Kernel methods for detecting the direction of time series

Summary. We propose two kernel based methods for detecting the time direction in empirical time series. First we apply a Support Vector Machine on the finitedimensional distributions of the time series (classification method) by embedding these distributions into a Reproducing Kernel Hilbert Space. For the ARMA method we fit the observed data with an autoregressive moving average process and test whether the regression residuals are statistically independent of the past values. Whenever the dependence in one direction is significantly weaker than in the other we infer the former to be the true one. Both approaches were able to detect the direction of the true generating model for simulated data sets. We also applied our tests to a large number of real world time series. The ARMA method made a decision for a significant fraction of them, in which it was mostly correct, while the classification method did not perform as well, but still exceeded chance level

Stylized facts of return series, robust estimates and three popular models of volatility

Financial return series of sufficiently high frequency display stylized facts such as volatility clustering, high kurtosis, low starting and slow-decaying autocorrelation function of squared returns and the so-called Taylor effect. In order to evaluate the capacity of volatility models to reproduce these facts, we apply both standard and robust measures of kurtosis and autocorrelation of squares to first-order Generalized Autoregressive Conditional Heteroscedasticity (GARCH), Exponential GARCH (EGARCH) and Autoregressive Stochastic Volaticity (ARSV) models. Robust measures provide a fresh view of stylized facts, which is useful because many financial time series can be viewed as being contaminated with outliers.