Stochastic chaos or ARCH effects in stock series?

Computational Science – ICCS 2008

2008

Abstract. We present a nonlinear structural stock market model which is a nonlinear deterministic process buffeted by dynamic noise. The market is composed of two typical trader types, the rational fundamentalists believing that the price of an asset is determined solely by its fundamental value and the boundedly rational noise traders governed by greed and fear. The interaction among heterogeneous investors determines the dynamics and the statistical properties of the system. We find the model is able to generate time series that exhibit dynamical and statistical properties closely resembling those of the S&P500 index, such as volatility clustering, fat tails (leptokurtosis), autocorrelation in square and absolute return, larger amplitude, crashes and bubbles. We also investigate the nonlinear dependence structure in our data. The results indicate that the GARCH-type model cannot completely account for all nonlinearity in our simulated market, which is thus consistent with the results from real markets. It seems that the nonlinear structural model is more powerful to give a satisfied explanation to market behavior than the traditional stochastic approach.

Section: Resultsmentioning

confidence: 99%

Heterogeneity and Endogenous Nonlinearity in an Artificial Stock Model

Shang

Computational Science – ICCS 2008

2008

“…(Sentana and Fiorentini, 2001;Kyrtsou and Terraza, 2002;Dufour et al, 2004). However, ARCH effect test is a strict heteroscedasticity test of residual.…”

Section: Heteroscedasticitymentioning

confidence: 99%

Crytic period analysis model of hydrological process and its application

Lin

Qian

2009

Hydrological Processes

Abstract:It is difficult to analyse the crytic period of the hydrological process, because hydrological time series is probably characterized by heteroscedasticity. To find out the crytic period, a model is constructed as follows: (1) after using zero-mean transformation for the data, to do Augmented Dickey-Fuller stationary test for the sequence, to build the corresponding AR(p) model and then to do ARCH effects test and white noise test for residual series; (2) for those time series that cannot pass through ARCH test, using logarithm transformation to reduce the heteroscedasticity, and then to redo step (1) until they pass through ARCH test and stationary test; (3) using periodogram analysis to determine all the possible the prime periods and further to put forward three kinds of tests to determine significance level of those prime periods. As examples, the hydrological processes of streamflow from 1784 to 1997 for the gauging stations of Alaer and Xinquman along Tarim River are analysed. After reducing their heteroscedasticity, AR(4) and AR(2) models are developed, respectively. Our results show that the streamflows from the two gauging stations have the same cryptic period of 42Ð7 years. Furthermore, the reliability for the crytic period model is testified by variance analysis, which shows that the crytic period model is useful and reliable.

“…There have been some meaningful results about chaos system with stochastic disturbances [13][14][15]. In [13], the ergodic theory and stochastic noise are considered.…”

Section: Introductionmentioning

confidence: 99%

“…In [13], the ergodic theory and stochastic noise are considered. Timedelay feedback control of the Van der Pol oscillator under the influence of white noise is investigated in [14].…”

Section: Introductionmentioning

confidence: 99%

Passivity-Sliding Mode Control of Uncertain Chaotic Systems with Stochastic Disturbances

Liu

Journal of Control Science and Engineering

2014

This paper is concerned with the stabilization problem of uncertain chaotic systems with stochastic disturbances. A novel sliding function is designed, and then a sliding mode controller is established such that the trajectory of the system converges to the sliding surface in a finite time. Using a virtual state feedback control technique, sufficient condition for the mean square asymptotic stability and passivity of sliding mode dynamics is derived via linear matrix inequality (LMI). Finally, a simulation example is presented to show the validity and advantage of the proposed method.