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In this chapter, we outline the statistical consequences of neglecting structural breaks and regime switches in autoregressive and GARCH models and propose two strategies to approach the problem. The first strategy is to identify regimes of constant unconditional volatility using a change point detector and estimate a separate GARCH model on the resulting segments. The second approach is to use a multiple-regime GARCH model, such as the Flexible Coefficient GARCH (FCGARCH) specification, where the regime-switches are governed by an observable variable. We apply both alternatives to an array of financial time series and compare their forecast performance.

Apart from the well-known, high persistence of daily financial volatility data, there is also a short correlation structure that reverts to the mean in less than a month. We find this short correlation time scale in six different daily financial time series and use it to improve the short-term forecasts from generalized auto-regressive conditional heteroskedasticity (GARCH) models. We study different generalizations of GARCH that allow for several time scales. On our holding sample, none of the considered models can fully exploit the information contained in the short scale. Wavelet analysis shows a correlation between fluctuations on long and on short scales. Models accounting for this correlation as well as long-memory models for absolute returns appear to be promising.

This volume of Advances in Econometrics is devoted to dynamic stochastic general equilibrium (DSGE) models, which have gained popularity in both academic and policy circles as a theoretically and methodologically coherent way of analyzing a variety of issues in empirical macroeconomics. The volume is divided into two parts. The first part covers important topics in DSGE modeling and estimation practice, including the modeling and role of expectations, the study of alternative pricing models, the problem of non-invertibility in structural VARs, the possible weak identification in new open economy macro models, and the modeling of trend inflation. The second part is devoted to innovations in econometric methodology. The papers in this section advance new techniques for addressing key theoretical and inferential problems and include discussion and applications of Laplace-type, frequency domain, empirical likelihood, and method of moments estimators.

Advances in Econometrics is a series of research annuals first published in 1982 by JAI Press. In this paper, we present a brief history of the series over its first 30 years. We describe key events in the history of the volume, and give information about the key contributors: editors, editorial board members, Advances in Econometrics Fellows, and authors who have contributed to the great success of the series.

Advances in Econometrics is a series of research volumes first published in 1982 by JAI Press. The authors present an update to the history of the Advances in Econometrics series. The initial history, published in 2012 for the 30th Anniversary Volume, describes key events in the history of the series and provides information about key authors and contributors to Advances in Econometrics. The authors update the original history and discuss significant changes that have occurred since 2012. These changes include the addition of five new Senior Co-Editors, seven new AIE Fellows, an expansion of the AIE conferences throughout the United States and abroad, and the increase in the number of citations for the series from 7,473 in 2012 to over 25,000 by 2022.

We examine the Stein-rule shrinkage estimator for possible improvements in estimation and forecasting when there are many predictors in a linear time series model. We consider the Stein-rule estimator of Hill and Judge (1987) that shrinks the unrestricted unbiased ordinary least squares (OLS) estimator toward a restricted biased principal component (PC) estimator. Since the Stein-rule estimator combines the OLS and PC estimators, it is a model-averaging estimator and produces a combined forecast. The conditions under which the improvement can be achieved depend on several unknown parameters that determine the degree of the Stein-rule shrinkage. We conduct Monte Carlo simulations to examine these parameter regions. The overall picture that emerges is that the Stein-rule shrinkage estimator can dominate both OLS and principal components estimators within an intermediate range of the signal-to-noise ratio. If the signal-to-noise ratio is low, the PC estimator is superior. If the signal-to-noise ratio is high, the OLS estimator is superior. In out-of-sample forecasting with AR(1) predictors, the Stein-rule shrinkage estimator can dominate both OLS and PC estimators when the predictors exhibit low persistence.