Financial Econometrics

Peijie Wang

• Publisher: Routledge
• Year: 2005
• Print ISBN: 9780415224550
• eBook ISBN: 9781134591114
• Topic: Business
• Subtopic: Business General
• Index: Business

This book which provides an overview of contemporary topics related to the modelling of financial time series, is set against a backdrop of rapid expansions of interest in both the models themselves and the financial problems to which they are applied. This excellent textbook covers all the major developments in the area in recent years in an informative as well as succinct way. Refreshingly, every chapter has a section of two or more examples and a section of empirical literature, offering the reader the opportunity to practice the kind of research going on in the area. This approach helps the reader develop interest, confidence and momentum in learning contemporary econometric topics

1 Stochastic processes and financial time series

1.1 Introduction

Statistics is the analysis of events and the association of events, with a probability. Econometrics pays attention to economic events, the association between these events, and between these events and human beings’ decision making – government policy, firms’ financial leverage, individuals’ investment/consumption choice, and so on. The topics of this book, Financial Econometrics, focus on the variables and issues of financial economics, the financial market and the participants.

The financial world is an uncertain universe where events take place every day, every hour and every second. Information arrives randomly and so do the events. Nonetheless, there are regularities and patterns in the variables to be identified, effects of a change on the variables to be assessed, and links between the variables to be established. Financial Econometrics attempts to perform analyses of these kinds through employing and developing various relevant statistical procedures.

There are generally two types of economic and financial variables, one is the rate (flow) variable and the other the level (stock) variable. The first category measures the speed at which, for example, wealth is generated, or goods are consumed, or savings are made, at one point in time (continuous time) or over a short interval of time (discrete time). The second category works out the amount of wealth being accumulated over a period (continuous time) or in a few of short-time intervals (discrete time). Before we can establish links and chains of influence among the variables in concern, which are in general random or stochastic, we have to assess first their individual characteristics. With what probability may the variable take a certain value, that is, how likely is it that an event (the variable taking a given value) may occur? Such assessment of the characteristics of individual variables is made through the analysis of their statistical distributions. Bearing this in mind, a number of stochastic processes, which are commonly encountered in empirical research in economics and finance, are presented, compared and summarised in the next section. The behaviour and valuation of economic and financial variables are discussed in association with these stochastic processes in Section 1.3, with further extension and generalisation.

Independent identical distribution (i.i.d.) and normality in statistical distributions are commonly supposed to be met, though from time to time we would modify the assumptions to fit real world problems more appropriately. If the rate/flow variables are, as widely assumed, normally distributed (also i.i.d.) around a constant mean, then their corresponding level/stock variables would be log normally distributed around a mean which is increasing exponentially over time, and the level/stock variable in logarithms is normally distributed around a mean which is increasing linearly over time. This is the reason why we usually work with the level variables in their logarithms.

The classification of financial variables into rate variables and level variables gives rise to stationarity and non-stationarity in financial time series, though there might be no clear-cut match of the economic and financial characteristic and the statistical characteristic in empirical research. Related to this issue, Chapter 2 analyses unit roots and presents procedures for testing for unit roots. The chapter then introduces the idea of cointegration, where a combination of two or more non-stationary variables becomes stationary. This is a special type of link among stochastic variables, implying that there exists a so-called long-run relationship. The chapter also extends the analysis to cover common trends and common cycles, the other major types of links among stochastic variables in economics and finance.

One of the violations to the i.i.d. assumption is heteroscedasticity, that is, the variance is not the same for each of the residuals; and modifications are consequently required in the estimation procedure. The basics of this issue and the ways to handle it are a topic in introductory econometrics or statistics. What we introduce in Chapter 3 is specifically a kind of variance which changes with time, or timevarying variance. Time-varying variance or time-varying volatility is frequently found in many financial time series and so has to be dealt with seriously. Two types of time-varying volatility models are discussed, one is generalised autoregressive conditional heteroscedasticity (GARCH) and the other is stochastic volatility.

How persistent is the effect of a shock is important in financial markets. It is not only related to the response of, say, financial markets to a piece of news, but is also related to policy changes, of the government or of the firm. This issue is addressed in Chapter 4, which also incorporates impulse response analysis, a related subject which we reckon should be under the same umbrella. Regime shifts are important in the economy and financial markets as well, in that regime shifts or breaks in the economy and market conditions are often observed, but the difficulties are that regime shifts are not easily captured by conventional regressional analysis and modelling. Therefore Markov switching is introduced in Chapter 5 to handle these issues more effectively. The approach helps improve our understanding about an economic process and its evolving mechanism constructively.

Some economic and financial variables have built-in fundamental relationships between them. One of such fundamental relationships is that between income and value. Economists regard that the value of an asset is derived from its future income generating power. The higher the income generating power, the more valuable is the asset. Nevertheless, whether this law governing the relationship between income and value holds is subject to empirical scrutiny. Chapter 6 addresses this issue with the help of econometric procedures which identify and examine the time series characteristics of the variables involved.

Econometric analysis can be carried out in the conventional time domain as was discussed above, and can also be performed through some transformations. Analysis in the state space is one of such endeavours, presented in Chapter 7. What the state space does is to model the underlying mechanisms through the changes and transitions in the state of its unobserved components, and establish the links between the variables in concern, which are observed, and those unobserved state variables. It explains the behaviour of externally observed variables by examining the internal, dynamic and...

Table of contents

• Cover Page
• Title Page
• Copyright Page
• List of illustrations
• Preface
• Acknowledgements
• 1 Stochastic processes and financial time series
• 2 Unit roots, cointegration and other comovements in time series
• 3 Time-varying volatility models – GARCH and stochastic volatility
• 4 Shock persistence and impulse response analysis
• 5 Modelling regime shifts
• 6 Present value models and tests for rationality and market efficiency
• 7 State space models and the Kalman filter
• 8 Frequency domain analysis of time series
• 9 Research tools and sources of information