Simulation-based methods for time series diagnostics
We present sampling-based methodologies for the estimation of structural time series in the presence of outliers and structural shifts. We start by considering a simple structural model: a local level model, in the presence of outliers and level shifts. The existence of shocks is accounted for by including a product of intervention variables in the measurement and transition equations. These factors are composed of the product of an indicator variable and a parameter for the magnitude of the intervention variable, defining the size of the shocks. The Gibbs sampler is the Markov chain Monte Carlo method used for estimating the intervention model. Our contribution is in the use of a uniform prior distribution for the size of intervention variables. We show that this choice provides advantages over the usual multinomial and normal prior assumptions. The methodology is extended to a basic structural model. Using this model formulation, we consider 4 types of shocks: outliers, level, slope and seasonal shifts. The use of simulation based methods for this range of different breaks in structural models is not dealt with in the existing literature. By using the Gibbs sampler, we simultaneously estimate all the hyperparameters, detect the position of the shocks and estimate their size. Finally, we consider the local level model in the presence of outliers and level shifts for the case where one of the hyperparameters is equal to zero. In this situation, simulation based methods usually assume a multinomial prior distribution for the size of the intervention variables. We use a uniform prior, and present a two stages sampling scheme. In this two stage process the Gibbs sampler is first run on an auxiliary data set which has the same shocks as the original data set. For all the methods presented, performance is assessed by Monte Carlo studies and empirical applications to real data sets.