Cointegration And Long Horizon Forecasting

Imposing cointegration on a forecasting system, if cointegration is present, is believed to improve long-horizon forecasts. Contrary to this belief, at long horizons nothing is lost by ignoring cointegration when the forecasts are evaluated using standard multivariate forecast accuracy measures. In fact, simple univariate Box-Jenkins forecasts are just as accurate. Our results highlight a potentially important deficiency of standard forecast accuracy measures—they fail to value the maintenance of cointegrating relationships among variables—and we suggest alternatives that explicitly do so.

Imposing cointegration on a forecasting system, if cointegration is present, is believed to improve long-horizon forecasts. Contrary to this belief, at long horizons nothing is lost by ignoring cointegration when the forecasts are evaluated using standard mutivariate forecast accuracy measures. In fact, simple univariate Box-Jenkins forecasts are just as accurate. Our results highlight a potentially important deficiency of standard forecast accuracy measures-they fail to value the maintenance of cointegrating relationships among variables-and we suggest alternatives tht explicitly do so.

Exchange rate forecasts are generated using some popular monetary models of exchange rates in conjunction with several estimation techniques. We propose an alternative set of criteria for evaluating forecast rationality which entails the following requirements: the forecast and the actual series i) have the same order of integration, ii) are cointegrated, and iii) have a cointegrating vector consistent with long run unitary elasticity of expectations. When these conditions hold, we consider the forecasts to be consistent.' We find that it is fairly easy for the generated forecasts to pass the first requirement. However, according to the Johansen procedure, cointegration fails to hold the farther out the forecasts extend. At the one year ahead horizon, most series and their respective forecasts do not appear cointegrated. Of the cointegrated pairs, the restriction of unitary elasticity of forecasts with respect to actual appears not to be rejected in general. The exception to this pattern is in the case of the error correction models in the longer subsample. Using the Horvath-Watson procedure, which imposes a unitary coefficient restriction, we find fewer instances of consistency, but a relatively higher proportion of the identified cases of consistency are found at the longer horizons.

A collection of essays in honour of Clive Granger. The chapters are by some of the world's leading econometricians, all of whom have collaborated with and/or studied with both) Clive Granger. Central themes of Granger's work are reflected in the book with attention to tests for unit roots and cointegration, tests of misspecification, forecasting models and forecast evaluation, non-linear and non-parametric econometric techniques, and overall, a careful blend of practical empirical work and strong theory. The book shows the scope of Granger's research and the range of the profession that has been influenced by his work.

This book provides a formal analysis of the models, procedures, and measures of economic forecasting with a view to improving forecasting practice. David Hendry and Michael Clements base the analyses on assumptions pertinent to the economies to be forecast, viz. a non-constant, evolving economic system, and econometric models whose form and structure are unknown a priori. The authors find that conclusions which can be established formally for constant-parameter stationary processes and correctly-specified models often do not hold when unrealistic assumptions are relaxed. Despite the difficulty of proceeding formally when models are mis-specified in unknown ways for non-stationary processes that are subject to structural breaks, Hendry and Clements show that significant insights can be gleaned. For example, a formal taxonomy of forecasting errors can be developed, the role of causal information clarified, intercept corrections re-established as a method for achieving robustness against forms of structural change, and measures of forecast accuracy re-interpreted.

Forecasting in the presence of structural breaks and model uncertainty are active areas of research with implications for practical problems in forecasting. This book addresses forecasting variables from both Macroeconomics and Finance, and considers various methods of dealing with model instability and model uncertainty when forming forecasts.

This Handbook provides up-to-date coverage of both new and well-established fields in the sphere of economic forecasting. The chapters are written by world experts in their respective fields, and provide authoritative yet accessible accounts of the key concepts, subject matter, and techniques in a number of diverse but related areas. It covers the ways in which the availability of ever more plentiful data and computational power have been used in forecasting, in terms of the frequency of observations, the number of variables, and the use of multiple data vintages. Greater data availability has been coupled with developments in statistical theory and economic analysis to allow more elaborate and complicated models to be entertained; the volume provides explanations and critiques of these developments. These include factor models, DSGE models, restricted vector autoregressions, and non-linear models, as well as models for handling data observed at mixed frequencies, high-frequency data, multiple data vintages, methods for forecasting when there are structural breaks, and how breaks might be forecast. Also covered are areas which are less commonly associated with economic forecasting, such as climate change, health economics, long-horizon growth forecasting, and political elections. Econometric forecasting has important contributions to make in these areas along with how their developments inform the mainstream.

If foreign exchange market participants form rational forecasts of future exchange rates, we should expect that these forecasts should be closely matched to subsequent realizations. Specifically, rational forecasts of a time series and the observed series itself should be cointegrated. In this paper, we apply this insight to multiple exchange rate series and a corresponding set of market expectations of future values of the exchange rate series. We build a cointegration (and associated error-correction) model of actual and expected exchange rates for five exchange rates against the U.S. Dollar, using weekly expectations data from Money Market Services, International for the 1986 - 1997 period. Our empirical work produces very strong evidence of cointegration between the exchange rate series and the expected rates series. We find strong evidence that existing work that ignores the impact of error-correction is significantly misspecified. At the shortest forecast horizon, the error-correction term dominates all other determinants of changes in expected exchange rates in our sample and indicates a sensible response by market participants to past mistakes in forecasting future rates. At longer forecast horizons, error-correction remains very important, but lagged changes in actual and expected rates also play a role. We find limited evidence of threshold effects in our error-correction models.

Several authors have recently investigated the predictability of exchange rates by fitting a sequence of long-horizon error-correction regressions. By considering the implied vector error-correction model, we show that little is to be gained from estimating such regressions for horizons greater than one time period. We also show that in small to medium samples the long-horizon procedure gives rise to spurious evidence of predictive power. A simulation study demonstrates that even when using this technique on two independent series, estimates, diagnostic statistics and graphical evidence incorrectly suggest a high degree of predictability of the dependent variable.