Volume 13, Issue 3

We compare the ability of correlation and threshold effects in a stochastic volatility model to capture the asymmetric relationship between stock returns and volatility. The parameters are estimated using maximum likelihood based on the extended Kalman filter and uses numerical integration over the latent volatility process. The stochastic volatility model with only correlation does a better job of capturing asymmetry than a threshold stochastic volatility model even though it has fewer parameters. We develop a stochastic volatility model that includes both threshold effects and correlated innovations. We find that the general model with both threshold effects and correlated innovations dominates purely threshold and correlated models. In this augmented model volatility and returns are negatively correlated, and volatility is more persistent, less volatile and higher following negative returns even after counting for the negative correlation.

The issue of poverty traps is assessed using quantile regression. An augmentation of the usual convergence regressions by quadratic and cubic terms is used with emphasis on curve fitting rather than parameter estimation. The results show that the generic mechanism leading to poverty traps predominantly applies to countries with relatively low levels of income per capita or per worker that simultaneously have low growth rates in the vicinity and below the lowest quintile of the growth rate distribution. The validity of the results is supported by a nonparametric variant of quantile regression.

To match the stylized facts of high frequency financial time series precisely and parsimoniously, this paper presents a finite mixture of conditional exponential power distributions where each component exhibits asymmetric conditional heteroskedasticity. We provide weak stationarity conditions and unconditional moments to the fourth order. We apply this new class to Dow Jones index returns. We find that a two-component mixed exponential power distribution dominates mixed normal distributions with more components, and more parameters, both in-sample and out-of-sample. In contrast to mixed normal distributions, all the conditional variance processes become stationary. This happens because the mixed exponential power distribution allows for component-specific shape parameters so that it can better capture the tail behaviour. Therefore, the more general new class has attractive features over mixed normal distributions in our application: less components are necessary and the conditional variances in the components are stationary processes. Results on NASDAQ index returns are similar.

The univariate Hodrick-Prescott filter depends on the noise-to-signal ratio that acts as a smoothing parameter. We first propose an optimality criterion for choosing the best smoothing parameters. We show that the noise-to-signal ratio is the unique minimizer of this criterion, when we use an orthogonal parametrization of the trend, whereas it is not the case when an initial-value parametrization of the trend is applied. We then propose a multivariate extension of the filter and show that there is a whole class of positive definite matrices that satisfy a similar optimality criterion, when we apply an orthogonal parametrization of the trend.

In this study, we use the 'heterogeneous autoregressive' (HAR) model and replace all squared returns with a squared range to estimate realized range-based volatility (RRV) forecasts for oil futures prices. Our findings demonstrate that the HAR-RRV models, involving volatility measures with a realized range-based estimator, successfully capture the long-term memory behavior of volatility in oil futures contracts. We find that realized range-based bi-power variation (RBV), which is also immune to jumps, is a better regressor for future volatility prediction, significantly outperforming the AR model. Similar to the findings for financial markets, we also find that the jump components of RRV have little predictive power for oil futures contracts.