Visual Inference for Linear Mixed Models
I started my AMSI Vacation Research Scholarship project by reading the paper ‘Large Dynamic Covariance Matrices’ (Engle et al. 2017), which proposed two methods to improve the estimation of large dynamic covariance matrices that are important for risk management and portfolio selection in finance.
One of the challenges of modelling financial time series is heteroskedasticity, which means that the volatility of the considered process is not constant, where volatility is the square root of the conditional variance of the log return given all the information available up to time t. A favoured model is Dynamic Conditional Correlation (DCC), derived from the GARCH family by Engle (1982). Engle et al. (2017) introduced a composite likelihood method to improve the model estimation performance in large dimensions. The other method they introduced was the nonlinear shrinkage method to help improve the performance of correcting in-sample biases of sample covariance matrix eigenvalues.
As we would like our new model to work in a financial dynamical network and help investigate the risk spillover effect. I studied another paper, ‘Networks in Risk Spillovers: A Multivariate GARCH Perspective’ (Monica et al. 2015), that introduced proximity matrices into the BEKK model (also derived from the GARCH family).
The aim of my summer research project was to combine these tools so that we could take into consideration the dependency structure of risk among the financial entities among a network, and at the same time obtain acceptable model performance in large dimensions.
We wrote the Matlab codes for our model, based on the MFE Toolbox by Kevin Sheppard and the Matlab codes used in the Engle et al. (2017), thanks to Prof. Michael Wolf for his generosity.
One of the problems we encountered was during the inference step where we’d like to revise our knowledge of the underlying network, based on the available information, that the Hessian matrix produced by the built-in Matlab function lacked accuracy. This problem was solved, but with some sacrifice of computational efficiency. We wish to investigate in this issue a bit more in future study. We have also taken advantage of the asymptotic normality of maximum composite likelihood estimators in the inference step, assuming some regularity conditions are met. These conditions are also of interest in our future study.
John Su was a recipient of a 2018/19 AMSI Vacation Research Scholarship.