We study estimation of large Dynamic Factor models implemented through the Expectation Maximization (EM) algorithm, jointly with the Kalman smoother. We prove that as both n and T diverge to infinity: (i) the estimated loadings are \sqrt{T}-consistent and asymptotically normal and equivalent to their Quasi Maximum Likelihood estimates; (ii) the estimated factors are \sqrt{n}-consistent and asymptotically normal and equivalent to their Weighted Least Squares estimates. Moreover, the estimated loadings are asymptotically as efficient as those obtained by Principal Components analysis, while the estimated factors are more efficient if the idiosyncratic covariance is sparse enough.

We propose a new measure of the output gap based on a dynamic factor model that is estimated on a large number of U.S. macroeconomic indicators and which incorporates relevant stylized facts about macroeconomic data (comovements, nonstationarity, and the slow drift in long-run output growth over time). We find that (1) from the mid-1990s to 2008, the U.S. economy operated above its potential and (2) in 2018:Q4, the labor market was tighter than the market for goods and services. Because it is mainly data-driven, our measure is a natural complementary tool to the theoretical models used at policy institutions.

Large-dimensional dynamic factor models and dynamic stochastic general equilibrium models, both widely used in empirical macroeconomics, deal with singular stochastic vectors, i.e., vectors of dimension r which are driven by a q-dimensional white noise, with $q<r$ . The present paper studies cointegration and error correction representations for an $I\left(1\right)$ singular stochastic vector ${\mathbf{y}}_t$ . It is easily seen that ${\mathbf{y}}_t$ is necessarily cointegrated with cointegrating rank $c\ge r-q$ . Our contributions are: (i) we generalize Johansen’s proof of the Granger representation theorem to $I\left(1\right)$ singular vectors under the assumption that ${\mathbf{y}}_t$ has rational spectral density; (ii) using recent results on singular vectors by Anderson and Deistler, we prove that for generic values of the parameters the autoregressive representation of ${\mathbf{y}}_t$ has a finite-degree polynomial. The relationship between the cointegration of the factors and the cointegration of the observable variables in a large-dimensional factor model is also discussed.

Purpose of this work is the study of cloud detection techniques. This work identifies the cloud cover of optical images acquired by the QuickBird satellite, comparing these with others of the same area, acquired by Landsat 7 in which there are no clouds. The images are combined using an early fusion technique [1]. The tool exploits the neighborhood model [2] for increasing the amount of information for the training set and the Singular Value Decomposition for carrying out the feature extraction [3]. In order to introduce these structures into thematic classification tasks by SVMs it was necessary develop a tree kernel function based on tree kernel function defined in SVM-LightTK. The aim of the tree kernel function is evaluate the similarity level between a generic couples of tree structures.In this paper we report the results obtained comparing the performance of different approaches in cloud classification problem. The final purpose is the production of cloud cover maps. Throughout such different experimental setups we measured the capabilities of each algorithm under different points of view. First of all, we considered the classification accuracy by computing traditional parameter such as overall accuracy. A second analysis regarded the efforts that are required in the design of optimal algorithms. Indeed, these techniques are characterized by different parameters that have to be appropriately tuned in order to obtain the best performance. Finally the robustness of the techniques has been also considered. In particular the classification accuracy has been evaluated also for images not considered in the training phase.