Stock index tracking requires to build a portfolio of stocks (a replica) whose behavior is as close as possible to that of a given stock index. Typically, much fewer stocks should appear in the replica than in the index, and there should be no low frequency or integrated (persistent) components in the tracking error. The latter property is not satisfied by many commonly used methods for index tracking. These are based on the in-sample minimization of a loss function, but do not take into account the dynamic properties of the index components. Moreover, most existing methods do not take into account the known structure of the index weight system. In this paper we represent the index components with a dynamic factor model. In this model the price of each stock in the index is driven by a set of common and idiosyncratic factors. Factors can be either integrated or stationary. We develop a procedure that, in a first step, builds a replica that is driven by the same persistent factors as the index. This procedure is grounded in recent results which suggest the application of principal component analysis for factor estimation even for integrated processes. In a second step, it is also possible to refine the replica so that it minimizes a specific loss function, as in the traditional approach. In both steps the replica weights depend on the existing information on the index weights system. An extended set of Monte Carlo simulations and an application to the most widely used index in the European stock market, the EuroStoxx50 index, provide substantial support for our approach.

This paper studies the estimation and inference of time-varying impulse response functions in structural vector autoregressions (SVARs) identified with external instruments. Building on kernel estimators that allow for nonparametric time variation, we derive the asymptotic distributions of the relevant quantities. Our estimators are simple and computationally trivial and allow for potentially weak instruments. Simulations suggest satisfactory empirical coverage even in relatively small samples as long as the underlying parameter instabilities are sufficiently smooth. We illustrate the methods by studying the time-varying effects of global oil supply news shocks on US industrial production.

We propose a new approach to forecasting the term structure of interest rates, which allows to efficiently extract the information contained in a large panel of yields. In particular, we use a large Bayesian Vector Autoregression (BVAR) with an optimal amount of shrinkage towards univariate AR models. The optimal shrinkage is chosen by maximizing the Marginal Likelihood of the model. Focusing on the US, we provide an extensive study on the forecasting performance of the proposed model relative to most of the existing alternative specifications. While most of the existing evidence focuses on statistical measures of forecast accuracy, we also consider alternative measures based on trading schemes and portfolio allocation. We extensively check the robustness of our results, using different datasets and Monte Carlo simulations. We find that the proposed BVAR approach produces competitive forecasts, systematically more accurate than random walk forecasts, even though the gains are small.

We propose a new model for measuring uncertainty and its effects on the economy, based on a large vector autoregression with stochastic volatility driven by common factors representing macroeconomic and financial uncertainty. The uncertainty measures reflect changes in both the conditional mean and volatility of the variables, and their impact on the economy can be assessed within the same framework. Estimates with U.S. data show substantial commonality in uncertainty, with sizable effects of uncertainty on key macroeconomic and financial variables. However, historical decompositions show a limited role of uncertainty shocks in macroeconomic fluctuations.

The COVID-19 pandemic has led to enormous data movements that strongly affect parameters and forecasts from standard Bayesian vector autoregressions (BVARs). To address these issues, we propose BVAR models with outlier-augmented stochastic volatility (SV) that combine transitory and persistent changes in volatility. The resulting density forecasts are much less sensitive to outliers in the data than standard BVARs. Predictive Bayes factors indicate that our outlier-augmented SV model provides the best fit for the pandemic period, as well as for earlier subsamples of high volatility. In historical forecasting, outlier-augmented SV schemes fare at least as well as a conventional SV model.