Final Report Summary - SFM (Supervision in Factor Models: Improving Economic Forecasts)
Dynamic factor models constitute an active and growing area of research, both in econometrics, in macroeconomics, and in finance. Many applications lie at the center of policy questions raised by the recent financial crises, such as the connections between yields on government debt, credit risk, inflation, and economic growth. One line of inquiry in this project focused on the idea of supervision, that is, the estimation of latent objects (time series or parameters) using information about a forecast target. An important application is the estimation of level, slope, and curvature factors from yield curve data, informing the factor estimates about a forecast target such as inflation or output growth. Other applications involve large macroeconomic data sets and climate data. The central mathematical object under study is a state-space model that features an observable forecast target in the state vector, thereby allowing the target to inform the estimation of the factors in the transition equation. Applications to yield curve data and a large set of macroeconomic time series covering the period 1960 through 2011 show that for selected time series such as unemployment, the supervised dynamic factor model can improve on the forecast performance of existing models. The computational framework developed for this project allows for a much faster estimation of the models, which often feature in excess of 100 parameters to be estimated. The results obtained are of interest to policy makers and policy analysts in governments and central banks, since they show a stronger forecast power of factors obtained from macroeconomic variables for key policy variables such as unemployment compared to earlier model specifications. They are also of interest to the private sector, since forecasting problems arise in a plethora of applied contexts, and the methods developed in this project are applicable to any situation where a forecast target variable is explained by few factors extracted from a large set of predictors.
Other lines of inquiry of the project focused on generalizations of the state-space model to time-varying factor loadings as well as on applications of the factor model to climate data as a new data environment for this model class. The consistency of a two-stage estimator that extracts principal components in the first step and then maximizes a likelihood function for the time-varying factor loadings, taking the principal components as factor estimates, has been proven. Several applications to macroeconomic data and to foreign exchange rates have been studied, and they have given new insights on the dependence of macroeconomic variables and international currency linkages on global financial and local factors. These results are of interest to the research community, since they allow the consideration of an entirely new class of models, they are of interest to policy makers and policy analysts in governments and central banks, since they allow new insights into the time-varying interrelations of macroeconomic key variables, and they are of interest to the private sector, since time-varying relationships between forecast targets and predictors are an issue in many forecast situations.
In the climate data environment, applications of the model to early instrumental temperature records have shown that the hypothesis that trends in the estimated phase of the annual cycle are driven by precession of Earth’s axis of rotation is most likely incorrect, and that the trending behavior is more likely the result of seasonally differential warming, in particular stronger warming in winter months than in summer months. This finding is of interest to climate researchers who have proposed several different possible explanations for the observed trends in phase. The new angle provided by our contribution, seasonally differing warming, allows to discard some of these explanations as statistically not very likely.
Other lines of inquiry of the project focused on generalizations of the state-space model to time-varying factor loadings as well as on applications of the factor model to climate data as a new data environment for this model class. The consistency of a two-stage estimator that extracts principal components in the first step and then maximizes a likelihood function for the time-varying factor loadings, taking the principal components as factor estimates, has been proven. Several applications to macroeconomic data and to foreign exchange rates have been studied, and they have given new insights on the dependence of macroeconomic variables and international currency linkages on global financial and local factors. These results are of interest to the research community, since they allow the consideration of an entirely new class of models, they are of interest to policy makers and policy analysts in governments and central banks, since they allow new insights into the time-varying interrelations of macroeconomic key variables, and they are of interest to the private sector, since time-varying relationships between forecast targets and predictors are an issue in many forecast situations.
In the climate data environment, applications of the model to early instrumental temperature records have shown that the hypothesis that trends in the estimated phase of the annual cycle are driven by precession of Earth’s axis of rotation is most likely incorrect, and that the trending behavior is more likely the result of seasonally differential warming, in particular stronger warming in winter months than in summer months. This finding is of interest to climate researchers who have proposed several different possible explanations for the observed trends in phase. The new angle provided by our contribution, seasonally differing warming, allows to discard some of these explanations as statistically not very likely.