Structural Changes, Level Shifts in Variance and the Frequency of Permanent Shocks

Trustees Of Boston University, Boston

Investigators

Abstract

The common theme of this project is structural change in economic time series but some tools developed will be used beyond this topic. There are five main projects described, each of which can lead to several research papers to be published in leading journals. 1) Testing for multiple structural changes in the variance of the errors in a linear regression model allowing for or testing concurrently for changes in the parameters of the conditional mean regression. This project provides methods based on a likelihood framework for a number of testing problems and for estimating the number of breaks in variance and in coefficients and to assess whether some are common. 2) The time series properties of the variability of stock returns (proxied by absolute returns). This project considers a simple stochastic level shift model and propose a method of estimation based on a State Space model with a mixture of Normal distribution. It shows how the model can be extended to allow the probability of shifts to be a function of other variables and, hence, deliver improved forecasts. 3) The frequency of permanent shocks. The project builds a stochastic model which can deliver estimates of the probability of a level shift or a slope change at any given period. The usual unit root model specifies the probability to be one, while for a trend-stationary process it is zero. This method allows a considerably broader picture, which can deliver useful practical implications. 4) Assessing the importance of level shifts in non-trending economic and financial time series via the shape of their autocorrelation function. 5) An alternative approach to evaluate the properties of structural change tests. This project uses the concept of Bahadur efficiency to compare the properties of tests for structural changes and show that it yields predictions in better agreement with the finite sample performance compared to the often used local asymptotic power analysis. It proposes deriving tests that are Bahadur optimal within a broad enough class. Broader Impact: The work proposed in this project will be valuable to applied researchers in various fields as well as to econometricians and statisticians. It not only provides new tools to answer economic (and other) questions of interest but also contains substantial empirical components that can shed new light on how to model economic variables, especially in the areas of macroeconomics and finance.