Essays in Financial and Macro Econometrics
Keywords: Econometrics
Time series

Theory suggests that physical commodity prices may exhibit nonlinear features such as bubbles and various types of asymmetries. Chapter one investigates these claims empirically by introducing a new time series model apt to capture such features. The data set is composed of 25 individual, continuous contract, commodity futures price series, representative of a number of industry sectors including softs, precious metals, energy, and livestock. It is shown that the linear causal ARMA model with Gaussian innovations is unable to adequately account for the features of the data. In the purely descriptive time series literature, often a threshold autoregression (TAR) is employed to model cycles or asymmetries. Rather than take this approach, we suggest a novel process which is able to accommodate both bubbles and asymmetries in a flexible way. This process is composed of both causal and noncausal components and is formalized as the mixed causal/noncausal autoregressive model of order (r; s). Estimating the mixed causal/noncausal model with leptokurtic errors, by an approximated maximum likelihood method, results in dramatically improved model fit according to the Akaike information criterion. Comparisons of the estimated unconditional distributions of both the purely causal and mixed models also suggest that the mixed causal/noncausal model is more representative of the data according to the Kullback-Leibler measure. Moreover, these estimation results demonstrate that allowing for such leptokurtic errors permits identification of various types of asymmetries. Finally, a strategy for computing the multiple steps ahead forecast of the conditional distribution is discussed.Chapter two considers a vector autoregressive model (VAR) model with stochastic volatility which appeals to the Inverse Wishart distribution. Dramatic changes in macroeconomic time series volatility pose a challenge to contemporary VAR forecasting models. Traditionally, the conditional volatility of such models had been assumed constant over time or allowed for breaks across long time periods. More recent work, however, has improved forecasts by allowing the conditional volatility to be completely time variant by specifying the VAR innovation variance as a distinct discrete time process. For example, Clark (2011) specifies the elements of the covariance matrix process of the VAR innovations as linear functions of independent nonstationary processes. Unfortunately, there is no empirical reason to believe that the VAR innovation volatility processes of macroeconomic growth series are nonstationary, nor that the volatility dynamics of each series are structured in this way. This suggests that a more robust specification on the volatility process--one that both easily captures volatility spill-over across time series and exhibits stationary behaviour--should improve density forecasts, especially over the long-run forecasting horizon. In this respect, we employ a latent Inverse Wishart autoregressive stochastic volatility specification on the conditional variance equation of a Bayesian VAR, with U.S. macroeconomic time series data, in evaluating Bayesian forecast efficiency against a competing specification by Clark (2011).