Markov-switching generalized additive models

We consider Markov-switching regression models, i.e. models for time series regression analyses where the functional relationship between covariates and response is subject to regime switching controlled by an unobservable Markov chain. Building on the powerful hidden Markov model machinery and the methods for penalized B-splines routinely used in regression analyses, we develop a framework for nonparametrically estimating the functional form of the effect of the covariates in such a regression model, assuming an additive structure of the predictor. The resulting class of Markov-switching generalized additive models is immensely flexible, and contains as special cases the common parametric Markov-switching regression models and also generalized additive and generalized linear models. The feasibility of the suggested maximum penalized likelihood approach is demonstrated by simulation and further illustrated by modelling how energy price in Spain depends on the Euro/Dollar exchange rate

A general approach to Bayesian portfolio optimization

We develop a general approach to portfolio optimization taking account of estimation risk and stylized facts of empirical finance. This is done within a Bayesian framework. The approximation of the posterior distribution of the unknown model parameters is based on a parallel tempering algorithm. The portfolio optimization is done using the first two moments of the predictive discrete asset return distribution. For illustration purposes we apply our method to empirical stock market data where daily asset logreturns are assumed to follow an orthogonal MGARCH process with t-distributed perturbations. Our results are compared with other portfolios suggested by popular optimization strategies. --Bayesian portfolio optimization,Gordin's condition,Markov chain Monte Carlo,Stylized facts

Stability of singular jump-linear systems with a large state space : a two-time-scale approach

This paper considers singular systems that involve both continuous dynamics and discrete events with the coefficients being modulated by a continuous-time Markov chain. The underlying systems have two distinct characteristics. First, the systems are singular, that is, characterized by a singular coefficient matrix. Second, the Markov chain of the modulating force has a large state space. We focus on stability of such hybrid singular systems. To carry out the analysis, we use a two-time-scale formulation, which is based on the rationale that, in a large-scale system, not all components or subsystems change at the same speed. To highlight the different rates of variation, we introduce a small parameter ε>0. Under suitable conditions, the system has a limit. We then use a perturbed Lyapunov function argument to show that if the limit system is stable then so is the original system in a suitable sense for ε small enough. This result presents a perspective on reduction of complexity from a stability point of view

Variable Selection and Model Averaging in Semiparametric Overdispersed Generalized Linear Models

We express the mean and variance terms in a double exponential regression model as additive functions of the predictors and use Bayesian variable selection to determine which predictors enter the model, and whether they enter linearly or flexibly. When the variance term is null we obtain a generalized additive model, which becomes a generalized linear model if the predictors enter the mean linearly. The model is estimated using Markov chain Monte Carlo simulation and the methodology is illustrated using real and simulated data sets.Comment: 8 graphs 35 page

Analysis of the time to sustained progression in Multiple Sclerosis using generalised linear and additive models

The course of multiple sclerosis (MS) is generally difficult to predict. This is due to the great inter-individual variability with respect to symptoms and disability status. An important prognostic endpoint for MS is the expected time to sustained disease progression. Using the Expanded Disability Status Scale (EDSS) this endpoint is here defined as a rise of 1.0 or 0.5 compared to baseline EDSS (5.5) which is confirmed for at least six months. The goal of this paper was threefold. It aimed at identifying covariates which significantly influence sustained progression, determining size and form of the effect of these covariates and estimating the survival curves for given predictors. To this end a piecewise exponential model utilizing piecewise constant hazard rates and a Poisson model were devised. In order to improve and simplify these models a method for piecewise linear parameterization of non-parametric generalized additive models (GAMs) was applied. The models included fixed and random effects, the posterior distribution was estimated using Markov Chain Monte Carlo methods (MCMC) as well as a penalized likelihood approach and variables were selected using Akaikes information criterium (AIC). The models were applied to data of placebo patients from worldwide clinical trials that are pooled in the database of the Sylvia Lawry Centre for Multiple Sclerosis Research (SLCMSR). Only with a pure exponential model and fixed effects, baseline EDSS and the number of relapses in the last 12 month before study entry had an effect on the hazard rate. For the piecewise exponential model with random study effects there was no effect of covariates on the hazard rate other than a slightly decreasing effect of time. This reflects the fact that unstable patients reach the event early and are therefore eliminated from the analysis (selection effect)

Modelling FX smile : from stochastic volatility to skewness

Imperial Users onl

Linear and nonlinear filtering in mathematical finance: a review

Copyright @ The Authors 2010This paper presents a review of time series filtering and its applications in mathematical finance. A summary of results of recent empirical studies with market data are presented for yield curve modelling and stochastic volatility modelling. The paper also outlines different approaches to filtering of nonlinear time series

A comparison of statistical models for short categorical or ordinal time series with applications in ecology

We study two statistical models for short-length categorical (or ordinal) time series. The first one is a regression model based on generalized linear model. The second one is a parametrized Markovian model, particularizing the discrete autoregressive model to the case of categorical data. These models are used to analyze two data-sets: annual larch cone production and weekly planktonic abundance.Comment: 18 page