Mr. Francis X. Diebold and Mr. Peter F. Christoffersen
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.
For the past quarter century, Switzerland’s real per capita growth rate has been substantially slower than in most other industrial countries. Unemployment has declined rapidly to 2.4 percent of the labor force in November 1999 from its 1997 peak of more than 5 percent. Inflation has edged up from exceptionally low levels. Switzerland’s longstanding current account surplus was above 9 percent of gross domestic product in 1998 and is estimated to have risen further in 1999. The franc has shadowed the euro closely since January 1999, fluctuating narrowly around 1.6 Sw F/euro.
This paper introduces methods that allow analysts to (i) decompose the estimates of unobserved quantities into observed data, (ii) to better understand revision properties of the model, and (iii) to impose subjective prior constraints on path estimates of unobserved shocks in structural economic models. For instance, a decomposition of the flexible-price output gap, or a technology shock, into contributions of output, inflation, interest rates, and other observed variables' contribution is feasible. The intuitive nature and analytical clarity of the suggested procedures are appealing for policy-related and forecasting models.
The paper proposes an algorithm that uses forecast encompassing tests for combining forecasts. The algorithm excludes a forecast from the combination if it is encompassed by another forecast. To assess the usefulness of this approach, an extensive empirical analysis is undertaken using a U.S. macroecoomic data set. The results are encouraging as the algorithm forecasts outperform benchmark model forecasts, in a mean square error (MSE) sense, in a majority of cases.
We use Bayesian estimation techniques to investigate whether money growth Granger-causes inflation in the United States. We test for Granger-causality out-of-sample and find, perhaps surprisingly given recent theoretical arguments, that including money growth in simple VAR models of inflation does systematically improve out-of-sample forecasting accuracy. This holds for a long forecasting sample 1960-2005, as well for more recent subperiods, including the Volcker and Greenspan eras. However, the contribution of money to inflation forecasting accuracy is quantitatively limited and tends to be smaller in recent subperiods, in particular in models that also include information on real GDP growth and interest rates.