Representation of continuous-time ARMA, CARMA, models is reviewed. Computational aspects of simulating and calculating the likelihood-function of CARMA are summarized. Some numerical properties are illustrated by simulations. Some real data applications are shown. -- CARMA ; maximum-likelihood ;...

We simulate a simplified version of the price process including bubbles and crashes proposed in Kreuser and Sornette (2018). The price process is defined as a geometric random walk combined with jumps modelled by separate, discrete distributions associated with positive (and negative) bubbles....

It is now an accepted fact that the majority of financial markets worldwide are neither normal nor constant, and South Africa is no exception. One idea that can be used to understand such markets and has been gaining popularity recently is that of regimes and regime-switching models. In this...

Financial risk managers routinely use non-linear time series models to predict the downside risk of the capital under management. They also need to evaluate the adequacy of their model using so-called backtesting procedures. The latter involve hypothesis testing and evaluation of loss functions....

This paper presents the R package GAS for the analysis of time series under the Generalized Autoregressive Score (GAS) framework of Creal et al. (2013) and Harvey (2013). The distinctive feature of the GAS approach is the use of the score function as the driver of time{variation in the...

This paper proposes tests for pairwise and multiple out-of-sample comparisons of parametric conditional quantile models. The tests rank the distance between actual and nominal conditional coverage w.r.t. the \textit{union} of information sets across models, for a given loss function. Our...

Risk factors and systematic factor strategies are fast becoming an integral part of the global asset management landscape. In this report, we provide an introduction to, and critique of, the factor investing paradigm in a South African setting. We initially discuss the general factor...

This paper tackles a core question of portfolio management: How ‘active' is an active portfolio? To answer this question holistically, we generalise the idea of Active Share by keeping the same calculation methodology but substituting in different types of portfolio and benchmark ‘weights'....