Dependence structures in financial time series: a chaos-theoretic approach

Of much interest in financial econometrics is the recovery of joint distributional behaviour of collections of contemporaneous financial time series, e.g., two related commodity price series, or two asset returns series. An approach to model their joint behaviour is to use copulas. Essentially, copulas are selected on the basis of a measure of correlation between the two series and are made to match their marginal properties. Of course, generalisations exist for more than two series. A possible limitation of this approach is that only linear correlations between series might be captured. We consider incorporating more general dependence structures, through the use of the correlation integral (as in the BDS test), as a means to refine the choice of candidate copulas in an empirical situation.Archimedean copula; copula; correlation integral; dependence; Poisson convergence

Outlier Treatment and Robust Approaches for Modeling Electricity Spot Prices

We investigate the effects of outlier treatment on the estimation of the seasonal component and stochastic models in electricity markets. Typically, electricity spot prices exhibit features like seasonality, mean-reverting behavior, extreme volatility and the occurrence of jumps and spikes. Hence, an important issue in the estimation of stochastic models for electricity spot prices is the estimation of a component to deal with trends and seasonality in the data. Unfortunately, in regression analysis, classical estimation routines like OLS are very sensitive to extreme observations and outliers. Improved robustness of the model can be achieved by (a) cleaning the data with some reasonable procedure for outlier rejection, and then (b) using classical estimation and testing procedures on the remainder of the data. We examine the effects on model estimation for different treatment of extreme observations in particular on determining the number of outliers and descriptive statistics of the remaining series after replacement of the outliers. Our findings point out the substantial impact the treatment of extreme observations may have on these issues.Electricity; price modeling; seasonal decomposition; price spike

Binary time series generated by chaotic logistic maps

This paper examines stochastic pairwise dependence structures in binary time series obtained from discretised versions of standard chaotic logistic maps. It is motivated by applications in communications modelling which make use of so-called chaotic binary sequences. The strength of non-linear stochastic dependence of the binary sequences is explored. In contrast to the original chaotic sequence, the binary version is non-chaotic with non-Markovian non-linear dependence, except in a special case. Marginal and joint probability distributions, and autocorrelation functions are elicited. Multivariate binary and more discretised time series from a single realisation of the logistic map are developed from the binary paradigm. Proposals for extension of the methodology to other cases of the general logistic map are developed. Finally, a brief illustration of the place of chaos-based binary processes in chaos communications is given.Binary sequence; chaos; chaos communications; dependence; discretisation; invariant distribution; logistic map; randomness

Statistical Tests for Lyapunov Exponents of Deterministic Systems

In order to develop statistical tests for the Lyapunov exponents of deterministic dynamical systems, we develop bootstrap tests based on empirical likelihood for percentiles and expectiles of strictly stationary processes. The percentiles and expectiles are estimated in terms of asymmetric least deviations and asymmetric least squares methods. Asymptotic distributional properties of the estimators are established.Bootstrap, chaos, empirical likelihood, expectile, percentile.

Does Company Specific News Effect the US, UK, and Australian Markets within 60 minutes?

The efficient market hypothesis states that an efficient market rapidly incorporates all available information into the price of the asset. It has been well established that no market, particularly the stock market, is truly efficient as there are too many traders with differing strategies, and differing access to and interpretation of information. Despite this there is considerable evidence that the stock market does assimilate new information into prices. There has however been little research into the intraday effect of company specific news. In this paper we investigate the intraday effect of company specific news on the US, UK, and Australian markets. We use a scheme to determine whether the markets react to news by determining the likelihood of certain events occurring, and the likelihood of news occurring within 60 minutes of them, and compare the two. We find that there is strong evidence that these markets do react to news within 60 minutes, and indicate which events are most likely to correlate to news.Return; Volatility; News

Adaptive orthogonal series estimation in additive stochastic regression models

In this paper, we consider additive stochastic nonparametric regression models. By approximating the nonparametric components by a class of orthogonal series and using a generalized cross-validation criterion, an adaptive and simultaneous estimation procedure for the nonparametric components is constructed. We illustrate the adaptive and simultaneous estimation procedure by a number of simulated and real examples.Adaptive estimation; additive model; dependent process; mixing condition; nonlinear time series; nonparametric regression; orthogonal series; strict stationarity; truncation parameter

Statistical tests for Lyapunov exponents of deterministic systems.

In order to develop statistical tests for the Lyapunov exponents of deterministic dynamical systems, we develop bootstrap tests based on empirical likelihood for percentiles and expectiles of strictly stationary processes. The percentiles and expectiles are estimated in terms of asymmetric least deviations and asymmetric least squares methods. Asymptotic distributional properties of the estimators are established.

Exact Maximum Likelihood estimation for the BL-GARCH model under elliptical distributed innovations

In this paper, we discuss the class of Bilinear GATRCH (BL-GARCH) models which are capable of capturing simultaneously two key properties of non-linear time series : volatility clustering and leverage effects. It has been observed often that the marginal distributions of such time series have heavy tails ; thus we examine the BL-GARCH model in a general setting under some non-Normal distributions. We investigate some probabilistic properties of this model and we propose and implement a maximum likelihood estimation (MLE) methodology. To evaluate the small-sample performance of this method for the various models, a Monte Carlo study is conducted. Finally, within-sample estimation properties are studied using S&P 500 daily returns, when the features of interest manifest as volatility clustering and leverage effects.BL-GARCH process, elliptical distribution, leverage effects, Maximum Likelihood, Monte Carlo method, volatility clustering.