Sequential testing for structural stability in approximate factor models

We develop a monitoring procedure to detect changes in a large approximate factor model. Letting $r$ be the number of common factors, we base our statistics on the fact that the $\left( r+1\right)$-th eigenvalue of the sample covariance matrix is bounded under the null of no change, whereas it becomes spiked under changes. Given that sample eigenvalues cannot be estimated consistently under the null, we randomise the test statistic, obtaining a sequence of \textit{i.i.d} statistics, which are used for the monitoring scheme. Numerical evidence shows a very small probability of false detections, and tight detection times of change-points

Consistent estimation of high-dimensional factor models when the factor number is over-estimated

A high-dimensional $r$-factor model for an $n$-dimensional vector time series is characterised by the presence of a large eigengap (increasing with $n$) between the $r$-th and the $(r+1)$-th largest eigenvalues of the covariance matrix. Consequently, Principal Component (PC) analysis is the most popular estimation method for factor models and its consistency, when $r$ is correctly estimated, is well-established in the literature. However, popular factor number estimators often suffer from the lack of an obvious eigengap in empirical eigenvalues and tend to over-estimate $r$ due, for example, to the existence of non-pervasive factors affecting only a subset of the series. We show that the errors in the PC estimators resulting from the over-estimation of $r$ are non-negligible, which in turn lead to the violation of the conditions required for factor-based large covariance estimation. To remedy this, we propose new estimators of the factor model based on scaling the entries of the sample eigenvectors. We show both theoretically and numerically that the proposed estimators successfully control for the over-estimation error, and investigate their performance when applied to risk minimisation of a portfolio of financial time series

A Multivariate Perspective for Modeling and Forecasting Inflation's Conditional Mean and Variance

We test the importance of multivariate information for modelling and forecasting in- flation's conditional mean and variance. In the literature, the existence of inflation's conditional heteroskedasticity has been debated for years, as it seemed to appear only in some datasets and for some lag lengths. This phenomenon might be due to the fact that inflation depends on a linear combination of economy-wide dynamic common fac- tors, some of which are conditionally heteroskedastic and some are not. Modelling the conditional heteroskedasticity of the common factors can thus improve the forecasts of inflation's conditional mean and variance. Moreover, it allows to detect and predict con- ditional correlations between inflation and other macroeconomic variables, correlations that might be exploited when planning monetary policies. The Dynamic Factor GARCH (DF-GARCH) by Alessi et al. [2006] is used here to exploit the relations between inflation and the other macroeconomic variables for inflation fore- casting purposes. The DF-GARCH is a dynamic factor model as the one by Forni et al. [2005], with the addition of an equation for the evolution of static factors as in Giannone et al. [2004] and the assumption of heteroskedastic dynamic factors. When comparing the Dynamic Factor GARCH with univariate models and with the classical dynamic factor models, the DF-GARCH is able to provide better forecasts both of inflation and of its conditional variance.Inflation, Factor Models, GARCH

Measuring Euro Area Monetary Policy Transmission in a Structural Dynamic Factor Model

We study the effects of euro area common monetary policy by means of a structural dynamic factor model estimated on a large panel of euro area quarterly series. While we estimate a flat response of prices to a monetary policy shock, which we explain as aggregation of heterogeneous country-specific responses, we find no relevant asymmetries between countries in terms of output reaction. However, for both Spain and Italy, we find asymmetries in consumption, investment and unemployment. The introduction of the single currency in 1999 has helped reducing asymmetries in price responses but not in consumption and investment.

Asymptotic equivalence of Principal Components and Quasi Maximum Likelihood estimators in Large Approximate Factor Models

This paper investigates the properties of Quasi Maximum Likelihood estimation of an approximate factor model for an $n$-dimensional vector of stationary time series. We prove that the factor loadings estimated by Quasi Maximum Likelihood are asymptotically equivalent, as $n\to\infty$, to those estimated via Principal Components. Both estimators are, in turn, also asymptotically equivalent, as $n\to\infty$, to the unfeasible Ordinary Least Squares estimator we would have if the factors were observed. We also show that the usual sandwich form of the asymptotic covariance matrix of the Quasi Maximum Likelihood estimator is asymptotically equivalent to the simpler asymptotic covariance matrix of the unfeasible Ordinary Least Squares. These results hold in the general case in which the idiosyncratic components are cross-sectionally heteroskedastic, as well as serially and cross-sectionally weakly correlated. This paper provides a simple solution to computing the Quasi Maximum Likelihood estimator and its asymptotic confidence intervals without the need of running any iterated algorithm, whose convergence properties are unclear, and estimating the Hessian and Fisher information matrices, whose expressions are very complex.Comment: arXiv admin note: text overlap with arXiv:2211.01921 which is written by the same autho

There is a significant divide in how countries of the Eurozone’s north and south react to changes in monetary policy.

The European Central Bank (ECB) is charged with maintaining price stability across the Eurozone, which it does via its monetary policies. While the euro has had some success in smoothing out the asymmetries within the Eurozone, Matteo Barigozzi finds that when the ECB changes monetary policy, the Eurozone’s southern countries experience fluctuations in prices and unemployment outside of the Eurozone’s average. He argues that these differences are down to the structural and socio-economic traits of countries such as Portugal, Greece, and Italy. National reforms that are aimed at bringing regulations more in line with the countries of the Eurozone’s north will help to smooth out the current asymmetries