UC Riverside

In chapter 1, we propose a generalized version of the autocontour-based methodology for dynamic specification testing (in-sample and out-of-sample) proposed in González-Rivera et al. (2011) (GR2011). The autocontour (ACR) proposed is the basis to construct very powerful tests to detect misspecification in the dynamics of the model and departures from the assumed conditional density but still has some limitations. To overcome these limitations, we propose a generalized autocontour (G-ACR) based on the probability integral transforms (PIT) of the assumed density model. The specification tests will be based now on the G-ACR device. We should also mention that because of the simplicity of G-ACR, the analytical expressions of the asymptotic variance-covariance matrices of the tests have a closed formulation and they depend only on the parameter a priori probability level associated with the G-ACR. In addition, they will be instances, e.g. multistep predictive densities in nonlinear models, in which the predictive density does not have a closed form solution and we need to resort to simulation or nonparametric methods, but yet we could obtain the PIT process from the simulated density. Once the PITs are in place, our methodology will be able to evaluate the multistep density forecast. In chapter 2, we extend the G-ACR methodology to the multivariate case and to random processes that are discrete. Our interest lies on the multivariate process of a vector of counts for which we specify the dynamics of the marginal densities of each process and a copula function that ties up the marginal to produce their multivariate distribution. As an illustration of the G-ACR methodology, we have analyzed a high frequency trivariate system of the number of trades in three US large banking institutions: Bank of America, JP Morgan Chase, and Wells Fargo. In chapter 3, we propose a robust out-of-sample density forecasting evaluation method in the presence of the instabilities based on Generalized Autocontour . We construct $Sup$ and $Avg$ types of statistics to explore the model's behavior of the environment instabilities. We have applied our tests to evaluate the density forecast performance of U.S. inflation produced by linear and Markov-switching Philips Curve.