Professor Yuanhua Feng from University of Paderborn (Germany) delivered seminar series in Center for Economic Research, Shandong University on Sept. 12, 2013, Sept. 13, 2013 and Sept.17, 2013.

The topic of the first seminar is “several semiparametric GARCH models and their application to decomposing financial risk”. Prof. Feng explained the well-known financial econometric models ARCH, GARCH models and many of their extensions, such as the TGARCH and the APARCH are all developed for modelling stationary return series. In practice it is however found that financial returns may exhibit non-stationary components, in particular a slowly changing scale function caused by changing macroeconomic environment. This problem can be solved using some semiparametric GARCH model, which combines a parametric GARCH model and nonparametric smoothing technique. Different SemiGARCH approaches are introduced in the literature. These proposals not only solve some important theoretical problems but also allow us to decompose financial risk into different components. The SemiGARCH models can also be extended to multivariate case to improve measures for portfolio risk or macroeconomic risk.

The second issue of the seminar is “semiparametric ACD and related models for analyzing high-frequency financial data”. Prof. Feng introduced nowadays detailed records of each transaction in financial market, called ultra-high-frequency financial data, are available. Different models for dealing with these data are introduced in the literature. The most well-known approach in this context is the ACD (autoregressive conditional duration) model for analyzing waiting time (duration) between two trades. However, transaction durations or other intraday quantities observed on one day often exhibit a non-stationary diurnal pattern. Prof. Feng discussed on different methods for dealing with this diurnal duration patterns, and then showed further extensions and applications of the ACD model, including the Log-ACD, a semiparametric Log-ACD and their application for modelling daily average transaction durations, daily trading numbers and daily trading volumes as well.

The third issue is “semiparametric long-memory financial time series models”. Prof. Feng interpreted the most well-known approach for modelling long memory in mean is the FARIMA (fractionally integrated ARMA) model. In the financial market it is observed that volatility or other related quantities may exhibit clear long memory. Different extensions of the FARIMA model to deal with long memory in volatility or transaction durations are introduced, including the FIGARCH (fractionally integrated GARCH), the FIACD (fractionally integrated ACD), the LM-GARCH (long-memory GARCH), the infinite order ARCH and the LARCH (linear ARCH) as well. Prof. Feng also introduced an adapted infinite order ARCH model including the LM-GARCH as a special case. Another possibility for modelling long memory is to analyze the data after the log-transformation. Now, long memory in volatility is transferred into long memory in mean and can hence be estimated directly using the FARIMA model. The reason for this is that the long memory parameter in the mean and in the volatility is often the same. Such models are called FI-Log-GARCH or FI-Log-ACD.