The purpose of this thesis is to investigate the financial volatility dynamics through the GARCH modelling framework. We use univariate and multivariate GARCH-type models enriched with long memory, asymmetries and power transformations. We study the financial time series volatility and co-volatility taking into account the structural breaks detected and focusing on the effects of the corresponding financial crisis events. We conclude to provide a complete framework for the analysis of volatility with major policy implications and benefits for the current risk management practices. We first investigate the volume-volatility link for different investor categories and orders, around the Asian crisis applying a univariate dual long memory model. Our analysis suggests that the behaviour of volatility depends upon volume, but also that the nature of this dependence varies with time and the source of volume. We further apply the vector AR-DCC-FIAPARCH and the UEDCC-AGARCH models to several stock indices daily returns, taking into account the structural breaks of the time series linked to major economic events including crisis shocks We find significant cross effects, time-varying shock and volatility spillovers, time-varying persistence in the conditional variances, as well as long range volatility dependence, asymmetric volatility response to positive and negative shocks and the power of returns that best fits the volatility pattern. We observe higher dynamic correlations of the stock markets after a crisis event, which means increased contagion effects between the markets, a continuous herding investors’ behaviour, as the in-crisis correlations remain high, and a higher level of correlations during the recent financial crisis than during the Asian. Finally, we study the High-frEquency-bAsed VolatilitY (HEAVY) models that combine daily returns with realised volatility. We enrich the HEAVY equations through the HYAPARCH formulation to propose the HYDAP-HEAVY (HYperbolic Double Asymmetric Power) and provide a complete framework to analyse the volatility process.

The statements that include sufficient detail to identify the probability distributions of future prices are asset price dynamics. In this research, using the empirical methods that could explain the historical prices and discuss about how prices change we investigate various important characteristics of the dynamics of asset pricing. The volatility changes can explain very important facts about the asset returns. Volatility could gauge the variability of prices over time. In order to do the volatility modelling we use the conditional heteroskedasticitc models. One of the most powerful tools to do so is using the idea of autoregressive conditional heteroskedastic process or ARCH models, which fill the gap in both academic and practical literature. In this work we detect the asymmetric volatility effect and investigate long memory properties in volatility in Canadian stock market index, using daily data from 1979 through 2015. On one hand, we show that there is an asymmetry in the equity market index. This is an important indication of how information impacts the market. On the other hand, we investigate for the long-range dependency in volatility and discuss how the shocks are persistence. By using the long memory-GARCH models, we not only take care of both short and long memory, but also we compute the d parameter that stands for the fractional decay of the series. By considering the breaks in our dataset, we compare our findings on different conditions to find the most suitable fit. We present the best fit for GARCH, EGARCH, APARCH, GJR-GARCH, FIGARCH, FIAPARCH, and FIEGARCH models.

This thesis aims to construct an optimal portfolio and model as well as forecast its volatility. The performance of the optimal portfolio is then compared to two benchmarks, namely, an equally weighted portfolio and the market index SP 500. The volatility is estimated by employing two GARCH-type models known as standard GARCH, and GJR-GARCH. The GJR-GARCH outperformed its counterpart in terms of Log-likelihood, AIC, and BIC. The forecast performance is compared based on two statistical errors, root mean squared error, and mean absolute error. The optimal portfolio outperformed its counterparts in both statistical errors. Moreover, standard GARCH gave lower statistics than GJR-GARCH. These empirical results are of important significance to portfolio management and risk management processes.

This dissertation comprises of three original contributions to empirical forecasting research. Chapter 1 introduces the dissertation. Chapter 2 contributes to the literature on hierarchical time series (HTS) modelling by proposing a disaggregated forecasting system for both inflation rate and its volatility. Using monthly data that underlies the Retail Prices Index for the UK, we analyse the dynamics of the inflation process. We examine patterns in the time-varying covariation among product-level inflation rates that aggregate up to industry-level inflation rates that in turn aggregate up to the overall inflation rate. The aggregate inflation volatility closely tracks the time path of this covariation, which is seen to be driven primarily by the variances of common shocks shared by all products, and by the covariances between idiosyncratic product-level shocks. We formulate a forecasting system that comprises of models for mean inflation rate and its variance, and exploit the index structure of the aggregate inflation rate using the HTS framework. Using a dynamic model selection approach to forecasting, we obtain forecasts that are between 9 and 155 % more accurate than a SARIMA-GARCH(1,1) for the aggregate inflation volatility. Chapter 3 is on improving forecasts using forecast combinations. The paper documents the software implementation of the open source R package for forecast combination that we coded and published on the official R package depository, CRAN. The GeomComb package is the only R package that covers a wide range of different popular forecast combination methods. We implement techniques from 3 broad categories: (a) simple non-parametric methods, (b) regression-based methods, and (c) geometric (eigenvector) methods, allowing for static or dynamic estimation of each approach. Using S3 classes/methods in R, the package provides a user-friendly environment for applied forecasting, implementing solutions for typical issues related to forecast combination (multicollinearity, missing values, etc.), criterion-based optimisation for several parametric methods, and post-fit functions to rationalise and visualise estimation results. The package has been listed in the official R Task Views for Time Series Analysis and for Official Statistics. The brief empirical application in the paper illustrates the package’s functionality by estimating forecast combination techniques for monthly UK electricity supply. Chapter 4 introduces HTS forecasting and forecast combination to a healthcare staffing context. A slowdown of healthcare budget growth in the UK that does not keep pace with growth of demand for hospital services made efficient cost planning increasingly crucial for hospitals, in particular for staff which accounts for more than half of hospitals’ expenses. This is facilitated by accurate forecasts of patient census and churn. Using a dataset of more than 3 million observations from a large UK hospital, we show how HTS forecasting can improve forecast accuracy by using information at different levels of the hospital hierarchy (aggregate, emergency/electives, divisions, specialties), compared to the naïve benchmark: the seasonal random walk model applied to the aggregate. We show that forecast combination can improve accuracy even more in some cases, and leads to lower forecast error variance (decreasing forecasting risk). We propose a comprehensive parametric approach to use forecasts in a nurse staffing model that has the aim of minimising cost while satisfying that the care requirements (e.g. nurse hours per patient day thresholds) are met.

Cette thèse porte sur l’étude de la mémoire longue de la volatilité des rendements d’actions. Dans une première partie, nous apportons une interprétation de la mémoire longue en termes de comportement d’agents grâce à un modèle de volatilité à mémoire longue dont les paramètres sont reliés aux comportements hétérogènes des agents pouvant être rationnels ou à rationalité limitée. Nous déterminons de manière théorique les conditions nécessaires à l’obtention de mémoire longue. Puis nous calibrons notre modèle à partir des séries de volatilité réalisée journalière d’actions américaines de moyennes et grandes capitalisations et observons le changement de comportement des agents entre la période précédant l’éclatement de la bulle internet et celle qui la suit. La deuxième partie est consacrée à la prise en compte de la mémoire longue en gestion de portefeuille. Nous commençons par proposer un modèle de choix de portefeuille à volatilité stochastique dans lequel la dynamique de la log-volatilité est caractérisée par un processus d’Ornstein-Uhlenbeck. Nous montrons que l’augmentation du niveau d’incertitude sur la volatilité future induit une révision du plan de consommation et d’investissement. Puis dans un deuxième modèle, nous introduisons la mémoire longue grâce au mouvement brownien fractionnaire. Cela a pour conséquence de transposer le système économique d’un cadre markovien à un cadre non-markovien. Nous fournissons donc une nouvelle méthode de résolution fondée sur la technique de Monte Carlo. Puis, nous montrons toute l’importance de modéliser correctement la volatilité et mettons en garde le gérant de portefeuille contre les erreurs de spécification de modèle. / This PhD thesis is about the study of the long memory of the volatility of asset returns. In a first part, we bring an interpretation of long memory in terms of agents’ behavior through a long memory volatility model whose parameters are linked with the bounded rational agents’ heterogeneous behavior. We determine theoretically the necessary condition to get long memory. Then we calibrate our model from the daily realized volatility series of middle and large American capitalization stocks. Eventually, we observe the change in the agents’ behavior between the period before the internet bubble burst and the one after. The second part is devoted to the consideration of long memory in portfolio management. We start by suggesting a stochastic volatility portfolio model in which the dynamics of the log-volatility is characterized by an Ornstein-Uhlenbeck process. We show that when the uncertainty of the future volatility level increases, it induces the revision of the consumption and investment plan. Then in a second model, we introduce a long memory component by the use of a fractional Brownian motion. As a consequence, it transposes the economic system from a Markovian framework to a non-Markovian one. So we provide a new resolution method based on Monte Carlo technique. Then we show the high importance to well model the volatility and warn the portfolio manager against the misspecification errors of the model.