We develop a framework to assess how successfully standard time series 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 series. The properties of these weighted averages are then compared to the asymptotic implications of a number of common time series models. We apply the framework to twenty U.S. macroeconomic and financial time series using frequencies lower than the business cycle.

Are asset prices useful predictors of inflation and real output growth? After reviewing the large literature on this topic, we undertake an empirical analysis of quarterly data for seven OECD countries spanning 1959-99. The literature review and the empirical analysis yield the same conclusions. Some asset prices predict inflation or output growth in some countries in some periods. Which series predicts what, when, and where is difficult to predict; being a good predictor historically is largely unrelated to subsequent performance. Intriguingly, forecasts that combine these individually unstable forecasts appear to improve reliably upon univariate benchmarks.

This paper studies the problems of estimation and inference in the linear trend model yt = α + βt + ut, where ut follows an autoregressive process with largest root ρ and β is the parameter of interest. We contrast asymptotic results for the cases | ρ | < 1 and ρ = 1 and argue that the most useful asymptotic approximations obtain from modeling ρ as local to unity. Asymptotic distributions are derived for the OLS, first-difference, infeasible GLS, and three feasible GLS estimators. These distributions depend on the local-to-unity parameter and a parameter that governs the variance of the initial error term κ. The feasible Cochrane–Orcutt estimator has poor properties, and the feasible Prais–Winsten estimator is the preferred estimator unless the researcher has sharp a priori knowledge about ρ and κ. The paper develops methods for constructing confidence intervals for β that account for uncertainty in ρ and κ. We use these results to estimate growth rates for real per-capita GDP in 128 countries.

Long-run forecasts of economic variables play an important role in policy, planning, and portfolio decisions. We consider forecasts of the long-horizon average of a scalar variable, typically the growth rate of an economic variable. The main contribution is the construction of prediction sets with asymptotic coverage over a wide range of data generating processes, allowing for stochastically trending mean growth, slow mean reversion, and other types of long-run dependencies. We illustrate the method by computing prediction sets for 10- to 75-year average growth rates of U.S. real per capita GDP and consumption, productivity, price level, stock prices, and population.

This paper proposes a model for, and investigates the consequences of, strong spatial dependence in economic variables. Our findings echo those of the corresponding “unit root” time series literature: Spatial unit root processes induce spuriously significant regression results, even with clustered standard errors or spatial HAC corrections. We develop large‐sample valid unit root and stationarity tests that can detect such strong spatial dependence. Finally, we use simulations to study strategies for valid inference in regressions with persistent spatial data, such as spatial analogues of first‐differencing transformations. Regressions from Chetty, Hendren, Kline, and Saez (2014) are used to illustrate the issues and methods.

We propose a method for constructing confidence intervals that account for many forms of spatial correlation. The interval has the familiar “estimator plus and minus a standard error times a critical value” form, but we propose new methods for constructing the standard error and the critical value. The standard error is constructed using population principal components from a given “worst‐case” spatial correlation model. The critical value is chosen to ensure coverage in a benchmark parametric model for the spatial correlations. The method is shown to control coverage in finite sample Gaussian settings in a restricted but nonparametric class of models and in large samples whenever the spatial correlation is weak, that is, with average pairwise correlations that vanish as the sample size gets large. We also provide results on the efficiency of the method.

Efficient estimators of cointegrating vectors are presented for systems involving deterministic components and variables of differing, higher orders of integration. The estimators are computed using GLS or OLS, and Wald Statistics constructed from these estimators have asymptotic x2 distributions. These and previously proposed estimators of cointegrating vectors are used to study long-run U.S. money (Ml) demand. Ml demand is found to be stable over 1900-1989; the 95% confidence intervals for the income elasticity and interest rate semielasticity are (.88,1.06) and (-.13, -.08), respectively. Estimates based on the postwar data alone, however, are unstable, with variances which indicate substantial sampling uncertainty.

Standard extreme value theory implies that the distribution of the largest observations of a large cross section is well approximated by a parametric model, governed by a location, scale and shape parameter. The extremes of a panel of independent cross sections are all governed by the same parameters as long as the underlying distribution as well as the size of the cross sections are time invariant. We derive inference about these parameters, and tests of the null hypothesis of time invariance, under asymptotics that do not require the number of extremes or the number of time periods to increase. We further apply Hamiltonian Monte Carlo techniques to estimate the path of time-varying parameters. We illustrate the approach in four examples of U.S. data: damages from weather-related disasters, financial returns, city sizes and firm sizes.

This paper examines empirically whether the measurement of trend inflation can be improved by using disaggregated data on sectoral inflation to construct indexes akin to core inflation but with a time-varying distributed lags of weights, where the sectoral weight depends on the timevarying volatility and persistence of the sectoral inflation series and on the comovement among sectors. The modeling framework is a dynamic factor model with time-varying coefficients and stochastic volatility as in Del Negro and Otrok (2008), and is estimated using U.S. data on seventeen components of the personal consumption expenditure inflation index.