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Large Precision Matrix Estimation for Time Series Data with Latent Factor Model

Large Precision Matrix Estimation for Time Series Data with Latent Factor Model

This video was recorded at Workshop on Sparsity in Machine Learning and Statistics, Cumberland Lodge 2009. Estimating a large precision (inverse covariance) matrix is difficult due to the curse of dimensionality. The sample covariance matrix is notoriously bad for estimating the covariance matrix when the dimension p of the multivariate vector is comparable or even larger than the number of time points n observed. It is singular and hence cannot be inverted for the precision matrix. We use the factor model and procedure proposed by Pan and Yao (2008) for multivariate time series data to carry out dimension reduction when p ≈ n or even p > n. A version of the unknown factors and the corresponding factor loadings matrix are obtained. We show that when each factor is shared by O(p)... Show More

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