Back to Departmental Colloquium: Spring 2016
Departmental Colloquium
Date: Tuesday, Jan 26, 2016
Time: 4:00PM
Location: LCB 219
*Tuesday*
Giovanni Motta
Columbia University
Title |
High-dimensional Dynamic Factor Models for Non-stationary Time Series |
Abstract |
High-dimensional time series are the most common type of dataset in the “big data” revolution. They arise in many areas, including neuroscience and econometrics. If the number of series is large, Principal Components Analysis is a powerful tool to reduce the dimensionality of the series. In the traditional (stationary) framework the latent factors can be recovered by the principal components of the (time-invariant) spectral-density matrix of the multivariate time series. If the parameters of the process are time-varying, the process becomes non-stationary in time. Our previous approach for fitting dynamic non-stationary factor models to multivariate time series is based on the principal components of the estimated time-varying spectral-density matrix. This approach allows the spectral matrix to be smoothly time-varying, which imposes very little structure on the moments of the underlying process. However, the estimation delivers time-varying filters that are two-sided and thus unsuitable for prediction. Moreover, the estimation of the spectral matrix strongly depends on the chosen bandwidths for smoothing over frequency and time. As an alternative, we propose a new semi-parametric approach in which only part of the model is allowed to be time-varying. More precisely, the latent factors admit a dynamic representation with time-varying auto-regressive coefficients while the loadings are constant over time. Estimation of the model parameters is accomplished by application of the EM algorithm and the Kalman filter. The time-varying parameters are modeled locally by polynomials and estimated by maximizing the likelihood locally. Compared to estimation of the factors by principal components, our new approach produces superior results in particular for small cross-sectional dimension. |
Computational Mathematics
Applied Mathematics