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22-12-2022

Forecasting in the presence of in-sample and out-of-sample breaks

Authors: Jiawen Xu, Pierre Perron

Published in: Empirical Economics | Issue 6/2023

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Abstract

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.

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We also compared the forecasting performance using Pesaran et al. (2006)’s composite and last regime model. Our RLS model performs better in most cases for forecasts computed every 12 months as in their paper. We do not include their model in our comparisons set due to computational constraints. Their method is highly computationally intensive and we could not apply it to forecasts computed every months. The sample obtained using forecasts computed every 12 months makes it too small for a valid MCS testing.

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Title: Forecasting in the presence of in-sample and out-of-sample breaks
Authors: Jiawen Xu
Pierre Perron
Publication date: 22-12-2022
Publisher: Springer Berlin Heidelberg
Published in: Empirical Economics / Issue 6/2023
Print ISSN: 0377-7332
Electronic ISSN: 1435-8921
DOI: https://doi.org/10.1007/s00181-022-02346-x

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