Efficient combined estimation under structural breaks

Hashem Pesaran has made many seminal contributions, among others, in the time series econometrics estimation and forecasting under structural break, see Pesaran and Timmermann (2005 , 2007 ), Pesaran, Pettenuzzo, and Timmermann (2006) , and Pesaran, Pick, and Pranovich (2013) . In this chapter, the authors focus on the estimation of regression parameters under multiple structural breaks with heteroskedasticity across regimes. The authors propose a combined estimator of regression parameters based on combining restricted estimator under the situation that there is no break in the parameters, with unrestricted estimator under the break. The operational optimal combination weight is between zero and one. The analytical finite sample risk is derived, and it is shown that the risk of the proposed combined estimator is lower than that of the unrestricted estimator under any break size and break points. Further, the authors show that the combined estimator outperforms over the unrestricted estimator in terms of the mean squared forecast errors. Properties of the estimator are also demonstrated in simulations. Finally, empirical illustrations for parameter estimators and forecasts are presented through macroeconomic and financial data sets.