Volume 20, Issue 4 - Special issue in honor of James Ramsey / Guest editor: Philip Rothman

The topic of this paper is testing the hypothesis of constant unconditional variance in GARCH models against the alternative that the unconditional variance changes deterministically over time. Tests of this hypothesis have previously been performed as misspecification tests after fitting a GARCH model to the original series. It is found by simulation that the positive size distortion present in these tests is a function of the kurtosis of the GARCH process. Adjusting the size by numerical methods is considered. The possibility of testing the constancy of the unconditional variance before fitting a GARCH model to the data is discussed. The power of the ensuing test is vastly superior to that of the misspecification test and the size distortion minimal. The test has reasonable power already in very short time series. It would thus serve as a test of constant variance in conditional mean models. An application to exchange rate returns is included.

A substantial amount of recent time series research has emphasized semi-parameteric estimators of a long memory parameter and we provide a selective review of the literature on this issue. We consider such estimators applied to the issue of estimating the parameters relating to a short memory process which is embedded within the long memory process. We consider the fractional differencing filter and the subsequent properties of a two step estimator of the short memory parameters. We conclude that while the semi-parametric estimators can have excellent properties in terms of estimating the long memory parameter, they do not have good properties when applied to the two step estimator of short memory I (0) parameters. In particular, these estimators compare poorly in terms of bias and mean squared error (MSE) with the systems based maximum likelihood estimator (MLE).

Milton Friedman and Anna Schwartz constructed an important macroeconomic dataset for the United Kingdom that spans 1878–1970. Numerous authors have modeled the demand for broad money on that dataset. Model selection is central to assessing the merits of the resulting empirical models, so the current paper re-evaluates that issue with computer-automated model selection. Some models are robust to the model selection path, as characterized through variations in target size, pre-search testing, fixity of regressors, impulse indicator saturation, representation of the general model, and choice of dependent variable. Model improvement is also feasible, with historically interpretable nonlinearities and structural breaks.

Ignored structural breaks in a VAR result in a misspecified model such that Granger causality tests are improperly sized; there is a bias towards a rejection of the null hypothesis of non-causality even when the null is correct. Instead of modeling structural breaks as being sharp, changes in the relationship between the maize and petroleum markets are likely to have occurred gradually. We show the flexible Fourier form has good size and power properties in testing for smooth structural change in a VAR. When applied to a VAR including maize and oil prices, we uncover important linkages between the two markets.

We develop a non-linear forecast combination rule based on copulas that incorporate the dynamic interaction between individual predictors. This approach is optimal in the sense that the resulting combined forecast produces the highest discriminatory power as measured by the receiver operating characteristic (ROC) curve. Under additional assumptions, this rule is shown to be equivalent to the quintessential linear combination scheme. To illustrate its usefulness, we apply this methodology to optimally aggregate two currently used leading indicators – the ISM new order diffusion index and the yield curve spread – to predict economic recessions in the United States. We also examine the sources of forecasting gains using a counterfactual experimental set up.

We carry out a pseudo out-of-sample density forecasting study for US GDP with an autoregressive benchmark and alternatives to the benchmark that include both oil prices and stochastic volatility. The alternatives to the benchmark produce superior density forecasts. This comparative density performance appears to be driven more by stochastic volatility than by oil prices, and it primarily occurs outside of the great recession. We use our density forecasts to compute a recession risk indicator around the great recession. The alternative model with the real price of oil generates the earliest strong signal of a recession; but it surprisingly indicates reduced recession immediately after the Lehman Brothers bankruptcy. Use of the “net oil-price increase” nonlinear transformation of oil prices does lead to warnings of highly elevated risk during the Great Recession.

Empirical volatility studies have discovered nonstationary, long-memory dynamics in the volatility of the stock market and foreign exchange rates. This highly persistent, infinite variance, but still mean reverting, behavior is commonly found with nonparametric estimates of the fractional differencing parameter, d , for financial volatility. In this paper, a fully parametric Bayesian estimator, robust to nonstationarity, is designed for the fractionally integrated, autoregressive, stochastic volatility (SV-FIAR) model. Joint estimates of the autoregressive and fractional differencing parameters of volatility are found via a Bayesian, Markov chain Monte Carlo (MCMC) sampler. Like [Jensen, M. J. 2004. “Semiparametric Bayesian Inference of Long-memory Stochastic Volatility.” Journal of Time Series Analysis 25: 895–922.], this MCMC algorithm relies on the wavelet representation of the log-squared return series. Unlike the Fourier transform, where a time series must be a stationary process to have a spectral density function, wavelets can represent both stationary and nonstationary processes. As long as the wavelet has a sufficient number of vanishing moments, this paper’s MCMC sampler will be robust to nonstationary volatility and capable of generating the posterior distribution of the autoregressive and long-memory parameters of the SV-FIAR model regardless of the value of d . Using simulated and empirical stock market return data, we find our Bayesian estimator producing reliable point estimates of the autoregressive and fractional differencing parameters with reasonable Bayesian confidence intervals for either stationary or nonstationary SV-FIAR models.

Does productivity growth increase or reduce unemployment? Theoretical and empirical analyses have generally provided mixed results. In this paper we analyze the empirical relationship between productivity and unemployment over different time frames using wavelet analysis. The scale-by-scale results from panel data and nonparametric regressions methods indicate that productivity-unemployment relationship is scale-dependent, that is changes over different time horizons. Specifically, productivity growth creates unemployment in the short and medium terms, but employment in the long run.