Johannes Tang Kristensen

Factor-based forecasting in the presence of outliers: Are factors better selected and estimated by the median than by the mean?

Abstract Macroeconomic forecasting using factor models estimated by principal components has become a popular research topic with many both theoretical and applied contributions in the literature. In this paper we attempt to address an often neglected issue in these models: The problem of outliers in the data. Most papers take an ad-hoc approach to this problem and simply screen datasets prior to estimation and remove anomalous observations. We investigate whether forecasting performance can be improved by using the original unscreened dataset and replacing principal components with a robust alternative. We propose to use an estimator based on least absolute deviations (LAD) as this alternative and establish a tractable method for computing the estimator. In addition to this we demonstrate the robustness features of the estimator through a number of Monte Carlo simulation studies. Finally, we apply the estimator in a simulated real-time forecasting exercise to test its merits. We use a newly compiled dataset of US macroeconomic series spanning the period 1971:2–2012:10. Our findings suggest that the chosen treatment of outliers does affect forecasting performance and that in many cases improvements can be made using a robust estimator such as the proposed LAD estimator.

Diffusion Indexes With Sparse Loadings

The use of large-dimensional factor models in forecasting has received much attention in the literature with the consensus being that improvements on forecasts can be achieved when comparing with standard models. However, recent contributions in the literature have demonstrated that care needs to be taken when choosing which variables to include in the model. A number of different approaches to determining these variables have been put forward. These are, however, often based on ad hoc procedures or abandon the underlying theoretical factor model. In this article, we will take a different approach to the problem by using the least absolute shrinkage and selection operator (LASSO) as a variable selection method to choose between the possible variables and thus obtain sparse loadings from which factors or diffusion indexes can be formed. This allows us to build a more parsimonious factor model that is better suited for forecasting compared to the traditional principal components (PC) approach. We provide an asymptotic analysis of the estimator and illustrate its merits empirically in a forecasting experiment based on U.S. macroeconomic data. Overall we find that compared to PC we obtain improvements in forecasting accuracy and thus find it to be an important alternative to PC. Supplementary materials for this article are available online.

Regularized estimation of structural instability in factor models: The US macroeconomy and the Great Moderation

This paper shows that the parsimoniously time-varying methodology of Callot and Kristensen (2015) can be applied to factor models. We apply this method to study macroeconomic instability in the US from 1959:1 to 2006:4 with a particular focus on the Great Moderation. Models with parsimoniously time-varying parameters are models with an unknown number of break points at unknown locations. The parameters are assumed to follow a random walk with a positive probability that an increment is exactly equal to zero so that the parameters do not vary at every point in time. The vector of increments, which is high dimensional by construction and sparse by assumption, is estimated using the Lasso. We apply this method to the estimation of static factor models and factor augmented autoregressions using a set of 190 quarterly observations of 144 US macroeconomic series from Stock and Watson (2009). We find that the parameters of both models exhibit a higher degree of instability in the period from 1970:1 to 1984:4 relative to the following 15 years. In our setting the Great Moderation appears as the gradual ending of a period of high structural instability that took place in the 1970s and early 1980s.

Vector Autoregressions with Parsimoniously Time Varying Parameters and an Application to Monetary Policy

This paper studies vector autoregressive models with parsimoniously time-varying parameters. The parameters are assumed to follow parsimonious random walks, where parsimony stems from the assumption that increments to the parameters have a non-zero probability of being exactly equal to zero. We estimate the sparse and high-dimensional vector of changes to the parameters with the Lasso and the adaptive Lasso. The parsimonious random walk allows the parameters to be modelled non parametrically, so that our model can accommodate constant parameters, an unknown number of structural breaks, or parameters varying randomly. We characterize the finite sample properties of the Lasso by deriving upper bounds on the estimation and prediction errors that are valid with high probability, and provide asymptotic conditions under which these bounds tend to zero with probability tending to one. We also provide conditions under which the adaptive Lasso is able to achieve perfectmodel selection. We investigate by simulations the properties of the Lasso and the adaptive Lasso in settings where the parameters are stable, experience structural breaks, or follow a parsimonious random walk. We use our model to investigate the monetary policy response to inflation and business cycle fluctuations in the US by estimating a parsimoniously time varying parameter Taylor rule. We document substantial changes in the policy response of the Fed in the 1970s and 1980s, and since 2007, but also document the stability of this response in the rest of the sample.