From point of view of traditional econometric modeling the critical condition in a system can be obtained under outside factor’s effect. However the reasons of critical events can be found in distinguishing property of these systems: the most economic and particular macroeconomic systems are complex nonlinear dynamical systems with a very special behavior. They can homeostatically tune their regime up in response to any new information or pressure. Using fractal methods it has been demonstrating an evidence of normal running of system’s parameters, requited scale free fluctuations in certain limits and examples suppressing of fluctuations which leads to highly unstable system’s dynamical regime and crises as a result. Based on an extended statistical analysis of exchange rate fluctuations, prove of importance this tendency plays role in the stability of the international monetary system has been provided.

O. Y. Uritskaya. The Fractals Methods of the Determination of the Criteria of Homeostatic Stability of Macroeconomic Systems // Management in the social and economic systems. // St. Petersburg: SPbSTU Press, 2006, p. 326-354.

Full text (in Russian)

Fig.  1. An example of a of currency from group H. Fractal indexes a before the crisis take values above the upper limit of norm 1.75. After the crisis, they are normalized and remain in the interval [1.25, 1.75] as it observed in time series from group N.

Fig.  2. Examples of time series of logarithmic increments r_t of daily average exchange rate for the Japanese yen and Turkish lira (rates against the USD).

Fig.  3. Expanding the range of values of logarithmic increments during the active phase of the crisis (Russian ruble, currency from group H). Before the crisis most fluctuations are suppressed, that does not provide any chances for homeostatic regulation. After the crisis the range stays close to values of logarithmic increments from group N.

O. Y. Uritskaya. Stability of the Open Macroeconomic Systems // Management in the Social and Economic Systems. // St. Petersburg: SPbSTU Press, 2006, p. 304-326.

 Full text (in Russian)

Fig. 1. Stability diagram of the dynamics of national currencies: the intensity σr of and statistical temperature T of currency fluctuations as a function of the fractal index a2 . The dashed lines correspond to the levels of deviation parameters N group for the value of three standard deviations (±3s) from the mean values.  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;  H and L – Unstable Developing countries, prior to crises: Bulgaria, Brazil, India, Kazakhstan, Mexico, Russia, Rumania, Turkey, Ecuador;  А – Unstable Developing Asian countries before the 1997 monetary crisis: Indonesia, Malaysia, Singapore, Thailand, Taiwan, Philippines, South Korea;  М – Marginally stable, Countries from groups Н, L and А after crises.

O. Y. Uritskaya. Making Decisions under Risk and Limited Information Conditions // St. Petersburg: SPbSTU Press, 2005, 108 p.

Fig. 1. Process transformation of data to the information. Preceding throw the physical, semantic and pragmatic filters significant part of important information can be lost with statistical and semantic noise or is not recognized as useful one.

Fig. 2. Antagonistic Game. If participants have the opposite goals, they can not negotiate and they have to hide information form each other, because in this case the gaincan be increased only if the opponent makes a mistake. The solution shown is most cautious one. In literature it calls pessimistic approach. But if your opponent is your enemy you have no other choice. The classic example of this game at the practice is gaining a new part of stable market. If you get it, somebody has to loose. But in real life this happens very rare, markets are use to grow and the opponents are not your real enemy, just partners with different goals and negotiation always is good solution.

Fig. 3. Bimatrix Game. For more reasonable choice than just guessing we usually ask for help from professionals. They are people, so have their own goals and interests in the situation. Result – the goals are not opposite, but just different and model become Bimatrix game. This name is used for 2 person games, if more is consider more – it just become too complicated to demonstrate in matrix form, but approach is good for any number of participants. Here everyone is interested in max gain, but have to choose depend on moving of other participant. In this particular example they probably never choose right strategy if only will not negotiate. In this case they can share they profit or some benefits. Here we still have some option to increase the gain with new inf from our opponent. What why the always pays off.

O. Y. Uritskaya. Organizing and planning at the company // St. Petersburg: SPbGTU Press, 2005, 236 p.

Annotation and contents (in Russian)

Fig.1 The Blake Mouton model.

O. Y. Uritskaya. Fractal Methods for Modeling and Forecasting of Currency Crises // Modelling and Analysis of Safety and Risk in Complex Systems. – Proc. FISS MASR, SPb., 2005. – pр. 210-215.( Fourth International Scientific School MASR – 2005 (Saint-Petersburg, Russia, June 28- July 1, 2005)

 Full text (in Russian)

Fig. 1 . Fractal regression model of currency crises. Using the results of the analysis of correlations between monetary crashes and fractal dynamics of exchange rate fluctuations, we have constructed a regression model allowing quantitative prediction of important crisis parameters (duration L, normalized magnitude W, maximum amount of currency devaluation x_max, exchange rate volatility sigma_1) using statistical characteristics of currency dynamics before the crisis (cumulative deviation S of the DFA exponent below 1.25 and above 1.75 levels, mean value x_0 and standard deviation sigma_0 of currency fluctuations). Basic model equations as well as the values of empirically obtained regression coefficients are shown in the table.  To estimate the performance of the constructed model, statistics of the predicted and values expressed as a percentage of the actual values observed during most significant currency crises which occurred during the studied period has been investigated. On average, the error of x_max in-sample prediction was only 5 %. The prediction of L was characterized by a larger discrepancy(~10%) which may reflect the fact that the crisis length is affected by fiscal measures undertaken by national governments during the period following its beginning stage.

O. Y. Uritskaya. Stability and Risk Evaluation in Economic systems // St. Petersburg: SPbGTU Press, 2005, 171 p.

Fig.  1. Examples of fluctuations in daily average exchange rates in the economic systems with different levels of stability: Russian ruble, Brazilean real, Indonesian rupia and European Currency unit.

Fig.  2. Classification of currency exchange rate fluctuations based on the estimation of DFA exponents ₁ (4–30 days) and ₂ (30–90 days). According to the efficient market hypothesis, the point ₁ = ₂ =1.5 corresponds to the optimal state of the national currency system with maximum long-term stability of the exchange rate. The countries were grouped according to the values of  parameters: 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; H and L – Unstable Developing countries, prior to crises: Bulgaria, Brazil, India, Kazakhstan, Mexico, Russia, Rumania, Turkey, Ecuador;  А – Unstable Developing Asian countries before the 1997 monetary crisis: Indonesia, Malaysia, Singapore, Thailand, Taiwan, Philippines, South Korea;  М – Marginally stable, Countries from groups Н, L and А after crises.

Fig. 3. An example of a time series from the group N (US dollar against the German mark), showing variations in the fractal indices ₁ and ₂ in the range of 1.25 to 1.75. Index ₂ does not cross these critical levels for 30 years.

Contents

Lecture 1. Economic Risk and Economic Information.

The reasons for appearance of risks in economics. Difficulties of scientific research in economics. Content and classification of economic information.

Lecture 2. Characteristics of the Economic Systems.

System essence of economic objects. Main system principles. The large interactive systems. System analysis.

Lecture 3. Stability of an Economic System.

Stability of an economic system; critical conditions and crises. Forms of economic system stability. The history of investigation of the equilibrium in economics. Self-organized nature of dynamical equilibrium.

Lecture 4. Mathematical Modeling of Economic Systems.

“Mathemazation” in science. Deterministic and stochastic models. Problems of complex system modeling. History of mathematical modeling in economics. Holistic approach to simulations.

Lecture 5. Preparing and Processing Economic Data

The problem of selecting economic system state variables. Direct economic observations. Economic time series. Requirement to economic time series. Fluctuations of economic indices.

Lecture 6. Time Series Analysis

History of time series analysis. Generated, deterministic and stochastic time series. Fluctuations and bifurcations in time series. Problem of management in the complex economic system.

Lecture 7. The Theory of Self-Organized Criticality.

Mechanisms of catastrophes in complex systems. Reasons of local instability and global stability of the complex system. Physical model. Fractal structure of time series produced by complex interactive systems.

Lecture 8. Fractals and Their Properties.

Fractional dimension. Scale invariance. Self-similarity. Geometric fractals. P.Bak’s theorem of complex equilibrium.

Lecture 9. Methods of Fractal Time Series Analysis.

Estimation of the fractal dimension of time series. Geometric and statistical methods of fractal dimension estimation and their comparative characterization.

Lecture 10. Forecasting Fractal Dynamics.

Modeling of stochastic processes. Efficient market hypothesis. Forecasting time series behavior. Interpretation of fractal analysis results. Persistent and anti-persistent behavior of economic processes. Using fractal analysis for system stability evaluation. Sub- and super-critical conditions of unstable complex system evolution.

Lecture 11. The Risk Factors in the Macroeconomic Systems.

The world facilities as a system. The world trade, the international migration of the production’s factors. International exchange and financial relations. The international economic integration.

Lecture 12. The World Currency System. The Exchange Rates.

The international exchange system and its evolution. Nominal and real exchange rates. Floating and fixed exchange rates. The devaluation and revaluation. The international exchange market.

Lecture 13. The Macroeconomic System’s Classification by the Level of Dynamical Stability.

Fractal analysis of currency time series. Classification of the currencies by the stability groups. Recovering of system stability after the economic crisis.

Lecture 14. Evaluating Economic System Stability.

Methodology of evaluation of exchange rate volatility by logarithmic returns. Comparison of volatility values of stable and unstable floating exchange rates. Optimal intensity of exchange rate fluctuations

Lecture 15. Modeling Characteristics of Active Phase of Economic Crisis.

Determination of normal range of nonstationary fluctuations of Peng’s critical exponent. Evaluating time series fractal structure Evaluation of accumulated deviation of Peng’s exponent beyond the normal range and its relation to crisis magnitude and duration. Fractal regression of monetary crashes.

Lecture 16. Estimating Risks by Statistical Methods.

Standard probabilistic and statistical methods for risk estimation and their inherent limitations. Risk Levels. Risk Factors. Risk Scales.

Lecture 17. Estimating Economic Risks by Fractal Methods.

Quantitative risk assessment by fractal methods. Pareto exponent and its economic interpretation. Examples of financial risk estimation by the Pareto exponent technique.

Lecture 18. The Methods of Economic Risk Reduction.

The main methods of reduction of the risk in economic systems. Insurance, standby, limiting, diversification and hedging as instruments of the reduction of the economic risk.

Problems

Problem 1. Estimation of the fractal dimension of time series by ruler method. Forecast and risk evaluation.

Problem 2. Quantitative risk assessment by fractal method. Insurance risk evaluation.

Training session. Computer game “Stock market tactics”: description and trading examples.

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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.

Full text (in Russian)

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).

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.

O. Y. Uritskaya. Basic Principles of the Decision-Making Theory // Methods and Practice in the Education.– St.Petersburg: SPbSTU Press, 2002. – p.151 –153.

 Full text (in Russian)

Fig. 1. Decision making process is most sensitive to the information that’s why classification of Decision making models by this criterion seems most universal.