Behavior Of Financial Time Series Research Articles

Binary indices of time series complexity measures and entropy plane

Complexity of time series is an important feature of dynamical systems such as financial systems. In order to bring out the complete non-linear behavior of financial time series, non-linear tools of complexity measurement like entropy measures are indispensable. Sample entropy (SampEn) and distribution entropy (DistEn) are popular methods of assessing the complexity in various fields. However, both sample entropy and distribution entropy show some limitations in detecting the complexity of stock markets. Therefore, we use two entropies as binary indices to analyze the complexity of time series and structure the entropy plane. In order to further improve the accuracy of the research results, we take the embedding dimension m as the variable, expand the entropy point into the entropy curve for further research. Furthermore, considering the shortcomings of sample entropy and distribution entropy in practical application, we generalize them by (i) replacing sample entropy and distribution entropy with multi-scale sample entropy and multi-scale distribution entropy; (ii) generalizing Shannon entropy as Tsallis entropy. Also, scale factor τ and entropic index q are taken respectively as variables to get the entropy curves. By using the artificial data, we confirm the rationality of using entropy points and entropy curves to study the complexity of time series. Finally, we apply this method to measure the complexity of real world financial time series, the results show that the entropy curves plotted by the financial time series obtained from different areas have significant differences.

A deep increasing–decreasing-linear neural network for financial time series prediction

Several neural network models have been proposed in the literature to predict the future behavior of financial time series. However, an intrinsic limitation arises from this particular prediction task with modeling via neural networks, since the prediction, when sampled in daily frequency, have 1-step-ahead delay with respect to real time series observations. In order to overcome such drawback, we present a deep increasing–decreasing-linear neural network (wherein each layer is composed of a set of increasing–decreasing-linear processing units) to predict the behavior of financial time series. In addition, we present a learning process to train the proposed model using a descending gradient-based approach. In order to assess the model’s prediction performance, we use twelve financial time series from relevant stock markets around the world. The obtained results show that the proposed model have competitiveness, in terms of predictive performance, and have better effectiveness when compared to recent models presented in the literature of time series prediction.

A simulation study on the distributions of disturbances in the GARCH model

AbstractGeneralized autoregressive conditional heteroskedastic (GARCH) model is a standard approach to study the volatility behaviour of financial time series. The original specification of GARCH model is developed based on Normal distribution for the disturbances, which cannot accommodate fat-tailed properties commonly existing in financial time series. Consequently, the resulting estimates are not efficient. Traditionally, the Student’s t-distribution and General Error Distribution (GED) are used alternatively to solve this problem. However, a recent study points out that those alternative distributions lack stability under aggregation. This leaves the appropriate choice of the distribution of disturbances in the GARCH model still an open question. In this paper, we present the theoretical features and desirability of the tempered stable distribution. Further, we conduct a series of simulation studies to demonstrate that the GARCH model with this distribution consistently outperforms those with the Norm...

Gibbs sampling approach to regime switching analysis of financial time series

We will introduce a Monte Carlo type inference in the framework of Markov Switching models to analyse financial time series, namely the Gibbs Sampling. In particular we generalize the results obtained in Albert and Chib (1993), Di Persio and Vettori (2014) and Kim and Nelson (1999) to take into account the switching mean as well as the switching variance case. In particular the volatility of the relevant time series will be treated as a state variable in order to describe the abrupt changes in the behaviour of financial time series which can be implied, e.g., by social, political or economic factors. The accuracy of the proposed analysis will be tested considering financial dataset related to the U.S. stock market in the period 2007–2014.

A Wavelet Based Approach for Multi-Scale Analysis and Predictability of Stock Returns

The aim of this paper is to demonstrate the effectiveness of alternative methods from the time-frequency domain in analyzing the behavior of financial time series. Traditional spectral methods are limited to frequency domain localization of information where time domain information is completely lost. Use of wavelet based techniques helps in retaining both frequency and time domain information. Stock market data is analyzed at different levels of time-scale resolution which makes it possible to perform a scale by scale analysis thus enabling us to analyze the data at different frequency oscillations together with localized time intervals. Multiresolution analysis of the discrete wavelet transform class is used to transform the BSE returns series into different sets of coefficients where each set contains coefficients that provide information corresponding to a particular time-scale resolution. The main coefficient series from the transformed time-series is used to make forecasts and the result is then compared with the result when forecasting is done directly using the original returns data. On the analyzed returns data we proved that forecasting using the wavelet transformed algorithm provides much accurate results as compared to forecasting applied directly to the original returns series The effectiveness of a wavelet based cross-correlation technique in analyzing the relation between two markets at different levels of time-frequency resolution is also demonstrated. This approach of multi-scale decomposition of a time-series using wavelet methodology allows us to detect changes in stock market behavior from a time-scale perspective where the data can be analyzed at different time horizons and frequencies simultaneously.

Multifractal diffusion entropy analysis: Optimal bin width of probability histograms

In the framework of Multifractal Diffusion Entropy Analysis we propose a method for choosing an optimal bin-width in histograms generated from underlying probability distributions of interest. The method presented uses techniques of Rényi’s entropy and the mean squared error analysis to discuss the conditions under which the error in the multifractal spectrum estimation is minimal. We illustrate the utility of our approach by focusing on a scaling behavior of financial time series. In particular, we analyze the S&P500 stock index as sampled at a daily rate in the time period 1950–2013. In order to demonstrate a strength of the method proposed we compare the multifractal δ-spectrum for various bin-widths and show the robustness of the method, especially for large values of q. For such values, other methods in use, e.g., those based on moment estimation, tend to fail for heavy-tailed data or data with long correlations. Connection between the δ-spectrum and Rényi’s q parameter is also discussed and elucidated on a simple example of multiscale time series.

Misspecification Testing for the Conditional Distribution Model in GARCH-Type Processes

In this article, we study goodness of fit tests for some distributions of the innovations which are usually adopted to explain the behavior of financial time series. Inference is developed in the context of GARCH-type models. Functional bootstrap tests are employed, assuming that the conditional means and variances of the model are correctly specified. The performances of the functional tests are assessed with a Monte Carlo experiment, based on some of the most common distributions adopted in the financial framework. The results of an application to the series of squared residuals from a PARCH(1,1) model fitted to a series of foreign exchange rates returns are also shown.

A statistical physics view of financial fluctuations: Evidence for scaling and universality

The unique scaling behavior of financial time series have attracted the research interest of physicists. Variables such as stock returns, share volume, and number of trades have been found to display distributions that are consistent with a power-law tail. We present an overview of recent research joining practitioners of economic theory and statistical physics to try to understand better some puzzles regarding economic fluctuations. One of these puzzles is how to describe outliers, i.e. phenomena that lie outside of patterns of statistical regularity. We review recent research, which suggests that such outliers may not in fact exist and that the same laws seem to govern outliers as well as day-to-day fluctuations.

Statistical regularities in the return intervals of volatility

We discuss recent results concerning statistical regularities in the return intervals of volatility in financial markets. In particular, we show how the analysis of volatility return intervals, defined as the time between two volatilities larger than a given threshold, can help to get a better understanding of the behavior of financial time series. We find scaling in the distribution of return intervals for thresholds ranging over a factor of 25, from 0.6 to 15 standard deviations, and also for various time windows from one minute up to 390 min (an entire trading day). Moreover, these results are universal for different stocks, commodities, interest rates as well as currencies. We also analyze the memory in the return intervals which relates to the memory in the volatility and find two scaling regimes, � � ∗ with α2 =0 .92 ± 0.04; these exponent values are similar to results of Liu et al. for the volatility. As an application, we use the scaling and memory properties of the return intervals to suggest a possibly useful method for estimating risk.

Dating Breaks in the Extremal Behavior of Financial Time Series

This paper studies the extremal behavior of emerging market bonds in relation to equities and bond returns of developed markets. Returns on emerging markets fixed income investments are known to behave like equity returns, yet many studies have used techniques that do not account for their thick tailed behavior. Since emerging markets are characterized by highly turbulent periods, we develop in this paper a test statistic for testing and dating breaks in the tail behavior of a series. Our test for extremal breaks is valid for GARCH data and for multiple breaks where the number of breaks can be known or unknown. Our finding is that while extremal movements of emerging market debt is characterized by three regimes with breakdates corresponding to the Asian/Russian crisis of 1997/1998 and the Argentinian crisis of 2001, extremal movements of equities and bond returns of developed markets are characterized by only a single break in 1997/1998. These findings and the methods introduced here have implications for value at risk methodologies that assume time invariant tail characteristics.

Likelihood inference in BL-GARCH models

The paper presents a procedure based on the EM algorithm for the indirect estimation of the parameters of BiLinear GARCH (BL-GARCH) models. BL-GARCH generalize the class of GARCH models by considering interactions of past shocks and volatilities in the conditional variance equation. In this way the response of the conditional variance to past information becomes asymmetric allowing to account for the so called leverage effect, typically characterizing the behaviour of financial time series. The results of an application to a time series of stock market returns are presented.