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5837 results in Econometrics and mathematical methods

Page 84 of 292

  • 8 - Modelling long-run relationships in finance

  • Chris Brooks, University of Reading
  • Book:
    Introductory Econometrics for Finance
    Published online:
    09 August 2018
    Print publication:
    02 May 2014, pp 353-414

  • Summary

    Learning outcomes

    In this chapter, you will learn how to

  • • Highlight the problems that may occur if non-stationary data are used in their levels form

  • • Test for unit roots

  • • Examine whether systems of variables are cointegrated

  • • Estimate error correction and vector error correction models

  • • Explain the intuition behind Johansen's test for cointegration

  • • Describe how to test hypotheses in the Johansen framework

  • • Construct models for long-run relationships between variables in EViews

    • Stationarity and unit root testing

    8.1.1 Why are tests for non-stationarity necessary?

    There are several reasons why the concept of non-stationarity is important and why it is essential that variables that are non-stationary be treated differently from those that are stationary. Two definitions of non-stationarity were presented at the start of chapter 6. For the purpose of the analysis in this chapter, a stationary series can be defined as one with a constant mean, constant variance and constant autocovariances for each given lag. Therefore, the discussion in this chapter relates to the concept of weak stationarity. An examination of whether a series can be viewed as stationary or not is essential for the following reasons:

  • The stationarity or otherwise of a series can strongly influence its behaviour and properties. To offer one illustration, the word ‘shock’ is usually used to denote a change or an unexpected change in a variable or perhaps simply the value of the error term during a particular time period.[…]

  • 14 - Conducting empirical research or doing a project or dissertation in finance

  • Chris Brooks, University of Reading
  • Book:
    Introductory Econometrics for Finance
    Published online:
    09 August 2018
    Print publication:
    02 May 2014, pp 626-666

  • Summary

    Learning outcomes

    In this chapter, you will learn how to

  • • Choose a suitable topic for an empirical research project in finance

  • • Draft a research proposal

  • • Find appropriate sources of literature and data

  • • Determine a sensible structure for the dissertation

  • • Set up and conduct a valid event study

  • • Employ the Fama-MacBeth and Fama-French approaches to testing asset pricing models and explaining the variation in asset returns

    • What is an empirical research project and what is it for?

    Many courses, at both the undergraduate and postgraduate levels, require or allow the student to conduct a project. This may vary from being effectively an extended essay to a full-scale dissertation or thesis of 10,000 words or more.

    Students often approach this part of their degree with much trepidation, although in fact doing a project gives students a unique opportunity to select a topic of interest and to specify the whole project themselves from start to finish. The purpose of a project is usually to determine whether students can define and execute a piece of fairly original research within given time, resource and reportlength constraints. In terms of econometrics, conducting empirical research is one of the best ways to get to grips with the theoretical material, and to find out what practical difficulties econometricians encounter when conducting research. Conducting the research gives the investigator the opportunity to solve a puzzle and potentially to uncover something that nobody else has; it can be a highly rewarding experience.

  • 10 - Switching models

  • Chris Brooks, University of Reading
  • Book:
    Introductory Econometrics for Finance
    Published online:
    09 August 2018
    Print publication:
    02 May 2014, pp 490-525

  • Summary

    Learning outcomes

    In this chapter, you will learn how to

  • • Use intercept and slope dummy variables to allow for seasonal behaviour in time series

  • • Motivate the use of regime switching models in financial econometrics

  • • Specify and explain the logic behind Markov switching models

  • • Compare and contrast Markov switching and threshold autoregressive models

  • • Describe the intuition behind the estimation of regime switching models

    • Motivations

    Many financial and economic time series seem to undergo episodes in which the behaviour of the series changes quite dramatically compared to that exhibited previously. The behaviour of a series could change over time in terms of its mean value, its volatility, or to what extent its current value is related to its previous value. The behaviour may change once and for all, usually known as a ‘structural break’ in a series. Or it may change for a period of time before reverting back to its original behaviour or switching to yet another style of behaviour, and the latter is typically termed a ‘regime shift’ or ‘regime switch’.

    10.1.1 What might cause one-off fundamental changes in the properties of a series?

    Usually, very substantial changes in the properties of a series are attributed to large-scale events, such as wars, financial panics – e.g. a ‘run on a bank’, significant changes in government policy, such as the introduction of an inflation target, or the removal of exchange controls, or changes in market microstructure – e.g. the ‘Big Bang’, when trading on the London Stock Exchange (LSE) became electronic, or a change in the market trading mechanism, such as the partial move of the LSE from a quote-driven to an order-driven system in 1997.

  • 11 - Panel data

  • Chris Brooks, University of Reading
  • Book:
    Introductory Econometrics for Finance
    Published online:
    09 August 2018
    Print publication:
    02 May 2014, pp 526-558

  • Summary

    Learning outcomes

    In this chapter, you will learn how to

  • • Describe the key features of panel data and outline the advantages and disadvantages of working with panels rather than other structures

  • • Explain the intuition behind seemingly unrelated regressions and propose examples of where they may be usefully employed

  • • Contrast the fixed effect and random effect approaches to panel model specification, determining which is the more appropriate in particular cases

  • • Estimate and interpret the results from panel unit root and cointegration tests

  • • Construct and estimate panel models in EViews

    • Introduction – what are panel techniques and why are they used?

    The situation often arises in financial modelling where we have data comprising both time series and cross-sectional elements, and such a dataset would be known as a panel of data or longitudinal data. A panel of data will embody information across both time and space. Importantly, a panel keeps the same individuals or objects (henceforth we will call these ‘entities’) and measures some quantity about them over time. This chapter will present and discuss the important features of panel analysis, and will describe the techniques used to model such data.

  • 1 - Introduction

  • Chris Brooks, University of Reading
  • Book:
    Introductory Econometrics for Finance
    Published online:
    09 August 2018
    Print publication:
    02 May 2014, pp 1-27

  • Summary

    Learning econometrics is in many ways like learning a new language. To begin with, nothing makes sense and it is as if it is impossible to see through the fog created by all the unfamiliar terminology. While the way of writing the models – the notation – may make the situation appear more complex, in fact it is supposed to achieve the exact opposite. The ideas themselves aremostly not so complicated, it is just a matter of learning enough of the language that everything fits into place. So if you have never studied the subject before, then persevere through this preliminary chapter and you will hopefully be on your way to being fully fluent in econometrics!

    Learning outcomes

    In this chapter, you will learn how to

  • • Compare nominal and real series and convert one to the other

  • • Distinguish between different types of data

  • • Describe the key steps involved in building an econometric model

  • • Calculate asset price returns

  • • Deflate series to allow for inflation

  • • Construct a workfile, import data and accomplish simple tasks in EViews

    • The chapter sets the scene for the book by discussing in broad terms the questions of what econometrics is, and what the ‘stylised facts’ are describing financial data that researchers in this area typically try to capture in their models. Some discussion is presented on the kinds of data we encounter in finance and how to work with them.

  • 3 - A brief overview of the classical linear regression model

  • Chris Brooks, University of Reading
  • Book:
    Introductory Econometrics for Finance
    Published online:
    09 August 2018
    Print publication:
    02 May 2014, pp 75-133

  • Summary

    Learning outcomes

    In this chapter, you will learn how to

  • • Derive the OLS formulae for estimating parameters and their standard errors

  • • Explain the desirable properties that a good estimator should have

  • • Discuss the factors that affect the sizes of standard errors

  • • Test hypotheses using the test of significance and confidence interval approaches

  • • Interpret p-values

  • • Estimate regression models and test single hypotheses in EViews

    • What is a regression model?

    Regression analysis is almost certainly the most important tool at the econometrician's disposal. But what is regression analysis? In very general terms, regression is concerned with describing and evaluating the relationship between a given variable and one or more other variables. More specifically, regression is an attempt to explain movements in a variable by reference to movements in one or more other variables.

    To make this more concrete, denote the variable whose movements the regression seeks to explain by y and the variables which are used to explain those variations by x1, x2, …, xk. Hence, in this relatively simple setup, it would be said that variations in k variables (the xs) cause changes in some other variable, y. This chapter will be limited to the case where the model seeks to explain changes in only one variable y (although this restriction will be removed in chapter 7).

    There are various completely interchangeable names for y and the xs, and all of these terms will be used synonymously in this book (see box 3.1).

  • Preface to the third edition

  • Chris Brooks, University of Reading
  • Book:
    Introductory Econometrics for Finance
    Published online:
    09 August 2018
    Print publication:
    02 May 2014, pp xxi-xxiv

  • Summary

    Sales of the first two editions of this book surpassed expectations (at least those of the author). Almost all of those who have contacted the author seem to like the book, and while other textbooks have been published since in the broad area of inancial econometrics, none are really at the introductory level. All of the motivations for the irst edition, described below, seem just as important today. Given that the book seems to have gone down well with readers, I have left the style largely unaltered but changed the structure slightly and added new material.

    The main motivations for writing the irst edition ofthe book were:

  • • To write a book that focused on using and applying the techniques rather than deriving proofs and learning formulae.

  • • To write an accessible textbook that required no prior knowledge of econometrics, but which also covered more recently developed approaches usually only found in more advanced texts.

  • • To use examples and terminology from finance rather than economics since there are many introductory texts in econometrics aimed at students of economics but none for students of finance.

  • • To litter the book with case studies of the use of econometrics in practice taken from the academic finance literature.

  • • To include sample instructions, screen dumps and computer output from a popular econometrics package. This enabled readers to see how the techniques can be implemented in practice.

  • • To develop a companion web site containing answers to end of chapter questions, PowerPoint slides and other supporting materials.

  • 12 - Limited dependent variable models

  • Chris Brooks, University of Reading
  • Book:
    Introductory Econometrics for Finance
    Published online:
    09 August 2018
    Print publication:
    02 May 2014, pp 559-590

  • Summary

    Learning outcomes

    In this chapter, you will learn how to

  • • Compare between different types of limited dependent variables and select the appropriate model

  • • Interpret and evaluate logit and probit models

  • • Distinguish between the binomial and multinomial cases

  • • Deal appropriately with censored and truncated dependent variables

  • • Estimate limited dependent variable models using maximum likelihood in EViews

    • Introduction and motivation

    Chapters 5 and 10 have shown various uses of dummy variables to numerically capture the information qualitative variables – for example, day-of-the-week effects, gender, credit ratings, etc. When a dummy is used as an explanatory variable in a regression model, this usually does not give rise to any particular problems (so long as one is careful to avoid the dummy variable trap – see chapter 10). However, there are many situations in financial research where it is the explained variable, rather than one or more of the explanatory variables, that is qualitative. The qualitative information would then be coded as a dummy variable and the situation would be referred to as a limited dependent variable and needs to be treated differently. The term refers to any problem where the values that the dependent variables may take are limited to certain integers (e.g. 0, 1, 2, 3, 4) or even where it is a binary number (only 0 or 1).

Introductory Econometrics for Finance
  • 3rd edition
  • Chris Brooks
  • Published online:
    09 August 2018
    Print publication:
    02 May 2014
  • This bestselling and thoroughly classroom-tested textbook is a complete resource for finance students. A comprehensive and illustrated discussion of the most common empirical approaches in finance prepares students for using econometrics in practice, while detailed case studies help them understand how the techniques are used in relevant financial contexts. Worked examples from the latest version of the popular statistical software EViews guide students to implement their own models and interpret results. Learning outcomes, key concepts and end-of-chapter review questions (with full solutions online) highlight the main chapter takeaways and allow students to self-assess their understanding. Building on the successful data- and problem-driven approach of previous editions, this third edition has been updated with new data, extensive examples and additional introductory material on mathematics, making the book more accessible to students encountering econometrics for the first time. A companion website, with numerous student and instructor resources, completes the learning package.

  • 4 - Trends

  • Philip Hans Franses, Dick van Dijk, Anne Opschoor
  • Book:
    Time Series Models for Business and Economic Forecasting
    Published online:
    28 May 2018
    Print publication:
    24 April 2014, pp 77-109

  • Summary

    The examples in Chapter 2 demonstrate that many time series in economics and business have a trending pattern, where for macroeconomic time series such trends typically move upwards. Although many practitioners would be able to indicate roughly what a trend is (“a general tendency for a variable to increase or decrease over time”), a formal definition of a trend cannot be given otherwise than in the context of a model. Put differently, only after we have agreed upon a time series model that (presumably) describes the data at hand, we can define a trend within this framework and discuss the “trend properties” of the time series in a meaningful way. In this book, the focus is on ARMA-type time series models, and hence the current chapter deals with trends within this model class.

    For several reasons it is important to investigate the appropriate formulation of the trend in a time series prior to putting effort into modeling other data features and forecasting. First and foremost, the trend will dominate long-run out-of-sample forecasts, although also short-run forecasts can be affected, as we will see in Section 4.4. An inadequate specification of the trend possibly leads to forecasts that are biased or inaccurate in other ways. Second, a time series that displays a trend is nonstationary, in the sense that it does not have a constant mean. In addition, depending on the nature of the trend, the unconditional variance of the series is not constant over time but increases with every new observation.

  • 9 - Multivariate time series

  • Philip Hans Franses, Dick van Dijk, Anne Opschoor
  • Book:
    Time Series Models for Business and Economic Forecasting
    Published online:
    28 May 2018
    Print publication:
    24 April 2014, pp 240-283

  • Summary

    Univariate time series models, as discussed in the previous chapters, can be very useful for descriptive analysis and for out-of-sample forecasting. Such univariate models are restrictive, however, in the sense that they rely purely on the history of the time series itself and do not try to exploit information present in other variables. Given that often economic variables are closely related with other variables, such information may be potentially useful and using it may lead to more realistic descriptions of the behavior of economic variables and also to more accurate out-of-sample forecasts. In fact, ignoring relationships with other variables may give rise to complications in the specification of an appropriate univariate time series model. It may be that the empirical specification of a univariate model is hampered by outliers and structural shifts, which may be attributed to one or more other variables than the yt variable under consideration. For example, the change in the trend of US industrial production around 1979.4 (see Figure 2.3) may be caused by the large oil price increase around that time. Additionally, the same oil price variable may be responsible for the large negative growth in production in 1974/1975, which seems to correspond to an innovation outlier. In other words, it may be worthwhile to include an oil price variable in a model for US industrial production to render it more realistic and more accurate.

Page 84 of 292