Extracting a robust US business cycle using a time‐varying multivariate model‐based bandpass filter

Detrending and business cycle facts

The business cycle analysis of Arthur F. Burns and Wesley C. Mitchell and the National Bureau of Economic Research presumed that aggregate economic variables evolve on a time scale defined by business cycle turning points rather than by months or quarters. Do macroeconomic variables appear to evolve on an economic rather than a calendar time scale? Evidence presented here suggests that they do. However, the estimated economic time scales are only weakly related to business cycle time scales, providing evidence against the view underlying traditional business cycle analysis. Copyright 1987 by University of Chicago Press.

Extracting Business Cycles using Semi-Parametric Time-Varying Spectra with Applications to US Macroeconomic Time Series

Neftci (1984) proposed a nonparametric test procedure for determining whether business cycles are asymmetric in the sense that contractions are steeper than expansions. He found evidence of this type of asymmetry in postwar quarterly U.S. unemployment variables.' This comment identifies a probable error in Neftci's empirical work that reverses the significance of his results for the unemployment rate, and it suggests that this test may have low power and be sensitive to measurement error.

We use factor-augmented predictive regressions to analyze the relation between nominal exchange rates and macroeconomic variables. Using a panel of 121 US macroeconomic time series, we estimate eight factors through principal component analysis. Those estimated factors have significant predictive power and can substantially improve the predictive power of purchasing power parity through both in-sample and out-of-sample analyses. The estimated macroeconomic factor, which co-moves with US stock market variables, has strong predictive power for nominal exchange rate fluctuations in the short run, while estimated factors, co-moving with interest rate spreads, government-issued bond yields and employment variables, have strong predictive power in the long run. Moreover, optimal factors selected by the BIC in the out-of-sample analysis differ greatly depending on the time points when forecasts are made. Finally, we show that factors extracted from a panel of 121 US time series data and those extracted from a panel of 215 Korean macroeconomic series together can predict a substantial portion of movements in the Korea–US bilateral exchange rate.

Apart from the percentage change in the price of crude oil, there is a growing tradition of using various nonlinear transformations of the price of crude oil to forecast real gross domestic product growth rates, equity returns, inflation and other macroeconomic variables. This study attempts to quantify the additional potential predictive power afforded by crude oil price volatility relative to widely used crude oil price‐based variables for more than 300 US macroeconomic time series at the monthly and the quarterly sampling frequency. We observe that regressions employing crude oil price realized volatility and crude oil price realized semivolatilities tend to afford a more consistent pattern of out‐of‐sample prediction gains relative to competitors using well‐known crude oil price measures and the autoregressive benchmark at the quarterly and monthly sampling frequency. While it is somewhat harder to find evidence of finite‐sample predictive gains relative to the benchmark, the evidence is stronger with respect to population‐level predictability 1 quarter (1 month) ahead for the model with crude oil price realized semivolatilities across the considered data and models. Furthermore, point (density) forecasts employing crude oil price realized volatility tend to be more accurate than corresponding forecasts produced under the crude oil price‐based predictive regressions in a horse race.

We develop a flexible semi‐parametric method for the introduction of time‐varying parameters in a model‐based signal extraction procedure. Dynamic model specifications for the parameters in the model are not required. We show that signal extraction based on Kalman filtering and smoothing can be made dependent on time‐varying sample spectra. Our new procedure starts with specifying the time‐varying spectrum as a semi‐parametric flexible spline function that can be formulated in state space form and can be treated by multivariate Kalman filter and smoothing methods. Next we show how a time series decomposition model can be made dependent on a time‐varying sample spectrum in a frequency domain analysis. The key insight is that the spectral likelihood function depends on the sample spectrum. The estimates of the model parameters are obtained by maximizing the spectral likelihood function. A time‐varying sample spectrum leads to a time‐varying spectral likelihood and hence we obtain time‐varying parameter estimates. The time series decomposition model with the resulting time‐varying parameters reflect the time‐varying spectrum accurately. This approach to model‐based signal extraction includes a bootstrap procedure to compute confidence intervals for the time‐varying parameter estimates. We illustrate the methodology by presenting a business cycle analysis for three quarterly US macroeconomic time series between 1947 and 2010. The empirical study provides strong evidence that the cyclical properties of macroeconomic time series have been changing over time. Copyright © 2010 John Wiley & Sons, Ltd.

Multivariate Bayesian Predictive Synthesis in Macroeconomic Forecasting

Trends and random walks in macroeconomic time series: A reappraisal

This study proposes methods for estimating Bayesian vector autoregressions (VARs) with a (semi-) automatic variable selection and an informative prior on the unconditional mean or steady-state of the system. We show that extant Gibbs sampling methods for Bayesian variable selection can be efficiently extended to incorporate prior beliefs on the steady-state of the economy. Empirical analysis, based on three major US macroeconomic time series, indicates that the out-of-sample forecasting accuracy of a VAR model is considerably improved when it combines both variable selection and steady-state prior information.

A Comparison of Estimation Methods for Dynamic Factor Models of Large Dimensions

This paper presents a new approach to constructing multistep combination forecasts in a nonstationary framework with stochastic and deterministic trends. Existing forecast combination approaches in the stationary setup typically target the in-sample asymptotic mean squared error (AMSE), relying on its approximate equivalence with the asymptotic forecast risk (AFR). Such equivalence, however, breaks down in a nonstationary setup. This paper develops combination forecasts based on minimizing an accumulated prediction errors (APE) criterion that directly targets the AFR and remains valid whether the time series is stationary or not. We show that the performance of APE-weighted forecasts is close to that of the optimal, infeasible combination forecasts. Simulation experiments are used to demonstrate the finite sample efficacy of the proposed procedure relative to Mallows/Cross-Validation weighting that target the AMSE as well as underscore the importance of accounting for both persistence and lag order uncertainty. An application to forecasting US macroeconomic time series confirms the simulation findings and illustrates the benefits of employing the APE criterion for real as well as nominal variables at both short and long horizons. A practical implication of our analysis is that the degree of persistence can play an important role in the choice of combination weights.

This article explores the relationship between commodity price cycles and the US business cycle. Commodity price cycles are known to foster capricious macroeconomic activity, and understanding their behaviour offers valuable economic insight. The US business cycle is a key indicator of the broader economic conditions, reflecting changes in economic activity, consumer spending, and overall market conditions. By examining the dynamics and interplay between these two cycles, this study provides insights into the potential synchronisation, lag, or lead between commodity price cycles and the US business cycle. The study employs a Fourier analysis of commodity price cycles and the US business cycle. In addition, the same empirical method will be used to analyse historical rainfall patterns in the US as a means of furthering the role of historical rainfall patterns in shaping agricultural productivity and subsequent price movements. Results show dominant cycles of 14.2 years throughout the commodity price dataset, 3.8 years within the US business cycle, and 14.2 years in US historical rainfall patterns. The study also identifies several factors that influence the relationship between these two cycles, including global demand, trade policies, and financial market fluctuations.

NE of the stylized facts that characterize an economy over the business cycle is the movement of prices with real output. In the literature on the demand and real theories of business cycles, the two main theories state that if movements of output result from demand shocks, prices are expected to be procyclical; by contrast, if shocks originate from the supply side then prices are expected to be countercyclical. Lucas provided evidence in support of a positive correlation between prices and real output [24][25]. Olson also argues that newclassical as well as Keynesian economics agree on the positive correlation between the variables in relevance [28]. The same holds in Mankiw [26]. Cooley and Ohanian confirm the price countercyclicality for the United States [11], and Backus and Kehoe confirm it for other countries [1]. By contrast, other studies have reached the opposite conclusions (Bernanke [2]). The pioneering works of Kydland and Prescott [20] and Long and Plosser [23] initiated an attempt to explain certain stylized facts of U.S. business cycle behavior. This attempt—the so-called real business cycle theory—considered that what is responsible for the presence of business cycle phenomena are exogenous technological shocks and the accompanying propagation mechanism generated by the behavior of economic agents to optimize their behavior within an environment characterized by rational expectations and market-clearing conditions. These business cycle models attempt to explain the fluctuations in macroeconomic aggregates via the technological or any other “real” channel supporting the presence of an inverse relationship between prices and output. Mankiw has criticized real business cycle models on the grounds that they show that prices are not procyclical [26]. Countercyclicality of prices connotes that prices and output are negatively correlated. Moreover, the countercyclical behavior of prices suggests that real output

This book is a tribute to Professor Andrew Harvey, who has been an active researcher for four decades, writing on many aspects of time series modeling with a particular focus on economic and more recently financial applications. As well as generating path breaking research articles, he has been unusually influential in writing research monographs and textbooks, and building and documenting software. A distinctive voice, he is perhaps the most influential scholar in the area of time series modeling using unobserved components in economics. This book covers three main topics: the theory and methodology for unobserved components time series models, applications of unobserved components time series models, and time series econometrics estimation and testing.