Forecasting in the presence of in and out of sample breaks

We present a frequentist-based approach to forecast time series in the presence of in-sample and out-of-sample breaks in the parameters of the forecasting model. We first model the parameters as following a random level shift process, with the occurrence of a shift governed by a Bernoulli process. In order to have a structure so that changes in the parameters be forecastable, we introduce two modifications. The first models the probability of shifts according to some covariates that can be forecasted. The second incorporates a built-in mean reversion mechanism to the time path of the parameters. Similar modifications can also be made to model changes in the variance of the error process. Our full model can be cast into a conditional linear and Gaussian state space framework. To estimate it, we use the mixture Kalman filter and a Monte Carlo expectation maximization algorithm. Simulation results show that our proposed forecasting model provides improved forecasts over standard forecasting models that are robust to model misspecifications. We provide two empirical applications and compare the forecasting performance of our approach with a variety of alternative methods. These show that substantial gains in forecasting accuracy are obtained.