Nonlinear dynamics in economics. A theoretical and statistical approach to agriculture markets
This study is motivated by the ``nonlinear'' perspective. It consists of five chapters that can be read almost independently of each other. The first chapter gives an introduction to nonlinear dynamics to a reader who is not familiar with the topic. There are a lot of interesting features about chaos that attract both specialists and nonspecialists. The introductory chapter is restricted to a selection of properties, which are important to understand the remaining chapters. The fundamental ideas are stated in a somewhat informal style using simple, worked-out cases from the natural sciences. Attention is given to the one-dimensional quadratic map as it exhibits almost all interesting properties. Aside from its theoretical properties, the nonlinear approach sheds a different light upon the traditional linear statistical methodology, which is outlined in view of the statistical part of the thesis. The second chapter deals with one of the simplest dynamic models in economics, namely the cobweb model, which is often used to describe a highly stylized version of an agricultural market. It is shown that the introduction of a nonlinear demand function to the cobwed model under adaptive expectations broades the possible range of dynamic outcomes significantly. Although it can hardly be assumed that such a simplified model -- be it linear or nonlinear -- is able to perfectly explain the real world data, it is necessary to examine some observed time series from agricultural markets for typical nonlinear behavior such as the occurence of asymmetric cycles, low-dimensional clustering in phase space, and possible short-time predictability. The third and the fourth chapters are concerned with detecting such special nonlinear patterns in the agricultural price series. The third chapter draws upon selection of relatively new tests for (non)linearity, as suggested in the nonlinear time series literature. The fourth chapter deals with a new neighbor forecasting algorithm to distinguish chaos from measurement noise. This method is quite promising because it can be applied to relatively short data sets such as the economic time series. An extremely simple robust test is proposed to accompany this algorithm in order to test is proposed to accompany this algorithm in order to test its forecast performance, in case the data is noise infected. The aim of the thesis is to show how complicated and interesting even the simplest dynamical system may become once the linearity assumption is given up. Looking at the data at hand, we can affirm that nonlinearities in agricultural time series cannot be considered as a rare phenomenon. Still, questions with respect to the modeling of such series are open are outlined in chapter five.
scientific article; zbMATH DE number 783770