Nonlinear Dynamics in Economics: A Theoretical and Statistical Approach to Agricultural Markets

ISBN-13: 9783540593744 / Angielski / Miękka / 1995 / 156 str.

Barbel Finkenstadt

Opis

1. 1 Introduction In economics, one often observes time series that exhibit different patterns of qualitative behavior, both regular and irregular, symmetric and asymmetric. There exist two different perspectives to explain this kind of behavior within the framework of a dynamical model. The traditional belief is that the time evolution of the series can be explained by a linear dynamic model that is exogenously disturbed by a stochastic process. In that case, the observed irregular behavior is explained by the influence of external random shocks which do not necessarily have an economic reason. A more recent theory has evolved in economics that attributes the patterns of change in economic time series to an underlying nonlinear structure, which means that fluctua tions can as well be caused endogenously by the influence of market forces, preference relations, or technological progress. One of the main reasons why nonlinear dynamic models are so interesting to economists is that they are able to produce a great variety of possible dynamic outcomes - from regular predictable behavior to the most complex irregular behavior - rich enough to meet the economists' objectives of modeling. The traditional linear models can only capture a limited number of possi ble dynamic phenomena, which are basically convergence to an equilibrium point, steady oscillations, and unbounded divergence. In any case, for a lin ear system one can write down exactly the solutions to a set of differential or difference equations and classify them."

Spis treści

1 Introduction.- 1.1 Introduction.- 1.2 The dynamics of the first order difference equations.- 1.3 Higher dimensional systems.- 1.4 What is chaos?.- 1.5 Chaos versus random noise.- 1.6 Chaos and statistics.- 2 A Nonlinear Cobweb Model.- 2.1 Introduction.- 2.2 The cobweb model.- 2.3 The model.- 2.4 Qualitative behavior.- 2.4.1 The period-doubling road to chaos.- 2.4.2 Chaos in the Li/Yorke sense.- 2.4.3 Dynamic behavior in the two-dimensional parameter plane.- 2.5 Summary.- 2.6 Appendix.- 3 Are Time Series From Agricultural Markets Nonlinear? The Case of German Prices.- 3.1 Introduction.- 3.2 The data.- 3.3 Correlation integral methods.- 3.3.1 The wing and shuffle diagnostics.- 3.3.2 The BDS test.- 3.3.3 Results of the BDS test.- 3.4 A nonlinear analysis of the time series.- 3.4.1 Some definitions.- 3.4.2 A nonlinear approach to time series modeling.- 3.4.3 Testing the linearity assumption.- 3.4.4 The effect of picking data at different time intervals.- 3.5 Appendix: Results of linear model fitting.- 3.5.1 Pig prices.- 3.5.2 Potato prices, sample 1–800.- 3.5.3 Egg prices.- 4 A Nearest Neighbor Approach to Forecast Nonlinear Time Series.- 4.1 The forecasting algorithm.- 4.2 A robust test.- 4.3 A simulation study.- 4.4 Results for commodity price series.- 4.5 Summary.- 4.6 Appendix: Simulation study results.- 4.7 Results for residuals of linear models fitted to the growth rates.- 5 Conclusions and Outlook.- 5.1 Summary and conclusions.- 5.2 Outlook: Modeling nonlinear time series.