GARCH-based robust clustering of time series

3nopartially_openIn this paper we propose different robust fuzzy clustering models for classifying heteroskedastic (volatility) time series, following the so-called model-based approach to time series clustering and using a partitioning around medoids procedure. The proposed models are based on a GARCH parametric modelingof the time series, i.e. the unconditional volatility and the time-varying volatility GARCH representation of the time series. We first suggest a timid robustification of the fuzzy clustering. Then, we propose three robust fuzzy clustering models belonging to the so-called metric, noise and trimmed approaches, respectively. Each model neutralizes the negative effects of the outliers in the clustering process in a different manner. In particular, the first robust model, based on the metric approach, achieves its robustness with respect to outliers by taking into account a “robust” distance measure; the second, based on the noise approach, achieves its robustness by introducing a noise cluster represented by a noise prototype; the third, based on the trimmed approach, achieves its robustness by trimming away a certain fraction of outlying time series. The usefulness and effectiveness of the proposed clustering models is illustrated by means of a simulation study and two applications in finance and economics.embargoed_20180131De Giovanni, Livia; D'Urso, Pierpaolo; Massari, RiccardoDE GIOVANNI, Livia; D'Urso, Pierpaolo; Massari, Riccard

Quantile Correlations: Uncovering temporal dependencies in financial time series

We conduct an empirical study using the quantile-based correlation function to uncover the temporal dependencies in financial time series. The study uses intraday data for the S\&P 500 stocks from the New York Stock Exchange. After establishing an empirical overview we compare the quantile-based correlation function to stochastic processes from the GARCH family and find striking differences. This motivates us to propose the quantile-based correlation function as a powerful tool to assess the agreements between stochastic processes and empirical data

On the Robustness of Ljung-Box and McLeod-Li Q Tests: A Simulation Study

In financial time series analysis, serial correlations and the volatility clustering effect of asset returns are commonly checked by Ljung-Box and McLeod-Li Q tests and filtered by ARMA-GARCH models. However, this simulation study shows that both the size and power performance of these two tests are not robust to heavily tailed data. Further, these Q tests may reject processes without ARMA-GARCH structures simply because of nonlinearity and conditionally heteroskedastic higher-order moments. These results imply that, to avoid misleading interpretations on time series data, these two tests should be used with care in practical applications.ARMA-GARCH

Stock returns, volume and stock price volatility : An empirical firm-level analysis

This paper examines the relation between stock returns and stock market volatility in an autoregressive conditional heteroskedasticity model framework. Using a GARCH-M model, we examine the relation between stock returns, volume and stock price volatility. Using daily returns from January 1990 until December 1999 for a sample of 20 firms listed on the Tokyo Stock Exchange, first of all, we examine if there exists a risk premium for stock return volatility. Second, using daily volume and a new measure of daily stock price volatility as a proxy for the amount of daily arrival of information, we try to find out how contemporaneous and lagged trading volume and volatility explain conditional volatility. As a result we find that (1) stock returns are positively related to the conditional variance but the correlation is not always significant. Only when introducing contemporaneous volume in the variance equation, the GARCH parameter in the mean equation becomes significant; (2) contemporaneous trading volume is positively correlated to the conditional variance and highly statistically significant, while lagged trading volume has a mixed impact on the conditional variance; (3) we find evidence that our new measure of stock price volatility using the daily high, low and closing price can catch information in return volatility. Both contemporaneous and lagged stock price volatility are positively related with the conditional variance and are highly significant. Volatility models for daily returns are therefore improved by including information such as the daily high and low price.　Together with volume our measure of stock price volatility can be very useful in explaining volatility clustering in daily returns; (4) introducing stock price volatility and volume in the GARCH variance equation reduces the persistence and significance of variance considerably but does not turn them insignificant. After controlling for the rate of information flow using volume and volatility, lagged squared residuals still contribute additional information about the variance of the stock return process. This is in contrast with the research of Lamoureux and Lastrapes (1990) who found empirical evidence that the ARCH effects vanish when volume is included as an explanatory variable in the conditional variance equation.松谷勉教授古稀記念特

The volatility of realized volatility

Using unobservable conditional variance as measure, latent-variable approaches, such as GARCH and stochastic-volatility models, have traditionally been dominating the empirical finance literature. In recent years, with the availability of high-frequency financial market data modeling realized volatility has become a new and innovative research direction. By constructing "observable" or realized volatility series from intraday transaction data, the use of standard time series models, such as ARFIMA models, have become a promising strategy for modeling and predicting (daily) volatility. In this paper, we show that the residuals of the commonly used time-series models for realized volatility exhibit non-Gaussianity and volatility clustering. We propose extensions to explicitly account for these properties and assess their relevance when modeling and forecasting realized volatility. In an empirical application for S&P500 index futures we show that allowing for time-varying volatility of realized volatility leads to a substantial improvement of the model's fit as well as predictive performance. Furthermore, the distributional assumption for residuals plays a crucial role in density forecasting. Klassifikation: C22, C51, C52, C5

Specification Testing for Multivariate Time Series Volatility Models

Volatility models have been playing an important role in economics and finance. Using a multivariate generalized spectral approach, we propose a new class of generally applicable omnibus tests for univariate and multivariate volatility models. Both GARCH models and stochastic volatility models are covered. Our tests have a convenient asymptotic null N(0,1) distribution, and can detect a wide range of misspecifications for volatility dynamics. Distinct from the existing tests for volatility models, our tests are robust to higher order time-varying moments of unknown form (e.g., time-varying skewness and kurtosis). Our tests check a large number of lags and are therefore expected to be powerful against neglected volatility dynamics that occurs at higher order lags or display long memory properties. Despite using a large number of lags, our tests do not suffer much from loss of a large number of degrees of freedom, because our approach naturally discounts higher order lags, which is consistent with the stylized fact that economic or financial markets are more affected by the recent past events than by the remote past events. No specific estimation method is required, and parameter estimation uncertainty has no impact on the limit distribution of the test statistics. Moreover, there is no need to formulate an alternative volatility model, and only estimated standardized residuals are needed to implement our tests. We do not have to calculate tedious score functions or derivatives of volatility models with respect to estimated parameters, which are model-specific and are required in some existing popular tests for volatility models. We examine the finite sample performance of the proposed tests. An empirical application to some popular GARCH models for stock returns illustrates our approachGeneralized spectral derivative, Kernel, Multivariate generalized spectrum, Multivariate GARCH models, Nonlinear volatility dynamics, Robustness, Specification testing, Stochastic Volatility Model, Time-varying higher order moments of unknown form.

Modelling Environmental Risk

As environmental issues have become increasingly important in economic research and policy for sustainable development, firms in the private sector have introduced environmental and social issues in conducting their business activities. Such behaviour is tracked by the Dow Jones Sustainable Indexes (DJSI) through financial market indexes that are derived from the Dow Jones Global Indexes. The sustainability activities of firms are assessed using criteria in three areas, namely economic, environmental and social. Risk (or uncertainty) is analysed empirically through the use of conditional volatility models of investment in sustainability-driven firms that are selected through the DJSI. The empirical analysis is based on financial econometric models to determine the underlying conditional volatility, with the estimates showing that there is strong evidence of volatility clustering, short and long run persistence of shocks to the index returns, and asymmetric leverage between positive and negative shocks to returns.Environmental sustainability index, environmental risk, conditional volatility, Dow Jones Sustainability Indexes, GARCH, GJR, persistence, shocks, asymmetry, moment condition, log-moment condition.

Modelling and Forecasting Volatility of Returns on the Ghana Stock Exchange Using GARCH Models

This paper models and forecasts volatility (conditional variance) on the Ghana Stock Exchange using a random walk (RW), GARCH(1,1), EGARCH(1,1), and TGARCH(1,1) models. The unique ‘three days a week’ Databank Stock Index (DSI) is used to study the dynamics of the Ghana stock market volatility over a 10-year period. The competing volatility models were estimated and their specification and forecast performance compared with each other, using AIC and LL information criteria and BDS nonlinearity diagnostic checks. The DSI exhibits the stylized characteristics such as volatility clustering, leptokurtosis and asymmetry effects associated with stock market returns on more advanced stock markets. The random walk hypothesis is rejected for the DSI. Overall, the GARCH (1,1) model outperformed the other models under the assumption that the innovations follow a normal distribution.Ghana Stock Exchange; developing financial markets; volatility; GARCH model