Quantile Regression for Cross-Sectional and Time Series Data: Applications in Energy Markets Using R

By Jorge M. Uribe and Montserrat Guillen

This brief addresses the estimation of quantile regression models from a practical perspective, which will support researchers who need to use conditional quantile regression to measure economic relationships among a set of variables. It will also benefit students using the methodology for the first time, and practitioners at private or public organizations who are interested in modeling different fragments of the conditional distribution of a given variable. The book pursues a practical approach with reference to energy markets, helping readers learn the main features of the technique more quickly. Emphasis is placed on the implementation details and the correct interpretation of the quantile regression coefficients rather than on the technicalities of the method, unlike the approach used in the majority of the literature. All applications are illustrated with R. 

 

• Language: English
• Publisher: Springer
• Release date: Mar 30, 2020
• ISBN: 9783030445041

Book preview

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2020

J. M. Uribe, M. GuillenQuantile Regression for Cross-Sectional and Time Series DataSpringerBriefs in Financehttps://doi.org/10.1007/978-3-030-44504-1_1

1. Why and When Should Quantile Regression Be Used?

Jorge M. Uribe¹ and Montserrat Guillen²  

(1)

Faculty of Economics and Business, Open University of Catalonia, Barcelona, Spain

(2)

Department of Econometrics, University of Barcelona, Barcelona, Spain

Montserrat Guillen

Email: [e-mail]

Abstract

Quantile regression is a way to disclose predictive relationships between a response variable and some regressors or explanatory variables when the interest is to find a causal link beyond the mean-to-mean effects. Quantile regression is a procedure to model the cut points of the cumulated conditional probability distribution of a response variable as a function of some covariates.

Keywords

Linear modelRegressionQuantilePercentilePredictive modelRisk analysisApplied quantile regression

Since Koenker and Basset’s (1978) seminal contribution, quantile regression models have gained significant importance for many fields of economics and beyond. Applications of quantile regression techniques in economics include recent studies on finance as in Fattouh et al. (2005) or Behr (2010); classical applications to modeling wages in labor economics (Chamberlain 1994; Buchinsky 1994); issues on the economics of education (Eide and Showalter 1998); inequality (Hao and Naiman 2007); modeling of prices and expenditure in different economic sectors such as traveling (Hung et al. 2010; Marrocu et al. 2015) or real estate (Zietz et al. 2008; Liao and Wang 2012); among other fields of economics—see also Koenker and Hallock (2001) and Fitzenberger et al. (2013). Outside economics, it has been used, for example, in genetics (Briollais and Durrieu 2014), medicine (Wei et al. 2006; Daniel-Spiegel et al. 2013), political science (Okada and Samreth 2012) or hydrology (Tareghian and Rasmussen 2013) to name some applications; see also Yu et al. (2003) for a recent summary of quantile regression research.

In sum, quantile regression enables the researcher to study the relationship between a set of variables not only at the center but also alongside the entire conditional distribution of the dependent variable.

In quantile regression models, the quantiles of a dependent variable are assumed to be linearly associated with a set of conditioning variables. In general, this translates into a nonlinear relationship between the dependent and the independent variables considering the whole distribution.

Quantile regression models constitute a promising tool for gaining a deeper understanding of financial markets and financial prices. In that context, the interest is not only on average prices, but also on volatility, i.e., on low or high extremes. Quantile regression is a way to find what influences the magnitude of the response in those areas that are located far from the central value and that are not necessarily found in symmetric positions with respect to the mean.

Quantile regression models are known to be robust to outliers in the sample, which is particularly relevant when analyzing financial time series, in which crises and booms are generally accompanied by abnormally high or low observations. Quantile regression models are as well semi-parametric and, therefore, they require minimal distributional assumptions on the underlying data generating process, which allows a pragmatic approach when modeling complex dynamics as those recorded for financial prices and returns. Additionally, quantile regression models offer larger flexibility than linear regression models for analyzing different market scenarios. That is, lower quantiles of the return distributions in a given market can be naturally associated with downmarkets, while the higher quantiles are intuitively associated with up-trending markets. Therefore, very high or very low quantiles are likely related to the study of financial phenomena of great interest for the financial literature, such as bubbles, contagion or episodes of financial distress, which are known precisely for emerging under extreme market situations.

In the same way, quantile regression models are particularly convenient over competing linear regression alternatives, when the error structure is rather heterogeneous, also as is the case of many economic or financial time series, and when errors are not well described by a Gaussian distribution. As we will see in the following chapters, conditional quantile regressions also offer an intuitive and convenient way to model asymmetries and different regimes in the model for time series such as electricity prices.

In this book, we present quantile regression from a practical perspective. We show how it can be implemented for cross-sectional data and for time series data [see Alexander et al. (2011) for a perspective combining both times series and cross-sectional data]. We provide a comprehensive overview of the interpretability of the results. For this purpose, we have chosen the context of energy markets, because it is an area where quantile regression can be easily implemented and understood. The same methodology can immediately be implemented to other areas of economics and finance, and even for a broader audience of social scientists and engineers.

The next chapter provides a minimum introduction to energy markets as a case of study for quantile regression implementation throughout the rest of the chapters. This introduction to energy economics can be skipped for readers who are already familiar with this field. However, it gives an overview of the problems that are addressed in many other areas, both from the perspective of a cross-sectional analysis and of a time series analysis.

Chapter 3 is a general presentation to the main concept of quantile estimation, quantile regression and the difference between conditional and unconditional quantile regression. This is an essential part for understanding the modeling approach. Chapter 4 shows the implementation of quantile regression in cross-sectional data. Data from a survey, including sample weights, are used to illustrate the methodology. Programs in R and detailed outputs are presented so that the reader can follow the interpretation of the results. Chapter 5 is devoted to quantile regression for time series. Again the implementation is illustrated using data for electricity prices in