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The aim of this paper is to examine the time scaling of the semivariance when returns are modeled by various types of jump-diffusion processes, including stochastic volatility models with jumps in returns and in volatility. In particular,…

We examine how the most prevalent stochastic properties of key financial time series have been affected during the recent financial crises. In particular we focus on changes associated with the remarkable economic events of the last two…

We consider the viability of a modularised mechanistic online machine learning framework to learn signals in low-frequency financial time series data. The framework is proved on daily sampled closing time-series data from JSE equity…

Stochastic volatility (SV) models mimic many of the stylized facts attributed to time series of asset returns, while maintaining conceptual simplicity. The commonly made assumption of conditionally normally distributed or…

In this paper we propose a semi-Markov modulated model of interest rates. We assume that the switching process is a semi-Markov process with finite state space E and the modulated process is a diffusive process. We derive recursive…

This dissertation investigates the ability of the Ising model to replicate statistical characteristics, or stylized facts, commonly observed in financial assets. The study specifically examines in the S&P500 index the following features:…

This paper aims to more effectively manage and mitigate stock market risks by accurately characterizing financial market returns and volatility. We enhance the Stochastic Volatility (SV) model by incorporating fat-tailed distributions and…

The increasing interest in renewable energy, particularly in wind, has given rise to the necessity of accurate models for the generation of good synthetic wind speed data. Markov chains are often used with this purpose but better models are…

We introduce a new class of continuous-time models of the stochastic volatility of asset prices. The models can simultaneously incorporate roughness and slowly decaying autocorrelations, including proper long memory, which are two stylized…

Technical and fundamental analysis are traditional tools used to analyze individual stocks; however, the finance literature has shown that the price movement of each individual stock correlates heavily with other stocks, especially those…

This paper explores stochastic modeling approaches to elucidate the intricate dynamics of stock prices and volatility in financial markets. Beginning with an overview of Brownian motion and its historical significance in finance, we delve…

In this paper, we outline a model of graph (or network) dynamics based on two ingredients. The first ingredient is a Markov chain on the space of possible graphs. The second ingredient is a semi-Markov counting process of renewal type. The…

Dynamic jumps in the price and volatility of an asset are modelled using a joint Hawkes process in conjunction with a bivariate jump diffusion. A state space representation is used to link observed returns, plus nonparametric measures of…

A new model for stocks markets using integer values for each stock price is presented. In contrast with previously reported models, the variables used in the model are not of binary type, but of more general integer type. It is shown how…

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…

In this research the technology of complex Markov chains is applied to predict financial time series. The main distinction of complex or high-order Markov Chains and simple first-order ones is the existing of aftereffect or memory. The…

One of the most important studies in finance is to find out whether stock returns could be predicted. This research aims to create a new multivariate model, which includes dividend yield, earnings-to-price ratio, book-to-market ratio as…

In this paper we consider the simulation-based Bayesian analysis of stochastic volatility in mean (SVM) models. Extending the highly efficient Markov chain Monte Carlo mixture sampler for the SV model proposed in Kim et al. (1998) and Omori…

Stock price change in financial market occurs through transactions in analogy with diffusion in stochastic physical systems. The analysis of price changes in real markets shows that long-range correlations of price fluctuations largely…

This paper estimates models of high frequency index futures returns using `around the clock' 5-minute returns that incorporate the following key features: multiple persistent stochastic volatility factors, jumps in prices and volatilities,…