Volume 3, Issue 2

The asymmetric response of conditional variances to positive versus negative news has been traditionally modeled with threshold specifications that allow only two possible regimes: low or high volatility. In this paper, the possibility of intermediate regimes is considered and modeled with the introduction of a smooth-transition mechanism in a GARCH specification. One important property of this model is that it permits an on-off ARCH effect, in which a time series can switch from a process with constant variance to a process with time-varying variance. On testing for the existence of a smooth-transition mechanism, there are nuisance parameters that are not identified under the null hypothesis. Nevertheless, it is possible to construct a Lagrange-multiplier test that is ¬2 p -distributed. A Monte Carlo simulation shows that the test has very good size and good power. A smooth-transition GARCH specification is tested and estimated with stock returns and exchange-rate data. While a threshold model is preferred for stock returns, a smooth-transition model is more likely for exchange rates.

This paper provides rules for anticipating business-cycle recessions and recoveries for countries showing asymmetric cycle durations. Based on a Schumpeterian framework, we analyze business cycles as sums of short-, medium-, and long-term cycles defined for a particular class of unobserved component models. By associating the trend with the low frequencies of the pseudo-spectrum in the frequency domain, manipulation of the spectral bandwidth allows us to define subjective length trends with specific properties. In this paper, we show how these properties can be exploited to anticipate business-cycle turning points, not only historically, but also in a true ex-ante forecasting exercise. This procedure is applied to U.S. post-World War II GNP quarterly data, as well as to another set of European countries.

This paper describes a GAUSS program of a Markov-chain sampling algorithm for GARCH models proposed by Nakatsuma (1998). This algorithm allows us to generate Monte Carlo samples of parameters in a GARCH model from their joint posterior distribution. The samples obtained by this algorithm are used for Bayesian analysis of the GARCH model. As numerical examples, GARCH models of simulated data and of weekly foreign exchange rate series are estimated and analyzed.