Monitoring Structural Stability of Dynamic Factor Models

This paper proposes a test for detecting out-of-sample structural change in factor-augmented regression (FAR) models, as a complement to the in-sample structural stability tests developed in recent literature. In a set-up with a large number, N, of time series whereby each has some predictive ability for the target variable, the common testing procedure is to first estimate factors from the N series using principle component analysis (PCA) - a procedure that itself introduces randomness - before testing for the stability of the predictive coefficients for the estimated factors. In the out-of-sample setting where a new observation arrives sequentially, one thus needs to account for the randomness in the successively estimated factors when monitoring stability. To do so, we introduce a rescaling mechanism to augment the fluctuation-monitoring test developed by Chu, Stinchcombe, and White (1996) for simple linear regressions. Under the null hypothesis of no structural change, we show that the proposed rescaled monitoring test asymptotically behaves as a Brownian bridge, and so the critical values derived in Chu et al. (1996) can be extended to FAR models. We also show that the rescaling test delivers a reasonable finite sample performance. As an empirical application, we use factors based on 132 macroeconomic series to predict U.S. monthly industrial production growth since 1985 and show that the rescaled test detects a clear break in the FAR predictive relationship in early 2009 after the Global Financial Crisis, whereas the traditional test delivers too many breaks throughout the sample. Detecting structural stability in real-time under FAR has clear relevance to various macro or financial forecasting and monitoring applications