We study behaviour of time series of daily closing values for USD and EURO vs. PLN exchange rates and their returns. It is known that financial data series are characterized by changing volatility, excess kurtosis and assymetry of their probability density, and that they show signs of long memory. Due to volatility clustering, can be modelled with use of ARCH and GARCH type models, in which first equation -- describing expected value of the series -- can be of ARMA type, second equation describes conditional variance. It has been shown that additional explanatory variables in the expected value equation can improve quality of modelling and of forecasts. For bilateral exchange rates models such additional variables can be stock indices of corresponding countries. Cointegration analysis of exchange rates and stock indices is performed to check whether there is a stable dynamic economic equlibrium between them. The tools applied in such research stem originally from technical if not physical applications: the Hurst exponent, from hydrological study of 1950's; the ARMA models, from Box and Jenkins fundamental monograph of 1970's; cointegration analysis, from Engle and Granger concepts of equlibrium path as stable attractor; the Hansen stability tests and time-varying-parameter cointegration analysis uses methods of spectral analysis to estimate in semiparametric way long-run variance matrix.

1. PRESENTATION: Behaviour of exchange rates, and logarithmic returns: long memory and cointegration, PDF document, version 1.5, 0.6MB

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