A Sparse Kalman Filter: A Non-Recursive Approach

We propose an algorithm to estimate unobserved states and shocks in a state-space model under sparsity constraints. Many economic models have a linear state-space form - for example, linearized DSGE models, VARs, time-varying VARs, and dynamic factor models. Under the conventional Kalman filter, which is essentially a recursive OLS algorithm, all estimated shocks are non-zero. However, the true shocks are often zero for multiple periods, and non-zero estimates are due to noisy data or ill-conditioning of the model. We show applications where sparsity is the natural solution. Sparsity of filtered shocks is achieved by applying an elastic-net penalty to the least-squares problem and improves statistical efficiency. The algorithm can be adapted for non-convex penalties and for estimates robust to outliers.