Please cite this article as: Ip, R.H.L., Li, W.K., Time varying spatio-temporal covariance models. Spatial Statistics (2015), http://dx. AbstractIn this paper, we introduce valid parametric covariance models for univariate and multivariate spatio-temporal random fields. In contrast to the traditional models, we allow the model parameters to vary over time. Since variables in applications usually exhibit seasonality or changes in dependency structures, the allowance of varying parameters would be beneficial in terms of improving model flexibility. Conditions in constructing valid covariance models and discussions on practical implementation will be provided. As an application, a set of air pollution data observed from a monitoring network will be modeled. It is found that the time varying model performs better in prediction compared with the traditional models.

Realized moments of higher order computed from intraday returns are introduced in recent years. The literature indicates that realized skewness is an important factor in explaining future asset returns. However, the literature mainly focuses on the whole market and on the monthly or weekly scale. In this paper, we conduct an extensive empirical analysis to investigate the forecasting abilities of realized skewness and realized kurtosis towards individual stock's future return and variance in the daily scale. It is found that realized kurtosis possesses significant forecasting power for the stock's future variance. In the meanwhile, realized skewness is lack of explanatory power for the future daily return for individual stocks with a short horizon, in contrast with the existing literature.