Autoregressive density modeling with the Gaussian process mixture transition distribution

We develop a mixture model for transition density approximation, together with soft selection, in the presence of noisy and heterogeneous nonlinear dynamics. Our builds on Gaussian distribution (MTD) continuous state spaces, extending component means functions that are modeled using process (GP) priors. The resulting flexibly captures lag dependence when several components active, identifies low-order while inferring relevant lags few averages over multiple competing single-lag models to quantify/propagate uncertainty. Sparsity-inducing priors weights aid selecting subset active lags. hierarchical specification follows conventions both GP regression MTD models, admitting convenient Gibbs sampling scheme posterior inference. demonstrate properties proposed two simulated real time series, emphasizing approximation lag-dependent densities selection. In most cases, decisively recovers important features. provides simple, yet flexible framework preserves useful distinguishing characteristics class.