We develop a framework to assess how successfully standard times eries models explain low-frequency variability of a data series. The low-frequency information is extracted by computing a finite number of weighted averages of the original data, where the weights are low-frequency trigonometric...

Long-run forecasts of economic variables play an important role in policy, planning, and portfolio decisions. We consider long-horizon forecasts of average growth of a scalar variable, assuming that first differences are second-order stationary. The main contribution is the construction of...

We develop a Bayesian latent factor model of the joint evolution of GDP per capita for 113 countries over the 118 years from 1900 to 2017. We find considerable heterogeneity in rates of convergence, including rates for some countries that are so slow that they might not converge (or diverge) in...

We develop inference methods about long-run comovement of two time series. The parameters of interest are defined in terms of population second-moments of lowfrequency trends computed from the data. These trends are similar to low-pass filtered data and are designed to extract variability...

Many questions in economics involve long-run or trend variation and covariation in time series. Yet, time series of typical lengths contain only limited information about this long-run variation. This paper suggests that long-run sample information can be isolated using a small number of...

We propose a Bayesian procedure for exploiting small, possibly long-lag linear predictability in the innovations of a finite order autoregression. We model the innovations as having a log-spectral density that is a continuous mean-zero Gaussian process of order 1/√T. This local embedding makes...

The average length of business cycle contractions in the United States fell from 20.5 months in the prewar period to 10.7 months in the postwar period. Similarly, the average length of business cycle expansions rose from 25.3 months in the prewar period to 49.9 months in the postwar period. This...

This paper develops a new procedure for assessing how well a given dynamic economic model describes a set of economic time series. To answer the question, the variables in the model are augmented with just enough error so that the model can exactly mimic the second moment properties of the...

This paper investigates forecasts of U.S. inflation at the 12-month horizon. The starting point is the conventional unemployment rate Phillips curve, which is examined in a simulated out of sample forecasting framework. Inflation forecasts produced by the Phillips curve generally have been more...

This paper examines two questions. The first is whether economic fluctuations-business cycles-are due to an accumulation of nall shocks or instead mostly to infrequent large shocks. The paper concludes that neither of these two extreme views accurately characterize fluctuations. The second...