Surrogate Data Analysis and Stochastic Chaotic Modelling: Application to Stock Exchange Returns Series

We investigate for evidence of complex-deterministic dynamics in financial returns time series. By combining the Surrogate Data Analysis inferential framework with the MG-GARCH (Kyrtsou and Terraza, 2003) modelling approach, we examine whether the sequences are characterized by aperiodic and nonlinear deterministic cycles or pure randomness. Our results support the hypothesis of complex nonlinear and non-stochastic dynamics in the data generating processes. According to our approach, markets can be assumed to be highly complex, high-dimensional, open and dissipative dynamical systems that need feedback as well as other kinds of inputs in order to operate. These inputs may come in the guise of noise or news. The inputs may also control the evolution of the system dynamics and the knowledge of their nature may allow us to forecast the future states of the market with greater accuracy. To this extent the MG-GARCH model provides a valuable insight on how a feedback mechanism can operate within the structure of stock returns processes and explain stylized facts.MG-GARCH, Surrogate Data Analysis, Chaos, Complexity

The Effects of Terrorism and War on the Oil and Prices Stock Indices Relationship

This paper, investigates the effect war and terrorism, have on the covariance between oil prices and the indices of four major stock markets - the American S&P500 and the European DAX, CAC40 and FTSE100 - using nonlinear BEKK-GARCH type models. Findings reported herein indicate that the covariance between stock and oil returns is affected by war. A tentative explanation is that the two wars examined here, predispose investors and market agents for more profound and longer lasting effects. On the other hand, in the case of terrorist incidents that, vis-à-vis war, are of a more transitory nature and one-off security shocks, only the co-movement between CAC40, DAX and oil returns is affected. No significant impact for the same terrorist events is observed in the relationship between the S&P500, FTSE100 and oil returns. This difference in the reaction may tentatively be interpreted as indicating that the latter markets are more efficient in absorbing the impact of terrorist attacks.war, terrorism, crude oil, stock market returns, co-movement

A survey on cycles and chaos (part I)

There are two contracting viewpoints concerning the explanation of observed fluctuations in economic and financial markets. According to the first view (Newclassical) the main source of fluctuations is to be found in exogenous, random shocks to fundamentals. According to the second view (Keynesian) a significant part of observed fluctuations is caused by non-linear economic laws. Even in the absence of any external shocks, non-linear market laws can generate endogenous business fluctuations. The discovery of chaotic, seemingly random looking dynamical behaviour in simple deterministic models sheds important new light on this debate. In order to detect non-linear structures in economic and financial data a certain number of tests, some based on chaos theory, have been developed. In this paper, we will briefly discuss several statistical techniques devised to detect independence and non-linearity in time-series data (part I). In a next issue of the journal, we shall also try to make a simple presentation of the basic notions of chaos, and then describe the related econometric tools (part II)

The Impact of Information Signals on Market Prices when Agents have Non-linear Trading Rules

Several methods have been developed for filtering seasonal influences and extreme returns in financial and economic time series. The theoretical support for these approaches is rather questionable since it focuses on the effects of shocks on prices and not on their sources. Removing such effects modifies the true generating system of market dynamics because of the non-proportional character of non-linearity. Thus, taking into account that the underlying process of economic time series is highly non-linear we cannot be certain a priori what the impact of new information will be on the dynamic structure of a system. The main contribution of this paper is to demonstrate using the methodology of simulations the eventual distortions in time series data arising from the arrival of news when agents follow non-linear trading strategies. We argue that if news can really modify the dynamical behaviour of a system, then the methodology of filtering exogenous distortions needs to be re-examined

A survey on cycles and chaos (part II)

This paper is an extension of a previous publication in the journal Historical Social Research (Vol. 26, No. 4, 2001, p. 208-219). Our treatment begins with a simple presentation of the basic notions of chaos, and then describes the related econometric tools

The Effects of Terrorism and War on the Oil and Prices Stock Indices Relationship

This paper, investigates the effect war and terrorism, have on the covariance between oil prices and the indices of four major stock markets - the American S&P500 and the European DAX, CAC40 and FTSE100 - using nonlinear BEKK-GARCH type models. Findings reported herein indicate that the covariance between stock and oil returns is affected by war. A tentative explanation is that the two wars examined here, predispose investors and market agents for more profound and longer lasting effects. On the other hand, in the case of terrorist incidents that, vis-\ue0-vis war, are of a more transitory nature and one-off security shocks, only the co-movement between CAC40, DAX and oil returns is affected. No significant impact for the same terrorist events is observed in the relationship between the S&P500, FTSE100 and oil returns. This difference in the reaction may tentatively be interpreted as indicating that the latter markets are more efficient in absorbing the impact of terrorist attacks

Energy Sector Pricing: One the Role of Neglected Nonlinearity

Modern economies have been subjected to a number of shocks during the past several years such as the burst of the Internet bubble, terrorist attacks, corporate scandals, the war in Iraq, the uncertainty about energy prices, and the recent subprime mortgage crisis. In particular, during the last few years, the energy shock has caused concerns for potential stagflation for both the United States and numerous other countries. We perform numerous univariate tests for non-linearity and chaotic structure using price data from the energy sector to resolve whether the sector\u27s fundamentals or exogenous shocks drive these prices

Accounting for outliers and calendar effects in surrogate simulations of stock return sequences

Surrogate Data Analysis (SDA) is a statistical hypothesis testing framework for the determination of weak chaos in time series dynamics. Existing SDA procedures do not account properly for the rich structures observed in stock return sequences, attributed to the presence of heteroscedasticity, seasonal effects and outliers. In this paper we suggest a modification of the SDA framework, based on the robust estimation of location and scale parameters of mean-stationary time series and a probabilistic framework which deals with outliers. A demonstration on the NASDAQ Composite index daily returns shows that the proposed approach produces surrogates that faithfully reproduce the structure of the original series while being manifestations of linear-random dynamics.Comment: 21 pages, 7 figure