Maximum Simulated Likelihood Approach Research Articles

Stochastic volatility models: conditional normality versus heavy-tailed distributions

Most of the empirical applications of the stochastic volatility (SV) model are based on the assumption that the conditional distribution of returns, given the latent volatility process, is normal. In this paper, the SV model based on a conditional normal distribution is compared with SV specifications using conditional heavy-tailed distributions, especially Student's t-distribution and the generalized error distribution. To estimate the SV specifications, a simulated maximum likelihood approach is applied. The results based on daily data on exchange rates and stock returns reveal that the SV model with a conditional normal distribution does not adequately account for the two following empirical facts simultaneously: the leptokurtic distribution of the returns and the low but slowly decaying autocorrelation functions of the squared returns. It is shown that these empirical facts are more adequately captured by an SV model with a conditional heavy-tailed distribution. It also turns out that the choice of the conditional distribution has systematic effects on the parameter estimates of the volatility process. Copyright © 2000 John Wiley & Sons, Ltd.

Accommodating variations in responsiveness to level-of-service measures in travel mode choice modeling

An individual’s responsiveness to level-of-service variables affects her or his travel mode choice for a trip. This responsiveness will, in general, vary across individuals based on observed (to an analyst) and unobserved (to an analyst) individual characteristics. The current paper formulates a multinomial-logit based model of travel mode choice that accommodates variations in responsiveness to level-of-service measures due to both observed and unobserved individual characteristics in a comprehensive manner. The choice probabilities in the resulting model are evaluated using Monte Carlo simulation techniques and the model parameters are estimated using a maximum simulated likelihood approach. The model is applied to examine the impact of improved rail service on weekday, business travel in the Toronto—Montreal corridor. The empirical results show that not accounting adequately for variations in responsiveness across individuals leads to a statistically inferior data fit and also to inappropriate evaluations of policy actions aimed at improving inter-city transportation services.

Stochastic Volatility Models: Conditional Normality Versus Heavy-Tailed Distributions

Most of the empirical applications of the stochatic volatility (SV) model are based on the assumption that the conditional distribution of returns given the latent volatility process is normal. In this paper the SV model based on a conditional normal distribution is compared with SV specifications using conditional heavy-tailed distributions, especially Student's t-distribution and the generalized error distribution. To estimate the SV specifications a simulated maximum likelihood approach is applied. The results based on German stock market data reveal that the SV model with a conditional normal distribution does not adequately account for the two following empirical facts simultaneously: the leptokurtic distribution of the returns and the low but slowly decaying autocorrelation functions of the squared returns. It is shown that these empirical facts are more adequately captured by a SV model with a conditional heavy-tailed distribution. Finally, it turns out that the choice of the conditional distribution has systematic effects on the parameter estimates of the volatility process.