Time Series Analysis for Economists

Preface

Empirical macroeconomics often involves the analysis of time series data, such as GDP, inflation, and interest rates, which are distinct from those utilized in cross-sectional studies. The goal of this book is to bridge the gap between introductory time series textbooks and theoretical econometrics. In modern applied research, a rudimentary comprehension of the subject often proves insufficient. Though computational tasks can be executed through simple computer commands, practitioners must go below the surface to understand the intricacies and limitations of the techniques involved. However, an exhaustive exploration of advanced econometric theories would be excessive for practical purposes. For instance, introductory textbooks would caution against running OLS on non-stationary time series, citing the risk of spurious regression. Students often accept this as a rule of thumb without a grasp of its underlying rationale. Yet, delving into intricate topics such as Itô calculus is unnecessary for empirical researchers.

This book seeks to acquaint readers with the time series topics essential for understanding and conducting empirical research, with a focus on macroeconomic applications. In addition to introducing basic concepts and applications, the book endeavors to elevate comprehension to a deeper level by elucidating the “why” alongside the “what” and “how.” However, the objective is not to provide an exhaustive treatment replete with formal proofs; rather, emphasis is placed on providing intuitive explanations. Consequently, readers may encounter instances of informal proofs where a more formal approach is deemed unnecessary for applied works. This book can be read as intermediary materials between undergraduate econometrics and more rigorous treatments of the subject, such as Hamilton’s Time Series Analysis.

The materials presented are drawn from or influenced by various sources, which are listed in the References at the end of the book without being cited individually in the context.

Regarding notations, I use lowercase letters for random variables, such as \(x_t\) and \(y_t\). Realizations of random variables are expressed as \(x_1\), \(x_2\), and so on. The context will make it clear whether I am referring to a random variable or its realizations. Capital letters are reserved for matrices, such as \(A\) and \(B\). Vectors and matrices are sometimes written in bold for emphasizing, such as \(\boldsymbol X\) and \(\boldsymbol y\); but mostly, in plain format, \(X\) and \(y\), provided that they will not lead to confusion. Greek letters are preferred for parameters, such as \(\alpha\) and \(\beta\). Estimators are indicated with a hat, such as \(\hat{\alpha}\) and \(\hat{\beta}\).

I use the statistical language R whenever programming is involved. I am aware that there are many time series solutions available in R. To avoid burdening readers with excessive packages, I stick to base R as much as possible with a little help from the zoo package.

I would like to emphasize that my knowledge and understanding of the subject are limited, and I acknowledge that there may be mistakes or areas where I could have provided a more accurate explanation. I deeply appreciate any feedback or corrections from readers that could improve the accuracy and clarity of this book.