Sigma Point Filters for Dynamic Nonlinear Regime Switching Models

Abstract

In this paper we take three well known Sigma Point Filters, namely the Unscented Kalman Filter, the Divided Difference Filter, and the Cubature Kalman Filter, and extend them to allow for a very general class of dynamic nonlinear regime switching models. Using both a Monte Carlo study and real data, we investigate the properties of our proposed filters by using a regime switching DSGE model solved using nonlinear methods. We find that the proposed filters perform well. They are both fast and reasonably accurate, and as a result they will provide practitioners with a convenient alternative to Sequential Monte Carlo methods. We also investigate the concept of observability and its implications in the context of the nonlinear filters developed and propose some heuristics. Finally, we provide in the RISE toolbox, the codes implementing these three novel filters.

Modelling Occasionally Binding Constraints Using Regime-Switching

“…In particular, the framework we present can (1) be applied to large(r) models, (2) easily accommodate/handle complementary slackness problems, (3) be used to solve models at higher-orders of perturbations if more non-linearity is desirable, (4) accommodate multiple constraints simultaneously. These features make the strategy attractive also from an estimation standpoint: there are e cient non-linear filters for this type of problems (Binning & Maih, 2015).…”

Estimating Macroeconomic Models of Financial Crises: An Endogenous Regime-Switching Approach

“…To deal with this issue, we took the following steps: first, we estimated a version of the model without working capital and the occasionally binding constraint, this step yield an initial estimate of the exogenous processes and the non-financial parameters; second, conditional on these initial estimates, we performed a grid search over the remaining parameters (κ, φ, γ 0 , and γ 1 ) to find high posterior regions; third, from the high posterior regions of the grid search, we used a mode-finding routine to identify the posterior mode, which forms the basis for our empirical results; lastly, we sampled 500, 000 times from the posterior with a random-walk Metropolis-Hastings algorithm to explore the parameter space around the mode and characterize credible sets for the parameter estimates. 15 14 See Binning and Maih (2015) for a comparison between the Sigma Point filter and the Particle Filter in a regime-switching context, which includes degeneracy issues.…”

“…As Julier and Uhlmann (1999) note, the critical assumption taken to apply the UKF is that the prediction density and the filtering density are both Gaussian. The filtering and smoothing largely follow Binning and Maih (2015). The filter starts by combining the state vector and exogenous disturbances into a single vector, X a t−1 = [X t−1 , t ] , with the following mean and covariance matrix conditional on Y 1:t−1 and regime s t−1 :…”

Switching volatility in a nonlinear open economy

“…This characteristic is generally captured by MS processes in which a second-order approximation is required to analyze volatility shocks (Andreasen, 2010). For this purpose, we use nonlinear approximation algorithms and …lters to estimate our MSDSGE models (Binning and Maih, 2015;Maih, 2015). However, for the various reasons presented in Appendix A, we develop and use a generalization of the quadratic Kalman …lter applied to MSDSGE models.…”