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Über dieses Buch

In the last two years or so, I was most fortunate in being given opportunities of lecturing on a new methodology to a variety of audiences in Britain, China, Finland, France and Spain. Despite my almost Confucian attitude of preferring talking (i.e. a transient record) to writing (i.e. a permanent record), the warm encouragement of friends has led to the ensuing notes. I am also only too conscious of the infancy of the methodology introduced in these notes. However, it is my sincere hope that exposure to a wider audience will accelerate its maturity. Readers are assumed to be familiar with the basic theory of time series analysis. The book by Professor M.B. Priestley (1981) may be used as a general reference. Chapter One is addressed to the general question: "why do we need non-linear time series models?" After describing some significant advantages of linear models, it singles out several major limitations of linearity. Of course, the selection reflects my personal view on the subject, which is only at its very beginning, although there does seem to be a general agreement in the literature that time irr'eversibility and limit cycles are among the most obvious.

Inhaltsverzeichnis

Frontmatter

Chapter One. Introduction

Abstract
In our endeavours to understand the changing world around us, observations of one kind or another are frequently made sequentially over time. The record of sunspots is a classic example, which may be traced as far back as 28 B.C. (see, e.g. Needham, 1959, p. 435).
Howell Tong

Chapter Two. Some Basic Concepts

Abstract
As soon as we leave the relatively comfortable world of linearity, we are faced with an infinitude of possible choices of ɕ, the generic models. Nature is full of surprises and awareness of its infinite variety is an accumulative learning process, which is itself non-linear. It seems therefore that there will always be the necessity of different approaches to non-linear time series model building.
Howell Tong

Chapter Three. Threshold Models

Abstract
The idea of using piecewise linear models in a systematic way for the modelling of discrete time series data was first mentioned in Tong (1977a) and reported in Tong (1978a, 1978b, 1980). A comprehensive account, together with numerous applications and discussion, is available in Tong and Lim (1980).
Howell Tong

Chapter Four. Identification

Abstract
A fundamental difficulty in statistical analysis is the choice of an appropriate model. This is particularly pronounced in time series analysis. The book by Box and Jenkins (1970) has been successful in popularizing linear time series models through the formulation of an iterative process of model building, consisting of the stages of identification, estimation and diagnostic checking. This approach is commonly referred to as the Box-Jenkins approach. It seems that the general philosophy of this approach is to allow the modeller a fair degree of flexibility in exercising his subjective judgement as to which one of several candidate models he may adopt. The approach has been popular and, in the hands of experienced time series analysts, many successful results have been reported. Their emphasis on diagnostic checking is particularly relevant in the present context.
Howell Tong

Chapter Five. Some Case Studies

Abstract
One of the exciting phenomena in ecology is population cycles. This inspired people like A. J. Lotka of the United States and V. Vol terra of France more than half a century ago into a theoretical study, which later developed into a scientific discipline. Their well-known models (see §2.2) for cyclical predator-prey patterns provided an explanation that seemed satisfactory for a brief period. However, it has been pointed out in §2.2 that the simple Lotka-Volterra type equation has a phase diagram in the form of a centre, which is in general a point away from the origin. The trajectory is, by the nature of the problem, confined to the first quadrant, and it turns out to be such that in order to produce very large fluctuations in the numbers of the two interacting species described by the equation, it is sufficient to start with only a few members of each species. This is often not the case with ecological observations. This type of model is now superseded by more realistic ones. A comprehensive review of the subject is given by Oster and Ipaktchi (1978), in which a fundamental conservation law of population biology has been postulated.
Howell Tong

Backmatter

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