Quantitative Dynamics » Articles

Predictability of electricity prices (Energy Economics, 2015)

Olga — Sat, 04 Apr 2015 20:27:25 +0000

In this project we investigated predictability of electricity prices in the Canadian provinces of Alberta and Ontario, as well as in the US Mid-C market. Using scale-dependent detrended fluctuation analysis, spectral analysis, and the probability distributionanalysis we showed that the studied markets exhibit strongly anti-persistent properties suggesting that their dynamics can be predicted based on historic price records across the range of time scales from one hour to one month. For both Canadian markets, the price movements reveal three types of correlated behavior which can be used for forecasting. The discovered scenarios remain the same on different time scales up to one month as well as for on- and off- peak electricity data. These scenarios represent sharp increases of prices and are not present in the Mid-C market due to its lower volatility. We argue that extreme price movements in this market should follow the same tendency as the more volatile Canadian markets. The estimated values of the Pareto indices suggest that the prediction of these events can be statistically stable. The results obtained provide new relevant information for managing financial risks associated with the dynamics of electricity derivatives over time frame exceeding one day.

Uritskaya O.Y., Uritsky V.М. Predictability of price movements in deregulated electricity markets // Energy Economics, Volume 49, May 2015, Pages 72–81

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Fig.1. Time series of hourly electricity prices in Alberta (left), Ontario (center) and Mid-C (right) markets. Fromtop to bottom: all hourly prices, on-peak prices, and off-peak prices. Alberta electricity prices demonstrate significantly higher fluctuations than those in Ontariomarket, plotted on the same vertical scale. Fluctuations of electricity prices in Mid-C have twice as low amplitude as that in Ontario, and about 5 times smaller than in Alberta.

Fig.2. Dependence of the detrended variation F and the local scale-dependent DFA slope α on the time scale n for all hourly, on- and off-peak electricity prices in Alberta (left), Ontario (center), and Mid-C (right) markets. The presented statistics reveal complex correlated structure of price movements with quasi-periodic components associated with daily and weekly cycles. In all presented data sets the scale-dependent DFA exponent is significantly below the level 1.5 defining the state of informational efficiency,which provides an opportunity of forecasting the prices over wide ranges of time scales.

Fig.3. Diagrams of aggregated price movements for several time scales n ranging from 1 to 720 h. Most of the plots have a distinctly asymmetric shape reflecting a casual relationship between the pricemovements. For the Alberta and Ontario plots (first and second columns), the asymmetry of the cloud of points assumes anti-persistent dependence which can be used for price forecasting. The Mid-C diagrams (third column) take a different formdepending on the aggregation scale,with the persistent and anti-persistent tendencies found at n=1 and n = 12, correspondingly.

Analysis of the US Stock Market (Int J Bifurcation & Chaos, 2008)

Olga — Tue, 15 Apr 2008 00:01:53 +0000

Based on the detrended fluctuation analysis of the Dow Jones Industrial Average (DJIA) index, we demonstrate that the U.S. stock market operates close to the state predicted by the efficient market hypothesis. The observed transient deviations from this state are shown to have a statistical origin as they also appear in purely random geometric Brownian motion models of the DJIA dynamics.

Serletis А., Uritskaya O.Y., & Uritsky V.М. Detrended Fluctuation Analysis of the US Stock Market // International Journal of Bifurcation and Chaos, Vol. 18 (2), 2008 – p. 599-603.

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Fig. 1. The comparative dynamics of the Dow Jones industrial average and a simulated geometric Brownian motion time series. Inset: DFA functions of both signals in the range 4–256 days.

Multiscale inefficiency (Energy Economics, 2008)

Olga — Sat, 05 Apr 2008 01:46:39 +0000

One of the basic features of efficient markets is the absence of correlations between price increments leading to random walk-type behavior of prices. In this paper, we propose a new approach for measuring deviations from the efficient market state based on an analysis of scale-dependent fractal exponent characterizing correlations at different time scales. The approach is applied to two electricity markets, Alberta and Mid Columbia (Mid-C), as well as to the AECO Alberta natural gas market (for purposes of providing a comparison between storable and non-storable commodities). We show that price fluctuations in all studied markets are not efficient, with electricity prices exhibiting multiscale correlated behavior which is significantly different from the monofractal model.

Uritskaya O.Y., Serletis А. Quantifying Multiscale Inefficiency in Electricity Markets // Energy Economics, Vol. 30, Issue 6, November 2008, p. 3109-3117

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Fig 1. Power spectra of electricity and natural gas prices.

Fig 2. Average and Extreme Values of DFA Exponents.

Self-organization in US money (Physica A, 2007)

Olga — Thu, 05 Apr 2007 03:18:48 +0000

In this study, we continued the research by Serletis and Shintani by applying the method of detrended fluctuation analysis (DFA) introduced by Peng and adapted to the analysis of long-range correlations in economic data by Uritskaya to investigate the dynamical structure of United States money and velocity measures. We used monthly data over the time period from 1959:1 to 2006:2, at each of the four levels of monetary aggregation, M1, M2, M3, and MZM, making comparisons among simple-sum, Divisia, and currency equivalent methods of aggregation. The results suggest that the sum and Divisia monetary aggregates are more appropriate for measuring long-term tendencies in money supply dynamics while the currency equivalent aggregates are more sensitive measures of short-term processes in the economy.

Serletis А., Uritskaya O.Y. Detecting Signatures of Stochastic Self-Organization in US Money and Velocity Measures // Physica A, Vol.385 (1), 2007. – p. 281-291.

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Fig. 1. Time series and DFA plots for sum, Divisia, and CE money measures at M1 level of monetary aggregation.

Criteria of Homeostatic Stability (Management in Social & Economic Systems, 2006)

Olga — Fri, 14 Apr 2006 23:47:49 +0000

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.

Stability of Macroeconomic Systems (SPbSTU Press, 2006)

Olga — Wed, 12 Apr 2006 01:43:40 +0000

The results of theoretical research of conditions of stability in macroeconomic systems have been presented. Based on review of resent publications it has been shown that the macroeconomic systems are complex interactive systems and their crisis dynamic can be investigated with using of fractal analysis methods. The most stable dynamic state of the macroeconomic complex system is condition of self-organizing criticality, which characterized by fractal structure of corresponded time series with dimension 1.5 indicated effective market theory. Economic and financial crises are related to sub- and supercritical regimes of system’s dynamic, which can be revealed by deviations of fluctuations intensity and fractal parameters beyond the normal limits well before crises start.

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

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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.

Forecasting Crisis Magnitude ( Proc. SPIE, 2005)

Olga — Mon, 23 May 2005 00:51:22 +0000

We demonstrate a possibility of using fractal analysis methods for understanding nonlinear dynamical mechanisms of catastrophic events in economic systems and quantifying their global stability. Based on an analysis of floating currency exchange rates in more than 30 countries for a 10-year period, it is found that deviations of national monetary systems from optimally stable states correlate with deviations of the detrended fluctuation analysis (DFA) index of currency fluctuations from its normal value of 1.5 satisfying the efficient market hypothesis. The observed dependence is used for classifying long-term stability of national currencies as well as for revealing various forms of distortion of stable currency dynamics prior to large-scale crises. It is shown that monetary crashes are usually preceded by prolonged periods of abnormal (decreased or increased) DFA index values, with its after-crash value tending to 1.5, which is characteristic of stable exchange rate dynamics. The range of the DFA index consistent with crisis-free long-term exchange rate fluctuations is determined, and several typical scenarios of currency dynamics beyond this range are identified. Statistically significant relations (R=0.99, р<0.01) between the duration and the magnitude of currency crises considered as functions of the degree of distortion of stable fractal pattern of exchange rate dynamics are found and interpreted in terms of the self-organized criticality framework. The regression parameters of the obtained relations are shown to be nearly equal for both small-scale and large-scale crises indicating a possibility of a common instability mechanism of these events, and are used as a basis for forecasting of monetary crisis magnitude and duration over various time scales. For determination of the forecast accuracy and reliability, the statistics of ratios between predicted and measured values of both parameters has been investigated. The resulting average rations for in-sample forecasting of crisis magnitude are 101.8%7.7%, р<0.05 for increased DFA index and 100.8%2.5% for decreased DFA index. The duration forecasting has provided wider confidence intervals (102.9%15.3% and 103.9%8.8%, correspondingly), which can be related with interference of national governments during the post-crisis period. The developed technique can be used for real-time monitoring of dynamical stability of floating exchange rate systems and creating advanced early-warning-system models for currency crisis prevention.

O. Y. Uritskaya. Forecasting of Magnitude and Duration of Currency Crises Based on Analysis of Distortions of Fractal Scaling in Exchange Rate Fluctuations // Noise and Fluctuations in Econophysics and Finance. Eds. D.Abbott, J.-Ph.Bouchaud, X.Gabaix. – Proc. SPIE Vol.5848, 2005. – p. 17-26 (Third SPIE International Symposium on Fluctuations and Noise (Austin, USA, 2005)).

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Fig. 1. Example of unstable currency dynamics (group Н, developing countries during periods preceding large-scale monetary crashes: Bulgaria, Brazil, India, Kazakhstan, Mexico, Russia, Rumania, Turkey, Ecuador) including a period of large-scale crisis. Before this event, DFA exponents had systematically increased values above the limit 1.75 of normal DFA exponent variations. After the crisis, both exponents returned to the interval [1.25, 1.75] signaling a normalization of dynamical stability of studied monetary system.

Fig. 2. Normalized crisis magnitude as a function of cumulative fractal indices characterizing the degree of fractal distortions in time series of exchange rate fluctuations with ₂< 1.25 (left) or ₂> 1.75 (right)

Fig. 3. Crisis duration (in days) as a function of the same parameters as in Fig. 2.

New Methods in Crisis Modeling (Proc. FISS MASR, 2005)

Olga — Sun, 24 Apr 2005 00:55:17 +0000

Results of fractal analysis of daily exchange rate fluctuations of floating currencies for a 10-year period are presented. It is shown that monetary crashes are usually preceded by prolonged periods of abnormal fractal exponent. Regression relations between duration and magnitude of currency crises and the degree of distortion of monofractal patterns of exchange rate dynamics are found and have been used as a basic ingredient of a forecasting technique which provided correct in-sample predictions of monetary crisis magnitude and duration over various time scales.

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)

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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.

Basics of Decision-Making Theory (SPbSTU Press, 2002)

Olga — Thu, 11 Apr 2002 02:41:27 +0000

Overview of the Decision-Making Theory lecture course for B.A. and M.A. graduate students of Management Department of University. A new method of teaching is presented which includes formulating and solving of inverse problems, i.e. providing the proof that given alternative is optimal. Students are given the opportunity to learn about basic stages of modeling and making decision processes, and, what is the most important, about the inherent limitations of quantitative and formalized methods in economics. This approach is systematically used for conducting training classes which allows the student to avoid many common mistakes and delusions related with applicability of mathematical methods in economics and business.

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.

Basics of Risk Theory (SPbSTU Press, 2002)

Olga — Thu, 11 Apr 2002 02:32:02 +0000

Outlines of a lecture course of advanced Economic Risk Theory created for M.A. graduate students specializing in economics, management and business areas. The lecture course summarizes an 8-years experience in adapting and clarifying for economists a number of complicated math theories are presented such as catastrophe theory, fractal theory and fractal analysis techniques. The course includes theoretic materials and computer games reproducing realistic conditions of risk-involving decision-making at currency exchanges and stock markets.

O. Y. Uritskaya. Introduction to Economic Risk Theory // Methods and Practice in the Education.– St.Petersburg: SPbGTU Press, 2002. – p.150 – 151.

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Fig. 1. The risk can be seen as a difference between the complexity and the extractable information.