CHAOTIC DYNAMICS IN ECONOMIC TIME‐SERIES

Journal of Monetary Economics, 1988

Journal of Monetary Economics, 1988

An empirical assessmez? of a linear-stochastic perspective for Canadian macroecono series is presented. The methods used are based on the mathematics of 'chaos'. Present evidence suggests that low-order deterministic chaos does not provide a satisfactory characterization of the data. The absence of significant nonlinear structure for the investment and unemployment series is of particular note in light of past findings with American data. The degree to which the use of a time trend can impose a pseudo-structure on the data is illhlstrated. *This research was partly supported by a grant from the Research Excellence Program of University of Guelph. We would like to thank William Brock, Roger Farmer, Chera Sayers, Jose Scheinkman for helpful discussions ab chaos. ne suggestions of an anonymous referee were quite useful. Our i~tellectu~ debt to acknowledged. Any deficiencies remain our responsibility.

Computational Economics, 2004

Existence theory in economics is usually in real domains such as the findingsof chaotic trajectories in models of economic growth, tâtonnement, oroverlapping generations models. Computational examples, however, sometimesconverge rapidly to cyclic orbits when in theory they should be nonperiodicalmost surely. We explain this anomaly as the result of digital approximationand conclude that both theoretical and numerical behavior can still illuminateessential features of the real data.

International Conference on Eurasian Economies 2016, 2016

Knowing of the chaos theory by the economists has caused the understanding of the difficulties of the balance in economy. The applications of the chaos theory related to economy have aimed to overcome these difficulties. Chaotic deterministic models with sensitive dependence on initial conditions provide a powerful tool in understanding the apparently random movements in financial data. The dynamic systems are analyzed by using linear and/or nonlinear methods in the previous studies. Although the linear methods used for stable linear systems, generally fails at the nonlinear analysis, however, they give intuition about the problem. Due to a nonlinear variable in the difference equations describing the dynamic systems, unpredictable dynamics may occur. The chaos theory or nonlinear analysis methods are used to examine such dynamics systems. The chaos that expresses an irregular condition can be characterized by "sensitive dependence on initial conditions". We employ four tests, viz. the BDS test on raw data, the BDS test on pre-filtered data, Correlation Dimension test and the Brock's Residual test. The financial markets considered are the stock market, the foreign exchange market. The results from these tests provide very weak evidence for the presence of chaos in Turkish financial markets. BIST, Exchange Rate and Gold Prices. In this study, the methods for the chaotic analysis of the time series, obtained based on the discrete or continuous measurements of a variable are investigated. The chaotic analysis methods have been applied on the time series of various systems. Chaos, is the way a deterministic system can behave in a disordered manner. For example sometimes chaotic situations can be seen in the flow of a liquid passing from a smooth pipe. Once the flow rate of the fluid passes a certain value, eddies are formed and the Newton laws lose their validity. Namely now the flow is chaotic. Although J. Henri Poincare is accepted as the father of chaos concept and theory, the most important contribution for the theory was made by Edward Lorenz who became a meteorology professor in M.I.T. in 1960. Lorenz entered data to his computer in order to prepare a simple weather forecast report and as a result showed the temperature values he found in graphics. Lorenz, restarted the function by increasing the randomly selected temperature values in small amounts that even a very sensitive thermometer cannot detect and found out that totally different functions were formed even though he expected functions would not create any difference in graphics. It was observed that the decrease and increase in graphics in long term caused a pattern like a butterfly.

The Pakistan Development Review, 1994

Recently there has been an increased interest in the theory of chaos by macroeconomists and fmancial economists. Originating in the natural sciences, applications of the theory have spread through various fields including brain research, optics, metereology, and economics. The attractiveness of chaotic dynamics is its ability to generate large movements which appear to be random, with greater frequency than linear models. Two of the most striking features of any macro-economic data are its random-like appearance and its seemingly cyclical character. Cycles in economic data have often been noticed, from short-run business cycles, to 50 years Kodratiev waves. There have been many attempts to explain them, e.g. Lucas (1975), who argues that random shocks combined with various lags can give rise to phenomena which have the appearance of cycles, and Samuelson (1939) who uses the familiar multiplier accelerator model. The advantage of using non-linear difference (or differential) equation...

2006

Chaotic deterministic models with sensitive dependence on initial conditions provide a powerful tool in understanding the apparently random movements in financial data. This study examines four financial markets in India, an emerging economy, for possible chaotic behavior. We employ four tests, viz. the BDS test on raw data, the BDS test on pre-filtered data, Correlation Dimension test and the Brock’s Residual test. The financial markets considered are the stock market, the foreign exchange market, the money market and the government securities market. The results from these tests provide very weak evidence for the presence of chaos in Indian financial markets.

Chaotic deterministic models with sensitive dependence on initial conditions provide a powerful tool in understanding the apparently random movements in financial data. This study examines four financial markets in India, an emerging economy, for possible chaotic behavior. We employ four tests, viz. the BDS test on raw data, the BDS test on pre-filtered data, Correlation Dimension test and the Brock's Residual test. The financial markets considered are the stock market, the foreign exchange market, the money market and the government securities market. The results from these tests provide very weak evidence for the presence of chaos in Indian financial markets.

Journal of Macroeconomics, 2006

This short paper is a comment on "Univariate tests for nonlinear structure" by Catherine Kyrtsou and Apostolos Serletis. We summarize their main results and discuss some of their conclusions concerning the role of outliers and noisy chaos. In particular, we include some new simulations to investigate whether economic time series may be characterized by low-dimensional noisy chaos.

The Journal of Finance, 1991

2015

Modeling of economic processes is the subject of numerous studies and analyzes. There are a variety of methods and research tools used. Attempts to describe the functioning of economic processes are taken within multiple disciplines, e.g. economics, mathematics, psychology. A variety of theories and methods used are reflected in the diversity of the obtained results and forecasts. In order to predict the future behavior of the stock market or currency market, various models are designed, which never give full assurance of success and are usually burdened, with investment risk. One of the newer concepts of modeling economic processes, such as the stock market or the currency market, is the deterministic chaos theory. It is an attempt to move away from the idea of the efficiency of capital markets and currency markets, towards a more universal view of the mechanisms governing them. Characteristics features, imbalances and positive feedback mechanism in time, are reflected in the descr...