider model transformations and corrections to reduce forecast-error biases, as usual at some cost in increased forecast-error variances. The analysis is illustrated by an empirical application to M1 in the UK.

Robustifying Forecasts from Equilibrium-Correction Models

In a non-stationary world subject to structural breaks, where model and mechanism differ, equilibrium-correction models are a risky device from which to forecast. Equilibrium shifts entail systematic forecast failure, and indeed forecasts will tend to move in the opposite direction to the data. A new explanation for the empirical success of second differencing is proposed. We consider model transformations based on additional differencing to reduce forecast-error biases, as usual at some cost in increased forecast-error variances. The analysis is illustrated by an empirical application to narrow money holdings in the UK.

Economic forecasting in a changing world

This article explains the basis for a theory of economic forecasting developed over the past decade by the authors. The research has resulted in numerous articles in academic journals, two monographs, Forecasting Economic Time Series, 1998, Cambridge University Press, and Forecasting Nonstationary Economic Time Series, 1999, MIT Press, and three edited volumes, Understanding Economic Forecasts, 2001, MIT Press, A Companion to Economic Forecasting, 2002, Blackwells, and the Oxford Bulletin of Economics and Statistics, 2005. The aim here is to provide an accessible, non-technical, account of the main ideas. The interested reader is referred to the monographs for derivations, simulation evidence, and further empirical illustrations, which in turn reference the original articles and related material, and provide bibliographic perspective

Non-Parametric Direct Multi-step Estimation for Forecasting Economic Processes

We evaluate the asymptotic and finite-sample properties of direct multi-step estimation (DMS) for forecasting at several horizons. For forecast accuracy gains from DMS in finite samples, mis-specification and non-stationarity of the DGP are necessary, but when a model is well-specified, iterating the one-step ahead forecasts may not be asymptotically preferable. If a model is mis-specified for a non-stationary DGP, omitting either negative residual serial correlation or regime shifts, DMS can forecast more accurately. Monte Carlo simulations clarify the non-linear dependence of the estimation and forecast biases on the parameters of the DGP, and explain existing results.Adaptive estimation, multi-step estimation, dynamic forecasts, model mis-specification.

Combining disaggregate forecasts or combining disaggregate information to forecast an aggregate

To forecast an aggregate, we propose adding disaggregate variables, instead of combining forecasts of those disaggregates or forecasting by a univariate aggregate model. New analytical results show the effects of changing coefficients, mis-specification, estimation uncertainty and mis-measurement error. Forecastorigin shifts in parameters affect absolute, but not relative, forecast accuracies; mis-specification and estimation uncertainty induce forecast-error differences, which variable-selection procedures or dimension reductions can mitigate. In Monte Carlo simulations, different stochastic structures and interdependencies between disaggregates imply that including disaggregate information in the aggregate model improves forecast accuracy. Our theoretical predictions and simulations are corroborated when forecasting aggregate US inflation pre- and post 1984 using disaggregate sectoral data. JEL Classification: C51, C53, E31Aggregate forecasts, Disaggregate information, forecast combination, inflation

The Properties of Model Selection when Retaining Theory Variables

Economic theories are often fitted directly to data to avoid possible model selection biases. We show that embedding a theory model that specifies the correct set of m relevant exogenous variables, x{t}, within the larger set of m+k candidate variables, (x{t},w{t}), then selection over the second set by their statistical significance can be undertaken without affecting the estimator distribution of the theory parameters. This strategy returns the theory-parameter estimates when the theory is correct, yet protects against the theory being under-specified because some w{t} are relevant.Model selection, theory retention

Forecasting economic aggregates by disaggregates

We suggest an alternative use of disaggregate information to forecast the aggregate variable of interest, that is to include disaggregate information or disaggregate variables in the aggregate model as opposed to first forecasting the disaggregate variables separately and then aggregating those forecasts or, alternatively, using only lagged aggregate information in forecasting the aggregate. We show theoretically that the first method of forecasting the aggregate should outperform the alternative methods in population. We investigate whether this theoretical prediction can explain our empirical findings and analyse why forecasting the aggregate using information on its disaggregate components improves forecast accuracy of the aggregate forecast of euro area and US inflation in some situations, but not in others. JEL Classification: C51, C53, E31Disaggregate information, Factor models, forecast model selection, Predictability, VAR

Regression Models with Data-based Indicator Variables

OLS estimation of an impulse-indicator coefficient is inconsistent, but its variance can be consistently estimated. Although the ratio of the inconsistent estimator to its standard error has a tdistribution, that test is inconsistent: one solution is to form an index of indicators. We provide Monte Carlo evidence that including a plethora of indicators need not distort model selection, permitting the use of many dummies in a general-to-specific framework. Although White’s (1980) heteroskedasticity test is incorrectly sized in that context, we suggest an improvement. Finally, a possible modification to impulse ‘intercept corrections’ is considered.