Three Essays on Nonlinear Time-series Econometrics

Abstract

This thesis is submitted in three chapters. Chapter 1 considers a regime-switching Levy framework, where all parameter values depend on the value of a continuous time Markov chain as per Chevallier and Goutte (2017), is employed to study US Corporate Option-Adjusted Spreads (OASs). For modelling purposes we assume a Normal Inverse Gaussian distribution, allowing heavier tails and skewness. After the Expectation - Maximization algorithm is applied to this general class of regime switching models, we compare the obtained results with time series models without jumps, including one with regime switching and one without. We find that a regime-switching Levy model clearly defines two regimes for A-, AA-, and AAA-rated OASs. We find further evidence of regime-switching effects, with data showing relatively pronounced jump intensity around the time of major crisis periods, thereby confirming the presence and importance of volatility regimes. Results indicate that ignoring the complex and dynamic dependence structure in favour of certain model assumptions may lead to a significant underestimation of risk. To the best of our knowledge, this study is the first time that Markov-switching Levy models have been employed to analyze the structure of option-adjusted spreads. Chapter 2 considers a little-used dataset to study the Japan's Real Estate Investment Trusts (REITs) market. We make use of copula theory and test for dependence between equity and REIT returns using several popular copula families. The copula families in our specification were: Gaussian, Student-$t$, Clayton, Frank, and Gumbel. The p-values were computed using parametric bootstrap replications. We motivate the argument presented, and provide the goodness-of-fit test results based on the Rosenblatt transform. We find that the dependence between the innovations of JREIT Composite and JREIT Office returns can be modelled by a Student-$t$ copula with 2.7 degrees of freedom and correlation parameter $\hat{\nu}$ = 0.93. All other models are rejected. To the best of our knowledge, this study represents the first time that copula theory has been applied to study REITs in Japan. Chapter 3 critiques a recent contribution to the financial econometrics literature, namely Chu et al. (2017), which provides the first examination of the time-series price behaviour of the most popular cryptocurrencies. We argue that insufficient attention was paid to correctly diagnosing the distribution of GARCH innovations. When these data issues are controlled for, their results lack robustness and may lead to either underestimation or overestimation of future risks. The main aim of this paper therefore is to provide an improved econometric specification. Particular attention is paid to correctly diagnosing the distribution of GARCH innovations by means of Kolmogorov type non-parametric tests and Khmaladze's martingale transformation. Numerical computation is carried out by implementing a Gauss-Kronrod quadrature. Parameters of GARCH models are estimated using maximum likelihood. For calculating p-values, the parametric bootstrap method is used. Further reference is made to the merits and demerits of statistical techniques presented in the related and recently published literature.