arXiv subjects

Richard H. Gerlach

Publications and source records attributed to Richard H. Gerlach.

3 recordsLinked to original sources

arXiv2021

Dynamic Quantile Function Models

Motivated by the need for effectively summarising, modelling, and forecasting the distributional characteristics of intra-daily returns, as well as the recent work on forecasting histogram-valued time-series in the area of symbolic data analysis, we develop a time-series model for forecasting quantile-function-valued (QF-valued) daily summaries for intra-daily returns. We call this model the dynamic quantile function (DQF) model. Instead of a histogram, we propose to use a $g$-and-$h$ quantile function to summarise the distribution of intra-daily returns. We work with a Bayesian formulation of the DQF model in order to make statistical inference while accounting for parameter uncertainty; an efficient MCMC algorithm is developed for sampling-based posterior inference. Using ten international market indices and approximately 2,000 days of out-of-sample data from each market, the performance of the DQF model compares favourably, in terms of forecasting VaR of intra-daily returns, against the interval-valued and histogram-valued time-series models. Additionally, we demonstrate that the QF-valued forecasts can be used to forecast VaR measures at the daily timescale via a simple quantile regression model on daily returns (QR-DQF). In certain markets, the resulting QR-DQF model is able to provide competitive VaR forecasts for daily returns.

stat.ME↗

arXiv2017

Semiparametric GARCH via Bayesian model averaging

As the dynamic structure of the financial markets is subject to dramatic changes, a model capable of providing consistently accurate volatility estimates must not make strong assumptions on how prices change over time. Most volatility models impose a particular parametric functional form that relates an observed price change to a volatility forecast (news impact function). We propose a new class of functional coefficient semiparametric volatility models where the news impact function is allowed to be any smooth function, and study its ability to estimate volatilities compared to the well known parametric proposals, in both a simulation study and an empirical study with real financial data. We estimate the news impact function using a Bayesian model averaging approach, implemented via a carefully developed Markov chain Monte Carlo (MCMC) sampling algorithm. Using simulations we show that our flexible semiparametric model is able to learn the shape of the news impact function from the observed data. When applied to real financial time series, our new model suggests that the news impact functions are significantly different in shapes for different asset types, but are similar for the assets of the same type.

stat.ME↗

arXiv2016

Estimating Quantile Families of Loss Distributions for Non-Life Insurance Modelling via L-moments

This paper discusses different classes of loss models in non-life insurance settings. It then overviews the class Tukey transform loss models that have not yet been widely considered in non-life insurance modelling, but offer opportunities to produce flexible skewness and kurtosis features often required in loss modelling. In addition, these loss models admit explicit quantile specifications which make them directly relevant for quantile based risk measure calculations. We detail various parameterizations and sub-families of the Tukey transform based models, such as the g-and-h, g-and-k and g-and-j models, including their properties of relevance to loss modelling. One of the challenges with such models is to perform robust estimation for the loss model parameters that will be amenable to practitioners when fitting such models. In this paper we develop a novel, efficient and robust estimation procedure for estimation of model parameters in this family Tukey transform models, based on L-moments. It is shown to be more robust and efficient than current state of the art methods of estimation for such families of loss models and is simple to implement for practical purposes.

q-fin.RM↗