Microeconomic modeling of financial time series with long term memory

In this paper we fix a microeconomic model of exchange rates and we give the explicit relation between model's parameters and its long memory properties. This avoids long numerical calibration procedures and allows to build the model with the parameters suitable for the required long memory degree.

[1]  G. Evans Pitfalls in Testing for Explosive Bubbles in Asset Prices , 1991 .

[2]  F. Breidt,et al.  The detection and estimation of long memory in stochastic volatility , 1998 .

[3]  W. Newey,et al.  A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelationconsistent Covariance Matrix , 1986 .

[4]  P. Robinson,et al.  Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression , 1991 .

[5]  A. Banerjee,et al.  A Simple Model of Herd Behavior , 1992 .

[6]  J. P. Garrahan,et al.  Correlated adaptation of agents in a simple market: a statistical physics perspective , 2000, cond-mat/0012269.

[7]  W. Andrew LO, . Long-Term Memory in Stock Market Prices, Econometrica, , . , 1991 .

[8]  C. Granger Long memory relationships and the aggregation of dynamic models , 1980 .

[9]  C. Granger,et al.  A long memory property of stock market returns and a new model , 1993 .

[10]  T. Bollerslev,et al.  MODELING AND PRICING LONG- MEMORY IN STOCK MARKET VOLATILITY , 1996 .

[11]  Leonard A. Smith,et al.  Distinguishing between low-dimensional dynamics and randomness in measured time series , 1992 .

[12]  C. Avery,et al.  Multidimensional Uncertainty and Herd Behavior in Financial Markets , 1998 .

[13]  I. Welch Sequential Sales, Learning, and Cascades , 1992 .

[14]  H. Föllmer Random economies with many interacting agents , 1974 .

[15]  Filippo Castiglione Diffusion and Aggregation in an Agent Based Model of Stock Market Fluctuations , 2000 .

[16]  B. Tirozzi,et al.  Distinguishing Between Chaotic And Stochastic Systems In Financial Time Series , 2002 .

[17]  P. Grassberger,et al.  Measuring the Strangeness of Strange Attractors , 1983 .

[18]  O. Bunke Feller, F.: An Introduction to Probability Theory and its Applications, Vol. II, John Wiley & Sons, Inc., New York‐London‐Sydney, 1966. XVIII + 626 S., 3 Abb., 2 Tab., Preis $ 12,00 , 1969 .

[19]  Clive W. J. Granger,et al.  An introduction to long-memory time series models and fractional differencing , 2001 .

[20]  Alan Kirman,et al.  Ants, Rationality, and Recruitment , 1993 .

[21]  George E. P. Box,et al.  Time Series Analysis: Forecasting and Control , 1977 .

[22]  C. Granger,et al.  Modeling volatility persistence of speculative returns: A new approach , 1996 .

[23]  J. Geweke,et al.  THE ESTIMATION AND APPLICATION OF LONG MEMORY TIME SERIES MODELS , 1983 .

[24]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1972 .

[25]  Hideki Takayasu,et al.  Dynamic numerical models of stock market price: from microscopic determinism to macroscopic randomness , 1998 .

[26]  A. Provenzale,et al.  Finite correlation dimension for stochastic systems with power-law spectra , 1989 .