Non-linear time series models with applications to financial data

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel UniversityThe 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

Modelling stock volatilities during financial crises: A time varying coefficient approach

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 decades in the volatility dynamics, including the underlying volatility persistence and volatility spillover structure. Using daily data from several key stock market indices, the results of our bivariate GARCH models show the existence of time varying correlations as well as time varying shock and volatility spillovers between the returns of FTSE and DAX, and those of NIKKEI and Hang Seng, which became more prominent during the recent financial crisis. Our theoretical considerations on the time varying modelwhich provides the platformupon which we integrate our multifaceted empirical approaches are also of independent interest. In particular, we provide the general solution for time varying asymmetric GARCH specifications, which is a long standing research topic. This enables us to characterize these models by deriving, first, their multistep ahead predictors, second, the first two time varying unconditional moments, and third, their covariance structure.Open Access funded by European Research Council under a Creative Commons license

Are there Structural Breaks in Realized Volatility?

Constructed from high-frequency data, realized volatility (RV) provides an efficient estimate of the unobserved volatility of financial markets. This paper uses a Bayesian approach to investigate the evidence for structural breaks in reduced form time-series models of RV. We focus on the popular heterogeneous autoregressive (HAR) models of the logarithm of realized volatility. Using Monte Carlo simulations we demonstrate that our estimation approach is effective in identifying and dating structural breaks. Applied to daily S&P 500 data from 1993-2004, we find strong evidence of a structural break in early 1997. The main effect of the break is a reduction in the variance of log-volatility. The evidence of a break is robust to different models including a GARCH specification for the conditional variance of log(RV).realized volatility, change point, marginal likelihood, Gibbs sampling, GARCH

Asymmetric effects and long memory in the volatility of Dow Jones stocks

Does volatility reflect a continuous reaction to past shocks or changes in the markets induce shifts in the volatility dynamics? In this paper, we provide empirical evidence that cumulated price variations convey meaningful information about multiple regimes in the realized volatility of stocks, where large falls (rises) in prices are linked to persistent regimes of high (low) variance in stock returns. Incorporating past cumulated daily returns as a explanatory variable in a flexible and systematic nonlinear framework, we estimate that falls of different magnitudes over less than two months are associated with volatility levels 20% and 60% higher than the average of periods with stable or rising prices. We show that this effect accounts for large empirical values of long memory parameter estimates. Finally, we analyze that the proposed model significantly improves out of sample performance in relation to standard methods. This result is more pronounced in periods of high volatility.Realized volatility, long memory, nonlinear models, asymmetric effects, regime switching, regression trees, smooth transition, value-at-risk, forecasting, empirical finance.

Asymmetric dynamics in the correlations of global equity and bond returns

JEL Classification: F3, G1, C5Correlation, International Finance, Variance Targeting

How Volatile is ENSO?

The El Niños Southern Oscillations (ENSO) is a periodical phenomenon of climatic interannual variability which could be measured through either the Southern Oscillation Index (SOI) or the Sea Surface Temperature (SST) Index. The main purpose of this paper is to analyze these two indexes in order to capture ENSO volatility. The empirical results show that both the ARMA(1,1)-GARCH(1,1) and ARMA(3,2)-GJR(1,1) models are suitable for modelling ENSO volatility. Moreover, 1998 is a turning point for the volatility of SOI, and the ENSO volatility has became stronger since 1998 which indicates that the ENSO strength has increased.GARCH;Volatility;EGARCH;GJR;ENSO;SOI;SOT

Measuring Asymmetry and Persistence in Conditional Volatility in Real Output: Evidence from Three East Asian Tigers Using a Multivariate GARCH approach

We search for evidence of conditional volatility in the quarterly real GDP growth rates of three East Asian tigers: Singapore, Hong Kong and Taiwan. The widely accepted exponential GARCH-type model is used to capture the existence of asymmetric volatility and the potential structural break points in the volatility. We find evidence of asymmetry and persistence in the volatility of GDP growth rates. It is noted that the identified structural breakpoints of volatility correspond reasonably well to the historical economic and political events in these economies. Policy implications are discussed.East Asia, Real Output, GARCH, structural changes, asymmetric volatility

The dynamic impact of uncertainty in causing and forecasting the distribution of oil returns and risk

The aim of this study is to analyze the relevance of recently developed news-based measures of economic policy and equity market uncertainty in causing and predicting the conditional quantiles of crude oil returns and risk. For this purpose, we studied both the causality relationships in quantiles through a non-parametric testing method and, building on a collection of quantiles forecasts, we estimated the conditional density of oil returns and volatility, the out-of-sample performance of which was evaluated by using suitable tests. A dynamic analysis shows that the uncertainty indexes are not always relevant in causing and forecasting oil movements. Nevertheless, the informative content of the uncertainty indexes turns out to be relevant during periods of market distress, when the role of oil risk is the predominant interest, with heterogeneous effects over the different quantiles levels.http://www.elsevier.com/locate/physa2019-10-01hj2018Economic

How Volatile is ENSO?

The El Niños Southern Oscillations (ENSO) is a periodical phenomenon of climatic interannual variability, which could be measured through either the Southern Oscillation Index (SOI) or the Sea Surface Temperature (SST) Index. The main purpose of this paper is to analyze these two indexes in order to capture the volatility inherent in ENSO. The empirical results show that both the ARMA(1,1)-GARCH(1,1) and ARMA(3,2)-GJR(1,1) models are suitable for modelling ENSO volatility accurately. The empirical results show that 1998 is a turning point, which indicates that the ENSO strength has increased since 1998. Moreover, the increasing ENSO strength is due to the increase in greenhouse gas emissions. The ENSO strengths for SST are predicted for the year 2030 to increase from 29.62% to 81.5% if global CO2 emissions increase by 40% to 110%, respectively. This indicates that we will be faced with an even stronger El Nino or La Nina in the future if global greenhouse gas emissions continue to increase unabated.ENSO; SOI; SOT; Greenhouse Gas Emissions; Volatility; GARCH; GJR; EGARCH

Modeling the Effect of Oil Price on Global Fertilizer Prices

The main purpose of this paper is to evaluate the effect of crude oil price on global fertilizer prices in both the mean and volatility. The endogenous structural breakpoint unit root test, the autoregressive distributed lag (ARDL) model, and alternative volatility models, including the generalized autoregressive conditional heteroskedasticity (GARCH) model, Exponential GARCH (EGARCH) model, and GJR model, are used to investigate the relationship between crude oil price and six global fertilizer prices. Weekly data for 2003-2008 for the seven price series are analyzed. The empirical results from ARDL show that most fertilizer prices are significantly affected by the crude oil price, which explains why global fertilizer prices reached a peak in 2008. We also find that that the volatility of global fertilizer prices and crude oil price from March to December 2008 are higher than in other periods, and that the peak crude oil price caused greater volatility in the crude oil price and global fertilizer prices. As volatility invokes financial risk, the relationship between oil price and global fertilizer prices and their associated volatility is important for public policy relating to the development of optimal energy use, global agricultural production, and financial integration.Volatility; Global fertilizer price; Crude oil price; Non-renewable fertilizers; Structural breakpoint unit root test