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2023 | Book

Introduction Read chapter Read first chapter

Time Series Econometrics

Learning Through Replication

Author: John D. Levendis

Publisher: Springer International Publishing

Book Series : Springer Texts in Business and Economics

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Wirtschaft"

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About this book

Revised and updated for the second edition, this textbook allows students to work through classic texts in economics and finance, using the original data and replicating their results. In this book, the author rejects the theorem-proof approach as much as possible, and emphasizes the practical application of econometrics. They show with examples how to calculate and interpret the numerical results.

This book begins with students estimating simple univariate models, in a step by step fashion, using the popular Stata software system. Students then test for stationarity, while replicating the actual results from hugely influential papers such as those by Granger & Newbold, and Nelson & Plosser. Readers will learn about structural breaks by replicating papers by Perron, and Zivot & Andrews. They then turn to models of conditional volatility, replicating papers by Bollerslev. Students estimate multi-equation models such as vector autoregressions and vector error-correction mechanisms, replicating the results in influential papers by Sims and Granger. Finally, students estimate static and dynamic panel data models, replicating papers by Thompson, and Arellano & Bond.

The book contains many worked-out examples, and many data-driven exercises. While intended primarily for graduate students and advanced undergraduates, practitioners will also find the book useful.

“How to best start learning time series econometrics? Learning by doing. This is the ethos of this book. What makes this book useful is that it provides numerous worked out examples along with basic concepts. It is a fresh, no-nonsense, practical approach that students will love when they start learning time series econometrics. I recommend this book strongly as a study guide for students who look for hands-on learning experience."

--Professor Sokbae "Simon" Lee, Columbia University, Co-Editor of Econometric Theory and Associate Editor of Econometrics Journal.

Table of Contents

Frontmatter
Chapter 1. Introduction
Abstract
The econometrics of cross sections relies on the fact that observations are independent. The opposite is the case with time series. Today’s data depends, at least in part, on yesterday’s data. There is inertia to the system. This chapter introduces some key notation and math behind time series econometrics. We also introduce Stata, some of its time series functions, and how to install the various user-written packages we will make use of throughout the text.
John D. Levendis
Chapter 2. ARMA(p,q) Processes
Abstract
An ARIMA model is made up of two components: an Autoregressive (AR) model and a Moving average (MA) model. Both rely on previous data to help predict future outcomes. AR and MA models are the building blocks of all our future work in this text. They are foundational, so we proceed slowly. First, we introduce the concept of stationarity and see what restrictions on the two models are required for stationarity. Then we turn to estimating the models, extracting the associated Impulse Response Functions, and using the models for forecating.
John D. Levendis
Chapter 3. Model Selection in ARMA(p,q) Processes
Abstract
Most time series methods are only valid if the underlying time series is stationary. A time series is stationary if its mean, variance, and autocovariance do not rely on the particular time period. In this chapter, we derive the conditions under which a process is stationary, and show some implications of this stationarity. To answer these questions we will learn about the so-called Box-Jenkins approach of comparing empirical autocorrelation functions and partial autocorrelation functions with their theoretical counterparts.
John D. Levendis
Chapter 4. Stationarity and Invertibility
Abstract
Most time series methods are only valid if the underlying time series is stationary. A time series is stationary if its mean, variance, and autocovariance do not rely on the particular time period. In this chapter, we derive the conditions under which a process is stationary, and show some implications of this stationarity.
John D. Levendis
Chapter 5. Nonstationarity and ARIMA(p,d,q) Processes
Abstract
Many economic and financial time series do not have a constant mean. Rather they show growth or decay. The type of growth–whether deterministic or stochastic–has important implications for policy. In this chpater we examine the different ways to detrend the data. We spend particular attention on the effects of “differencing” (and over-differencing) the data, especially in the context of random walk models with and without drift. We also introduce the ARIMA class of models.
John D. Levendis
Chapter 6. Seasonal ARMA(p,q) Processes
Abstract
Many financial and economic time series exhibit a regular cyclicality, periodicity, or “seasonality.” When econometricians say data is “seasonal”, they simply mean that there is some sort of periodicity, whether it is weekly, monthly or yearly. Seasonal models can be be deterministic or stochastic, stationary or integrated, additive or multiplicative.
John D. Levendis
Chapter 7. Unit Root Tests
Abstract
A process might be nonstationary without being a unit root. The two concepts are related, but they are not identical and it is common to confuse the two. A data series might be nonstationary because of a deterministic trend. Or it could be explosive. Or it can have a variance that is changing over time. In this chapter we explore some of the more common unit root tests and stationarity tests, including the Augmented Dickey-Fuller and Phillips-Perron tests
John D. Levendis
Chapter 8. Structural Breaks
Abstract
In 1979 Robet Lucas offered his famous “critique”: the economic parameters we estimate are not permanent and unchanging. They depend on the institutional framework in place at the time. Changes in economic policy—or of laws, regulations or geopolicics—affect not just the outcome of the economic process; they change the economic process itself. Therefore the parameters describing a structurally different economy will be different. Lucas, in effect, argued that econometrics should contend with “structural breaks,” the topic of this chapter. If practicing econometricians attempt to fit years’ worth of data to one unchanging model, they are likely committing a serious misspecification error. We need an econometric model that allows parameters to change. In this chapter, we explore the consequences of structural change and learn how to model it, especially when dealing with the related problem of unit roots. Along the way, we replicate the papers by Perron (1989) and Zivot and Andrews (1992), two seminal papers that established the econometrics of structural change.
John D. Levendis
Chapter 9. ARCH, GARCH, and Time-Varying Variance
Abstract
Given that risk (unpredictable ups and downs) and return are fundamental to finance, it is natural that financial econometricians would begin trying to model variance rigorously. Financial markets are notorious for their volatility, with periods of relative stability followed by periods of turbulence.
The fact that the variance today depends, in some part, on the variance yesterday implies that variance itself can be modeled as an autoregressive process. The fact that this change can be sudden raises questions of structural change. In this chapter, we take earlier models that focused on the level of a time series, and extend them to model variance.
John D. Levendis
Chapter 10. Vector Autoregressions I: Basics
Abstract
If we take the notion of general equilibrium seriously, then everything in the economy is related to everything else. For this reason, it is often impossible to say which variables are exogenous. Vector autoregressions or “VARs” attempt to model the many interdependencies between economic variables. The VAR generalizes earlier univariate autoregressive (AR) models by allowing a large number of variables depend on lagged values of their own and of other variables. Earlier concepts of stability, lag selection, and impulse response functions are also extended, and Granger causality is introduced. We also replicate an influential paper by Christopher Sims, the inventor of the VAR.
John D. Levendis
Chapter 11. Vector Autoregressions II: Extensions
Abstract
In the previous chapter we covered the basics of reduced-form VARs on stationary data.
John D. Levendis
Chapter 12. Cointegration and VECMs
Abstract
In this chapter we show how to model the long-run relationship between variables in their levels, even if they are integrated. This is possible if two or more variables are “cointegrated.” Two variables are cointegrated is the difference between them is stationary. Or, to put it loosely, they move in parallel. In this chapter we explore the concept of cointegration, error correction mechanisms, and some of the more popular tests of contegration.
John D. Levendis
Chapter 13. Static Panel Data Models
Abstract
We begin our section on panel data models by examining static models. We distinguish between fixed effects (FE) and random effects (RE) models, and how to choose between them using a Hausman test or Mundlak test. We discuss models which include time-FEs as well as country-FEs. Finally, we discuss the problem of cross-sectional dependence and how to test for such dependence.
John D. Levendis
Chapter 14. Dynamic Panel Data Models
Abstract
This chapter generalizes most of the topics from earlier in the book settings with panel data. We begin by introducing dynamic panel data models, and how to estimate them using the popular estimators introduced in a series of papers by Arellano, Bond, Blundell and Bover. We then explain how to test for stationarity using the so called “first generation” panel unit root tests; these tests extend the earlier time series tests to panels by retaining the assumption that panels are independent of one another. After this, “scond generation” tests are introduced; these tests can be used in the presence of cross sectional dependence. Finally, we discuss panel VARs, stability, impulse response functions, panel Granger causality, and panel cointegration tests.
John D. Levendis
Chapter 15. Conclusion
Abstract
Now that we have learned a bit about how to analyze time series data, we can use a bit of self reflection and humility. Econometrics is necessarily backward looking: a strong empirical result may not cointinue into the future. Further, econometrics shares more with rhetoric than with physics; it can be thought of as a form of argumentation rather than a search for immutable truth. Finally: your results are never unimpeachable, your analysis is never perfect, and you will never have the final word.
John D. Levendis
Backmatter
Metadata
Title
Time Series Econometrics
Author
John D. Levendis
Copyright Year
2023
Electronic ISBN
978-3-031-37310-7
Print ISBN
978-3-031-37309-1
DOI
https://doi.org/10.1007/978-3-031-37310-7