Statistics and Probability Commons^™

A new approach to inference in state space models is proposed, using approximate Bayesian computation (ABC). ABC avoids evaluation of an intractable likelihood by matching summary statistics computed from observed data with statistics computed from data simulated from the true process, based on parameter draws from the prior. Draws that produce a 'match' between observed and simulated summaries are retained, and used to estimate the inaccessible posterior; exact inference being feasible only if the statistics are suffi#14;cient. With no reduction to su#14;fficiency being possible in the state space setting, we pursue summaries via the maximization of

an auxiliary likelihood function. …

Motivated from a changing market environment over time, we consider high-dimensional data such as financial returns, generated by a hidden Markov model which allows for switching between different regimes or states. To get more stable estimates of the covariance matrices of the different states, potentially driven by a number of observations which is small compared to the dimension, we apply shrinkage and combine it with an EM-type algorithm. This approach will yield better estimates a more stable estimates of the covariance matrix, which allows for improved reconstruction of the hidden Markov chain. In addition to a simulation study and the …