A few characteristic exponents describing power law behaviors of roughness, coherence and persistence in stochastic time series are compared to each other. Relevant techniques for analyzing such time series are recalled in order to distinguish how the various exponents are measured, and what basic differences exist between each one. Financial time series, like the JPY/DEM and USD/DEM exchange r...

The traditional models of price, and its statistical signatures are often based on limiting assumptions, such as linearity. Moreover, the model developer is faced with the model selection problem, and model uncertainty. In this paper we introduce a method based on Grammatical Evolution (GE) to evolve models for predicting financial returns, and we examine the profitability of these models. Our ...

A simple quantitative measure of the self-similarity in time-series in general and in the stock market in particular is the scaling behavior of the absolute size of the jumps across lags of size k. A stronger form of self-similarity entails not only that this mean absolute value, but also the full distributions of lag-k jumps have a scaling behavior characterized by the above Hurst exponent. In...

Time series of prices as well as time series based on prices or time series which describe prices and their dynamism are called financial time series. These time series have some typical properties. There are two basic assumptions: normality and linearity of log returns of the financial time series. The distributions of log returns are usually skewed and more peaked that the normal distribution...

4 GARCH Models 7 4.1 Basic GARCH Specifications . . . . . . . . . . . . . . . . . . . 8 4.2 Diagnostic Checking . . . . . . . . . . . . . . . . . . . . . . . 11 4.3 Regressors in the Variance Equation . . . . . . . . . . . . . . . 12 4.4 The GARCH–M Model . . . . . . . . . . . . . . . . . . . . . . 12 4.5 The Threshold GARCH (TARCH) Model . . . . . . . . . . . . 12 4.6 The Exponential GARCH (EG...

A clustering procedure is introduced based on the Hausdorff distance as a similarity measure between clusters of elements. The method is applied to the financial time series of the Dow Jones industrial average (DJIA) index to find companies that share a similar behavior. Comparisons are made with other linkage algorithms. r 2007 Elsevier B.V. All rights reserved.

To reduce risk, investors seek assets that have high expected return and are unlikely to move in tandem. Correlation measures are generally used to quantify the connections between equities. The 2008 financial crisis, and its aftermath, demonstrated the need for a better way to quantify these connections. We present a machine learning-based method to build a connectedness matrix to address the ...

Time series of financial asset values exhibit well known statistical features such as heavy tails and volatility clustering. We propose a nonparametric extension of the classical Peaks-Over-Threshold method from Extreme Value Theory to fit the time varying volatility in situations where the stationarity assumption may be violated by erratic changes of regime, say. As a result, we provide a meth...