Underlying Dynamics of Typical Fluctuations of an Emerging Market Price Index: The Heston Model from Minutes to Months

We investigate the Heston model with stochastic volatility and exponential tails as a model for the typical price fluctuations of the Brazilian S\~ao Paulo Stock Exchange Index (IBOVESPA). Raw prices are first corrected for inflation and a period spanning 15 years characterized by memoryless returns is chosen for the analysis. Model parameters are estimated by observing volatility scaling and correlation properties. We show that the Heston model with at least two time scales for the volatility mean reverting dynamics satisfactorily describes price fluctuations ranging from time scales larger than 20 minutes to 160 days. At time scales shorter than 20 minutes we observe autocorrelated returns and power law tails incompatible with the Heston model. Despite major regulatory changes, hyperinflation and currency crises experienced by the Brazilian market in the period studied, the general success of the description provided may be regarded as an evidence for a general underlying dynamics of price fluctuations at intermediate mesoeconomic time scales well approximated by the Heston model. We also notice that the connection between the Heston model and Ehrenfest urn models could be exploited for bringing new insights into the microeconomic market mechanics.Comment: 20 pages, 9 figures, to appear in Physica

Hysteresis and economics - taking the economic past into account

The goal of this article is to discuss the rationale underlying the application of hysteresis to economic models. In particular, we explain why many aspects of real economic systems are hysteretic is plausible. The aim is to be explicit about the difficulties encountered when trying to incorporate hysteretic effects into models that can be validated and then used as possible tools for macroeconomic control. The growing appreciation of the ways that memory effects influence the functioning of economic systems is a significant advance in economic thought and, by removing distortions that result from oversimplifying specifications of input-output relations in economics, has the potential to narrow the gap between economic modeling and economic reality

Changing-regime volatility: A fractionally integrated SETAR model

This paper presents a 2-regime SETAR model with different long-memory processes in both regimes. We briefly present the memory properties of this model and propose an estimation method. Such a process is applied to the absolute and squared returns of five stock indices. A comparison with simple FARIMA models is made using some forecastibility criteria. Our empirical results suggest that our model offers an interesting alternative competing framework to describe the persistent dynamics in modeling the returns.SETAR ;Long-memory ;Stock indices ;Forecasting

Modeling the Use of Nonrenewable Resources Using a Genetic Algorithm

This paper shows, how a genetic algorithm (GA) can be used to model an economic process: the interaction of profit-maximizing oil-exploration firms that compete with each other for a limited amount of oil. After a brief introduction to the concept of multi-agent-modeling in economics, a GA-based resource-economic model is developed. Several model runs based on different economic policy assumptions are presented and discussed in order to show how the GA-model can be used to gain insight into the dynamic properties of economic systems. The remainder outlines deficiencies of GA-based multi-agent approaches and sketches how the present model can be improved.

Memory property in heterogeneously populated markets

This paper focuses on the long memory of prices and returns of an asset traded in a financial market. We consider a microeconomic model of the market, and we prove theoretical conditions on the parameters of the model that give rise to long memory. In particular, the long memory property is detected in an agents' aggregation framework under some distributional hypotheses on the market's parameters

Multivariate Fractionally Integrated APARCH Modeling of Stock Market Volatility: A multi-country study

Tse (1998) proposes a model which combines the fractionally integrated GARCH formulation of Baillie, Bollerslev and Mikkelsen (1996) with the asymmetric power ARCH speci¯cation of Ding, Granger and Engle (1993). This paper analyzes the applicability of a multivariate constant conditional correlation version of the model to national stock market returns for eight countries. We ¯nd this multivariate speci¯cation to be generally applicable once power, leverage and long-memory e®ects are taken into consideration. In addition, we ¯nd that both the optimal fractional di®erencing parameter and power transformation are remarkably similar across countries. Out-of-sample evidence for the superior forecasting ability of the multivariate FIAPARCH framework is provided in terms of forecast error statistics and tests for equal forecast accuracy of the various models.Asymmetric Power ARCH, Fractional integration, Stock returns, Volatility forecast evaluation

Dynamics of financial time series in an inhomogeneous framework

In this paper we provide a microeconomic model to investigate the long term memory of financial time series of one share. In the framework we propose, each trader selects a volume of shares to trade and a strategy. Strategies differ for the proportion of fundamentalist/chartist evaluation of price. The share price is determined by the aggregate price. The analyses of volume distribution give an insight of imitative structure among traders. The main property of this model is t the functional relation between its parameters at the micro and macro level. This allows an immediate calibration of the model to the long memory degree of the time series under examination, therefore opening the way to the understanding the emergence of stylized facts of the market through opinion aggregation