arXiv subjects

Richard Gerlach

Publications and source records attributed to Richard Gerlach.

17 recordsLinked to original sources

arXiv2025

Using quantile time series and historical simulation to forecast financial risk multiple steps ahead

A method for quantile-based, semi-parametric historical simulation estimation of multiple step ahead Value-at-Risk (VaR) and Expected Shortfall (ES) models is developed. It uses the quantile loss function, analogous to how the quasi-likelihood is employed by standard historical simulation methods. The returns data are scaled by the estimated quantile series, then resampling is employed to estimate the forecast distribution one and multiple steps ahead, allowing tail risk forecasting. The proposed method is applicable to any data or model where the relationship between VaR and ES does not change over time and can be extended to allow a measurement equation incorporating realized measures, thus including Realized GARCH and Realized CAViaR type models. Its finite sample properties, and its comparison with existing historical simulation methods, are evaluated via a simulation study. A forecasting study assesses the relative accuracy of the 1% and 2.5% VaR and ES one-day-ahead and ten-day-ahead forecasting results for the proposed class of models compared to several competitors.

q-fin.ST↗

arXiv2024

Financial Volatility and Risk Forecasting Incorporating a Larger Number of Realized Measures

Realised volatility has become increasingly prominent in volatility forecasting due to its ability to capture intraday price fluctuations. With a growing variety of realised volatility estimators, each with unique advantages and limitations, selecting an optimal estimator may introduce challenges. In this thesis, aiming to synthesise the impact of various realised volatility measures on volatility forecasting, we propose an extension of the Realised GARCH model that incorporates an autoencoder-generated synthetic realised measure, combining the information from multiple realised measures in a nonlinear manner. Our proposed model extends existing linear methods, such as Principal Component Analysis and Independent Component Analysis, to reduce the dimensionality of realised measures. The empirical evaluation, conducted across four major stock markets from January 2000 to June 2022 and including the period of COVID-19, demonstrates both the feasibility of applying an autoencoder to synthesise volatility measures and the superior effectiveness of the proposed model in one-step-ahead rolling volatility forecasting. The model exhibits enhanced flexibility in parameter estimations across each rolling window, outperforming traditional linear approaches. These findings indicate that nonlinear dimension reduction offers further adaptability and flexibility in improving the synthetic realised measure, with promising implications for future volatility forecasting applications.

q-fin.RM↗

arXiv2024

Loss-based Bayesian Sequential Prediction of Value at Risk with a Long-Memory and Non-linear Realized Volatility Model

A long memory and non-linear realized volatility model class is proposed for direct Value at Risk (VaR) forecasting. This model, referred to as RNN-HAR, extends the heterogeneous autoregressive (HAR) model, a framework known for efficiently capturing long memory in realized measures, by integrating a Recurrent Neural Network (RNN) to handle non-linear dynamics. Loss-based generalized Bayesian inference with Sequential Monte Carlo is employed for model estimation and sequential prediction in RNN HAR. The empirical analysis is conducted using daily closing prices and realized measures from 2000 to 2022 across 31 market indices. The proposed models one step ahead VaR forecasting performance is compared against a basic HAR model and its extensions. The results demonstrate that the proposed RNN-HAR model consistently outperforms all other models considered in the study.

q-fin.RM↗

arXiv2024

Semi-parametric financial risk forecasting incorporating multiple realized measures

A semi-parametric joint Value-at-Risk (VaR) and Expected Shortfall (ES) forecasting framework employing multiple realized measures is developed. The proposed framework extends the realized exponential GARCH model to be semi-parametrically estimated, via a joint loss function, whilst extending existing quantile time series models to incorporate multiple realized measures. A quasi-likelihood is built, employing the asymmetric Laplace distribution that is directly linked to a joint loss function, which enables Bayesian inference for the proposed model. An adaptive Markov Chain Monte Carlo method is used for the model estimation. The empirical section evaluates the performance of the proposed framework with six stock markets from January 2000 to June 2022, covering the period of COVID-19. Three realized measures, including 5- minute realized variance, bi-power variation, and realized kernel, are incorporated and evaluated in the proposed framework. One-step-ahead VaR and ES forecasting results of the proposed model are compared to a range of parametric and semi-parametric models, lending support to the effectiveness of the proposed framework.

q-fin.RM↗

arXiv2023

Global Neural Networks and The Data Scaling Effect in Financial Time Series Forecasting

Neural networks have revolutionized many empirical fields, yet their application to financial time series forecasting remains controversial. In this study, we demonstrate that the conventional practice of estimating models locally in data-scarce environments may underlie the mixed empirical performance observed in prior work. By focusing on volatility forecasting, we employ a dataset comprising over 10,000 global stocks and implement a global estimation strategy that pools information across cross-sections. Our econometric analysis reveals that forecasting accuracy improves markedly as the training dataset becomes larger and more heterogeneous. Notably, even with as little as 12 months of data, globally trained networks deliver robust predictions for individual stocks and portfolios that are not even in the training dataset. Furthermore, our interpretation of the model dynamics shows that these networks not only capture key stylized facts of volatility but also exhibit resilience to outliers and rapid adaptation to market regime changes. These findings underscore the importance of leveraging extensive and diverse datasets in financial forecasting and advocate for a shift from traditional local training approaches to integrated global estimation methods.

econ.EM↗

arXiv2022

A Bayesian realized threshold measurement GARCH framework for financial tail risk forecasting

This paper proposes an innovative threshold measurement equation to be employed in a Realized-GARCH framework. The proposed framework incorporates a nonlinear threshold regression specification to consider the leverage effect and model the contemporaneous dependence between the observed realized measure and hidden volatility. A Bayesian Markov Chain Monte Carlo method is adapted and employed for model estimation, with its validity assessed via a simulation study. The validity of incorporating the proposed measurement equation in Realized-GARCH type models is evaluated via an empirical study, forecasting the 1% and 2.5% Value-at-Risk and Expected Shortfall on six market indices with two different out-of-sample sizes. The proposed framework is shown to be capable of producing competitive tail risk forecasting results in comparison to the GARCH and Realized-GARCH type models.

q-fin.RM↗

arXiv2021

A Bayesian Long Short-Term Memory Model for Value at Risk and Expected Shortfall Joint Forecasting

Value-at-Risk (VaR) and Expected Shortfall (ES) are widely used in the financial sector to measure the market risk and manage the extreme market movement. The recent link between the quantile score function and the Asymmetric Laplace density has led to a flexible likelihood-based framework for joint modelling of VaR and ES. It is of high interest in financial applications to be able to capture the underlying joint dynamics of these two quantities. We address this problem by developing a hybrid model that is based on the Asymmetric Laplace quasi-likelihood and employs the Long Short-Term Memory (LSTM) time series modelling technique from Machine Learning to capture efficiently the underlying dynamics of VaR and ES. We refer to this model as LSTM-AL. We adopt the adaptive Markov chain Monte Carlo (MCMC) algorithm for Bayesian inference in the LSTM-AL model. Empirical results show that the proposed LSTM-AL model can improve the VaR and ES forecasting accuracy over a range of well-established competing models.

stat.ML↗

arXiv2021

Manifold Optimization Assisted Gaussian Variational Approximation

Gaussian variational approximation is a popular methodology to approximate posterior distributions in Bayesian inference especially in high dimensional and large data settings. To control the computational cost while being able to capture the correlations among the variables, the low rank plus diagonal structure was introduced in the previous literature for the Gaussian covariance matrix. For a specific Bayesian learning task, the uniqueness of the solution is usually ensured by imposing stringent constraints on the parameterized covariance matrix, which could break down during the optimization process. In this paper, we consider two special covariance structures by applying the Stiefel manifold and Grassmann manifold constraints, to address the optimization difficulty in such factorization architectures. To speed up the updating process with minimum hyperparameter-tuning efforts, we design two new schemes of Riemannian stochastic gradient descent methods and compare them with other existing methods of optimizing on manifolds. In addition to fixing the identification issue, results from both simulation and empirical experiments prove the ability of the proposed methods of obtaining competitive accuracy and comparable converge speed in both high-dimensional and large-scale learning tasks.

cs.LG↗

arXiv2021

A Semi-parametric Realized Joint Value-at-Risk and Expected Shortfall Regression Framework

A new realized conditional autoregressive Value-at-Risk (VaR) framework is proposed, through incorporating a measurement equation into the original quantile regression model. The framework is further extended by employing various Expected Shortfall (ES) components, to jointly estimate and forecast VaR and ES. The measurement equation models the contemporaneous dependence between the realized measure (i.e., Realized Variance and Realized Range) and the latent conditional ES. An adaptive Bayesian Markov Chain Monte Carlo method is employed for estimation and forecasting, the properties of which are assessed and compared with maximum likelihood through a simulation study. In a comprehensive forecasting study on 1% and 2.5 % quantile levels, the proposed models are compared to a range of parametric, non-parametric and semi-parametric models, based on 7 market indices and 7 individual assets. One-day-ahead VaR and ES forecasting results favor the proposed models, especially when incorporating the sub-sampled Realized Variance and the sub-sampled Realized Range in the model.

q-fin.RM↗

arXiv2020

Tail risk forecasting using Bayesian realized EGARCH models

This paper develops a Bayesian framework for the realized exponential generalized autoregressive conditional heteroskedasticity (realized EGARCH) model, which can incorporate multiple realized volatility measures for the modelling of a return series. The realized EGARCH model is extended by adopting a standardized Student-t and a standardized skewed Student-t distribution for the return equation. Different types of realized measures, such as sub-sampled realized variance, sub-sampled realized range, and realized kernel, are considered in the paper. The Bayesian Markov chain Monte Carlo (MCMC) estimation employs the robust adaptive Metropolis algorithm (RAM) in the burn in period and the standard random walk Metropolis in the sample period. The Bayesian estimators show more favourable results than maximum likelihood estimators in a simulation study. We test the proposed models with several indices to forecast one-step-ahead Value at Risk (VaR) and Expected Shortfall (ES) over a period of 1000 days. Rigorous tail risk forecast evaluations show that the realized EGARCH models employing the standardized skewed Student-t distribution and incorporating sub-sampled realized range are favored, compared to a range of models.

q-fin.RM↗

arXiv2019

Demand forecasting in supply chain: The impact of demand volatility in the presence of promotion

The demand for a particular product or service is typically associated with different uncertainties that can make them volatile and challenging to predict. Demand unpredictability is one of the managers' concerns in the supply chain that can cause large forecasting errors, issues in the upstream supply chain and impose unnecessary costs. We investigate 843 real demand time series with different values of coefficient of variations (CoV) where promotion causes volatility over the entire demand series. In such a case, forecasting demand for different CoV require different models to capture the underlying behavior of demand series and pose significant challenges due to very different and diverse demand behavior. We decompose demand into baseline and promotional demand and propose a hybrid model to forecast demand. Our results indicate that our proposed hybrid model generates robust and accurate forecast across series with different levels of volatilities. We stress the necessity of decomposition for volatile demand series. We also model demand series with a number of well known statistical and machine learning (ML) models to investigate their performance empirically. We found that ARIMA with covariate (ARIMAX) works well to forecast volatile demand series, but exponential smoothing with covariate (ETSX) has a poor performance. Support vector regression (SVR) and dynamic linear regression (DLR) models generate robust forecasts across different categories of demands with different CoV values.

stat.AP↗

arXiv2019

Semi-parametric Realized Nonlinear Conditional Autoregressive Expectile and Expected Shortfall

A joint conditional autoregressive expectile and Expected Shortfall framework is proposed. The framework is extended through incorporating a measurement equation which models the contemporaneous dependence between the realized measures and the latent conditional expectile. Nonlinear threshold specification is further incorporated into the proposed framework. A Bayesian Markov Chain Monte Carlo method is adapted for estimation, whose properties are assessed and compared with maximum likelihood via a simulation study. One-day-ahead VaR and ES forecasting studies, with seven market indices, provide empirical support to the proposed models.

q-fin.RM↗

arXiv2019

Bayesian Nonparametric Adaptive Spectral Density Estimation for Financial Time Series

Discrimination between non-stationarity and long-range dependency is a difficult and long-standing issue in modelling financial time series. This paper uses an adaptive spectral technique which jointly models the non-stationarity and dependency of financial time series in a non-parametric fashion assuming that the time series consists of a finite, but unknown number, of locally stationary processes, the locations of which are also unknown. The model allows a non-parametric estimate of the dependency structure by modelling the auto-covariance function in the spectral domain. All our estimates are made within a Bayesian framework where we use aReversible Jump Markov Chain Monte Carlo algorithm for inference. We study the frequentist properties of our estimates via a simulation study, and present a novel way of generating time series data from a nonparametric spectrum. Results indicate that our techniques perform well across a range of data generating processes. We apply our method to a number of real examples and our results indicate that several financial time series exhibit both long-range dependency and non-stationarity.

q-fin.ST↗

arXiv2018

Semi-parametric Dynamic Asymmetric Laplace Models for Tail Risk Forecasting, Incorporating Realized Measures

The joint Value at Risk (VaR) and expected shortfall (ES) quantile regression model of Taylor (2017) is extended via incorporating a realized measure, to drive the tail risk dynamics, as a potentially more efficient driver than daily returns. Both a maximum likelihood and an adaptive Bayesian Markov Chain Monte Carlo method are employed for estimation, whose properties are assessed and compared via a simulation study; results favour the Bayesian approach, which is subsequently employed in a forecasting study of seven market indices and two individual assets. The proposed models are compared to a range of parametric, non-parametric and semi-parametric models, including GARCH, Realized-GARCH and the joint VaR and ES quantile regression models in Taylor (2017). The comparison is in terms of accuracy of one-day-ahead Value-at-Risk and Expected Shortfall forecasts, over a long forecast sample period that includes the global financial crisis in 2007-2008. The results favor the proposed models incorporating a realized measure, especially when employing the sub-sampled Realized Variance and the sub-sampled Realized Range.

q-fin.RM↗

arXiv2018

Fighting Accounting Fraud Through Forensic Data Analytics

Accounting fraud is a global concern representing a significant threat to the financial system stability due to the resulting diminishing of the market confidence and trust of regulatory authorities. Several tricks can be used to commit accounting fraud, hence the need for non-static regulatory interventions that take into account different fraudulent patterns. Accordingly, this study aims to improve the detection of accounting fraud via the implementation of several machine learning methods to better differentiate between fraud and non-fraud companies, and to further assist the task of examination within the riskier firms by evaluating relevant financial indicators. Out-of-sample results suggest there is a great potential in detecting falsified financial statements through statistical modelling and analysis of publicly available accounting information. The proposed methodology can be of assistance to public auditors and regulatory agencies as it facilitates auditing processes, and supports more targeted and effective examinations of accounting reports.

stat.ML↗

arXiv2017

Bayesian Realized-GARCH Models for Financial Tail Risk Forecasting Incorporating Two-sided Weibull Distribution

The realized GARCH framework is extended to incorporate the two-sided Weibull distribution, for the purpose of volatility and tail risk forecasting in a financial time series. Further, the realized range, as a competitor for realized variance or daily returns, is employed in the realized GARCH framework. Further, sub-sampling and scaling methods are applied to both the realized range and realized variance, to help deal with inherent micro-structure noise and inefficiency. An adaptive Bayesian Markov Chain Monte Carlo method is developed and employed for estimation and forecasting, whose properties are assessed and compared with maximum likelihood, via a simulation study. Compared to a range of well-known parametric GARCH, GARCH with two-sided Weibull distribution and realized GARCH models, tail risk forecasting results across 7 market index return series and 2 individual assets clearly favor the realized GARCH models incorporating two-sided Weibull distribution, especially models employing the sub-sampled realized variance and sub-sampled realized range, over a six year period that includes the global financial crisis.

q-fin.RM↗

arXiv2016

Bayesian Semi-parametric Realized-CARE Models for Tail Risk Forecasting Incorporating Realized Measures

A new model framework called Realized Conditional Autoregressive Expectile (Realized-CARE) is proposed, through incorporating a measurement equation into the conventional CARE model, in a manner analogous to the Realized-GARCH model. Competing realized measures (e.g. Realized Variance and Realized Range) are employed as the dependent variable in the measurement equation and to drive expectile dynamics. The measurement equation here models the contemporaneous dependence between the realized measure and the latent conditional expectile. We also propose employing the quantile loss function as the target criterion, instead of the conventional violation rate, during the expectile level grid search. For the proposed model, the usual search procedure and asymmetric least squares (ALS) optimization to estimate the expectile level and CARE parameters proves challenging and often fails to convergence. We incorporate a fast random walk Metropolis stochastic search method, combined with a more targeted grid search procedure, to allow reasonably fast and improved accuracy in estimation of this level and the associated model parameters. Given the convergence issue, Bayesian adaptive Markov Chain Monte Carlo methods are proposed for estimation, whilst their properties are assessed and compared with ALS via a simulation study. In a real forecasting study applied to 7 market indices and 2 individual asset returns, compared to the original CARE, the parametric GARCH and Realized-GARCH models, one-day-ahead Value-at-Risk and Expected Shortfall forecasting results favor the proposed Realized-CARE model, especially when incorporating the Realized Range and the sub-sampled Realized Range as the realized measure in the model.

q-fin.RM↗