Regression Analysis of Economic Time Series Data

This part covers the time series analysis and consists of the following chapters:

• Chapter 22  Introduction to Time Series Regression and Forecasting
• Chapter 23  Estimation of Dynamic Causal Effects
• Chapter 24  Additional Topics in Time Series Regression

In Chapter 22, we introduce the basic concepts required for univariate time series methods. We cover autoregressions (AR) and autoregressive distributed lag (ADL) models, which are used for forecasting. We introduce stationarity, non-stationarity, and weak dependence conditions for time series data. We specify assumptions that are required for consistent estimation of the parameters in the AR and ADL models. We discuss popular information criteria used for selecting the optimal number of lag terms in the AR and ADL models. We explain how alternative models can be compared in terms of forecasting performance using the mean squared forecast error (MSFE). We discuss how non-stationarity can arise from deterministic and stochastic trends. We introduce the augmented Dickey-Fuller (ADF) statistic for testing unit roots. Finally, we show how autoregressions can be extended by assuming that the error term follows an AR process.

In Chapter 23, we show how time series data can be used to estimate the dynamic causal effects of a variable of interest on the dependent variable. We introduce the distributed lag model, which relates the dependent variable to the current and past values of the variable of interest. We show that the distributed lag model can be estimated by the OLS estimator under certain assumptions. We discuss strict and weak exogeneity conditions that ensure the consistency of the OLS estimator. For inference, we introduce heteroskedasticity-and-autocorrelation-consistent (HAC) standard errors. Finally, we apply the distributed lag model to measure the dynamic causal effect of freezing degree days on frozen concentrated orange juice prices collected from Orlando, the center of Florida’s orange-growing region.

In Chapter 24, we consider widely used multivariate time series and volatility models. We introduce the vector autoregressive (VAR) model, which is a multivariate extension of the ADL model. We discuss specification issues and show how the VAR model can be estimated. We define Granger causality and show how it can be tested in a VAR model. Next, we introduce cointegration to characterize the long-term equilibrium relationship among time series. We discuss the Engle-Granger two-step method for estimating cointegrated parameters and the Johansen test for cointegration. We then introduce the vector error correction model (VECM), a VAR model that includes error correction terms to account for the long-run relationship among the variables. Finally, we introduce ARCH and GARCH models for modeling time-varying volatility of the financial time series data.