We consider both frequentist and empirical Bayes forecasts of a single time series using a linear model with T observations and K orthonormal predictors. The frequentist formulation considers estimators that are equivariant under permutations (reorderings) of the regressors. The empirical Bayes...

This paper considers forecasting a single time series using more predictors than there are time series observations. The approach is to construct a relatively few indexes, akin to diffusion indexes, which are weighted averages of the predictors, using an approximate dynamic factor model....

Many economic models imply that ratios, simple differences, or `spreads' of variables are I(0). In these models, cointegrating vectors are composed of 1's, 0's and -1's, and contain no unknown parameters. In this paper we develop tests for cointegration that can be applied when some of the...

An experiment is performed to assess the prevalence of instability in univariate and bivariate macroeconomic time series relations and to ascertain whether various adaptive forecasting techniques successfully handle any such instability. Formal tests for instability and out-of-sample forecasts...

This paper catalogs the business cycle properties of 163 monthly U.S. economic time series over the three decades from 1959 through 1988. Two general sets of summary statistics are reported. The first set measures the comovement of each individual time series with a reference series representing...

The Index of Coincident Economic Indicators, currently compiled by the U.S. Department of Commerce, is designed to measure the state of overall economic activity. The index is constructed as a weighted average of four key macroeconomic time series, where the weights are obtained using rules that...

Seasonal adjustment procedures attempt to estimate the sample realizations of an unobservable economic time series in the presence of both seasonal factors and irregular factors. In this paper we consider a factor which has not been considered explicitly in previous treatments of seasonal...

This paper investigates the nature and the presence of bubbles in financial markets. Are bubbles consistent with rationality? If they are, do they, like Ponzi games, require the presence of new players forever? Do they imply impossible events in finite time, such as negative prices? Do they need...

This paper uses a dynamic factor model for the quarterly changes in consumption goods' prices to separate them into three independent components: idiosyncratic relative-price changes, a low-dimensional index of aggregate relative-price changes, and an index of equiproportional changes in all...

These essays by Clive W. J. Granger span more than four decades and cover major topics in spectral analysis, seasonality, nonlinearity, methodology, and forecasting. The introduction by Eric Gysels, Norman R. Swanson and Mark W. Watson places the essays in context and demonstrates their enduring...