Quantitative Dynamics » Book chapters

Optimal Exchange Rate (SPbSTU Press, 2004)

Olga — Sun, 11 Apr 2004 22:40:05 +0000

Financial stability of national currencies involved in the globalization process requires flexible regulation and control of exchange rate fluctuations dynamics. Government control of currency fluctuations aimed at reducing inflation trends is favorable for economic activity such as forward transactions, business planning, contracts etc. However, in the long term this control prevents national monetary systems from adapting to changeable global environment and can eventually produce large-scale currency crashes. In this paper, the optimal range of exchange rate volatility is evaluated that satisfies both short-scale and large-scale stability requirements of evolution of complex monetary systems. Using two independent methods of volatility estimation, it is shown that deliberate reduction of daily exchange rate fluctuations conducted on a systematic basis inevitably leads to unstable currency dynamics associated with abrupt changes of floating exchange rates and other negative consequences in the long-term. On the other hand, enhanced fluctuations of exchange rate returns described by heave-tailed Pareto-type probability distributions also indicate an unstable behavior of monetary systems.

O.Y. Uritskaya. Evaluation of Optimal Exchange Rate Fluctuations Range by Statistical Temperature Method // Modern Problems and Methods of an Improvement of Government Management.– St.Petersburg: SPbGTU Press, 2004. – p. 378 – 393.

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Fig. 1. Method of determining the statistical temperature T and the Pareto index _р for currency time series using histograms of logarithmic increments.

Fig. 2. Values of the statistical temperature T by groups of currencies: N – Economically developed countries: Great Britain, Greece, EU, Canada, New Zealand, Norway, USA, Swiss, Japan, Australia; D – Developing countries with relatively stable monetary systems: Israel, Columbia, Chili, South Africa; C – Unstable Developing countries, prior to crises: Bulgaria, Brazil, India, Kazakhstan, Mexico, Russia, Rumania, Turkey, Ecuador, Indonesia, Malaysia, Singapore, Thailand, Taiwan, Philippines, South Korea; M – the same currencies as in group C after the crisis.

Fig. 3. Examples of normal fluctuations T for time series currency from the group N (top)and nonstationary dynamics of the statistical temperature before and after the currency crises for currency from group C (bottom). The dashed line indicates the lower limit of the fluctuations T for currencies from stable group N.

Stability of Revenue Flows (SPbSTU Press, 2004)

Olga — Sun, 11 Apr 2004 02:58:53 +0000

Analysis of temporal fluctuations of the volume of income taxes collected in St.Petersburg administrative districts has been performed. The dynamics of the analyzed time series has a multiscale noise structure which includes both periodic and stochastic components. Using the Fourier spectral analysis technique, the Hurst’s rescaled range analysis and the Pareto distribution method, we have recognized the groups of districts with low and high stability of the 30-day microeconomic cycle. The results confirmed that during the considered period (1996-2000), the city economy was at stage of active formation and met general criteria of economic self-organization.

O. Y. Uritskaya. Investigation of Stability of Revenue Flows in St.Petersburg Administrative Districts by Fractal Analysis Methods // Modern Problems and Methods of an Improvement of Government Management.– St.Petersburg: SPbGTU Press, 2004. – p. 365 – 378.

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Fig. 1. Example of a time series of tax revenues (top) and its power spectrum (bottom). On the spectrum arrows show two main harmonics corresponding to a period of 7 and 30 days (data of the Moscowsky district of Sankt-Petersburg, Russia).

Fig. 2. Example of long-range dependence R/S as a function of time scale T, showing two sections with different Hurst index (data Center-2 district of Sankt-Petersburg, Russia).

Fractal Structure of Monetary Crashes (SPbSTU Press, 2004)

Olga — Sun, 11 Apr 2004 02:53:17 +0000

Nonstationary fractal analysis of currency exchange rate fluctuations in 162 countries with different political, financial and economical systems during the period of 1995-2002 has been conducted. The C.K.Peng’s detrended fluctuation analysis (DFA) is applied in order to reveal inflation tendencies and unstable regimes in currency dynamics over a broad range of temporal scales (5 minutes to 90 days). We show for the first time that the fractal structure of exchange rate fluctuations can be used as an indicator of monetary control system stability. In developed countries with strong economy, the DFA index remains close to the value of 1.5 predicted by the efficient market theory, even when the observation period includes short-term financial crises. In developing countries, the DFA index systematically diverges from this value revealing statistically significant correlations of increments (either positive or negative) over various delay times. Such dynamics are characteristic of a weak economy and, as the data analysis suggests, can be considered as a predictor of future monetary system crashes. In order to illustrate this possibility we have investigated the Asian financial crisis of 1997 and found that most of the involved countries whose monetary systems underwent catastrophic changes had been characterized by abnormal values of the DFA index of exchange rates fluctuations before the crisis. The depth of the crisis as well as the rate of the subsequent economic recovering also correlated with the DFA index. We interpret the obtained results in terms of the self-organized criticality (SOC) concept and demonstrate numerically that the observed scenarios of unstable currency dynamics can be associated with sub- or super-critical regimes of a disturbed SOC system. We also provide a technique for identification these regimes based on time series analysis and demonstrate how such information can be used for improving anti-crisis management strategies.

O. Y. Uritskaya. Effect of Disturbances of Fractal Temporal Structure in Currency Floating Exchange Rate Fluctuations on Characteristics of the Active Phase of Monetary Crashes // Modern Problems and Methods of Improvement of Government Management.– St.Petersburg: SPbGTU Press, 2004. – p.341 – 364.

Full text (in Russian)

Fig. 1. Example of dependence the Peng F function of currency fluctuations (Indian Rupee) on the time scale, showing the two sections with different values of the index .

Fig. 2. Example of the application of the method of the sliding window (360/1) to analyze the evolution of fractal time series indices (ECU).

Fig. 3. Examples of the accumulated deviations from the “norm” level in the time series of the Australian dollar and the Brazilian real.