Advances in non linear models for time series: methods and applications to economic and financial data

When linear models fail to explain the dynamic behavior of economic and financial time series, the researcher has to turn his attention to the nonlinear world. This work has been devoted to develop novel methodological proposals that may be useful in explaining the evolution over time of economic indicators and financial instruments. In Chapter 2, the well established Markov regime switching framework is extended letting the transition probabilities vary over time according to an observation-driven updating mechanism. An extensive simulation study shows the ability of our new model to track several dynamic patterns in transition probabilities. In the illustration to U.S. Industrial Production growth rate, we show that the model can capture the dynamic features of regime transition probabilities for means and variances. In Chapter 3, we adapt the new methodology in order to model the electricity spot prices. The Markov regime switching has been extensively used in literature to deal with the spikes that affect the evolution over time of this commodity prices. The non-homogenous occurrence of jumps may be successfully explained by an hidden Markov chain with time-varying transition probabilities that can be also influenced by exogenous variables. The information related to forecasted reserve margin and forecast demand can be easily included in our proposal to improve the model fit as well as to describe the occurrence of spikes. In Chapter 4, we propose a novel semi-nonparametric model to describe accurately the volatility of financial returns. The finite sample properties are investigated under both correct and incorrect model specification. The latter case suggests that our model is able to recover the functional form of volatility as long as the sample size increases. In empirical relevant settings, features like the asymmetric effect of negative and positive current shocks on future volatility, known as leverage effect, as well as the role played by the market condition in influencing the volatility evolution might be captured by our proposal