A two-state regime switching autoregressive model with an application to river flow analysis

We propose a regime switching autoregressive model and apply it to analyze daily water discharge series of River Tisza in Hungary. The dynamics is governed by two regimes, along which both the autoregressive coefficients and the innovation distributions are altering, moreover, the hidden regime indicator process is allowed to be non-Markovian. After examining stationarity and basic properties of the model, we turn to its estimation by Markov Chain Monte Carlo (MCMC) methods and propose two algorithms. The values of the latent process serve as auxiliary parameters in the first one, while the change points of the regimes do the same in the second one in a reversible jump MCMC setting. After comparing the mixing performance of the two methods, the model is fitted to the water discharge data. Simulations show that it reproduces the important features of the water discharge series such as the highly skewed marginal distribution and the asymmetric shape of the hydrograph.