An online estimation scheme for a Hull–White model with HMM-driven parameters

This paper considers the implementation of a mean-reverting interest rate model with Markov-modulated parameters. Hidden Markov model filtering techniques in Elliott (1994, Automatica, 30:1399–1408) and Elliott et al. (1995, Hidden Markov Models: Estimation and Control. Springer, New York) are employed to obtain optimal estimates of the model parameters via recursive filters of auxiliary quantities of the observation process. Algorithms are developed and implemented on a financial dataset of 30-day Canadian Treasury bill yields. We also provide standard errors for the model parameter estimates. Our analysis shows that within the dataset and period studied, a model with two regimes is sufficient to describe the interest rate dynamics on the basis of very small prediction errors and the Akaike information criterion.     

Forecasting with univariate TAR models

The forecasting stage in the analysis of a univariate threshold-autoregressive model, with exogenous threshold variable, has been developed in this paper via the computation of the so-called predictive distributions. The procedure permits one to forecast simultaneously the response and exogenous variables. An important issue in this work is the treatment of eventual missing observations present in the two time series before obtaining forecasts.     

Normalization in Econometrics

The issue of normalization arises whenever two different values for a vector of unknown parameters imply the identical economic model. A normalization implies not just a rule for selecting which among equivalent points to call the maximum likelihood estimate (MLE), but also governs the topography of the set of points that go into a small-sample confidence interval associated with that MLE. A poor normalization can lead to multimodal distributions, disjoint confidence intervals, and very misleading characterizations of the true statistical uncertainty. This paper introduces an identification principle as a framework upon which a normalization should be imposed, according to which the boundaries of the allowable parameter space should correspond to loci along which the model is locally unidentified. We illustrate these issues with examples taken from mixture models, structural vector autoregressions, and cointegration models.     

Pricing and hedging equity-indexed annuities via local risk-minimization

Lin et al. (2009) employed the Esscher transform method to price equity-indexed annuities (EIAs) when the dynamic of the market value of a reference asset was driven by a generalized geometric Brownian motion model with regime-switching. Some rare events (release of an unexpected economic figure, major political changes or even a natural disaster in a major economy) can lead to brusque variations in asset prices, and hence we sometimes need to consider jump models. This paper extends the model and analysis in Lin et al. (2009). Specifically, we assume that the financial market has a regime-switching jump-diffusion model, under which we price the point-to-point, the Asian-end, the high water mark and the annual reset EIAs by exploiting the local risk-minimization approach. The effects of the model parameters on the EIAs pricing are illustrated through numerical experiments. Meanwhile, we present the locally risk-minimizing hedging strategies for EIAs.     

Using the Reversible Jump MCMC Procedure for Identifying and Estimating Univariate TAR Models

One way that has been used for identifying and estimating threshold autoregressive (TAR) models for nonlinear time series follows the Markov chain Monte Carlo (MCMC) approach via the Gibbs sampler. This route has major computational difficulties, specifically, in getting convergence to the parameter distributions. In this article, a new procedure for identifying a TAR model and for estimating its parameters is developed by following the reversible jump MCMC procedure. It is found that the proposed procedure conveys a Markov chain with convergence properties.     

An FFT approach for option pricing under a regime-switching stochastic interest rate model

In this article, we investigate the pricing of European-style options under a Markovian regime-switching Hull–White interest rate model. The parameters of this model, including the mean-reversion level, the volatility of the stochastic interest rate, and the volatility of an asset’s value, are modulated by an observable, continuous-time, finite-state Markov chain. A closed-form expression for the characteristic function of the logarithmic terminal asset price is derived. Then, using the fast Fourier transform, a price of a European-style option is computed. In a two-state Markov chain case, numerical examples and empirical studies are presented to illustrate the practical implementation of the model.     

SMOOTH TRANSITION AUTOREGRESSIVE MODELS — A SURVEY OF RECENT DEVELOPMENTS

This paper surveys recent developments related to the smooth transition autoregressive (STAR) time series model and several of its variants. We put emphasis on new methods for testing for STAR nonlinearity, model evaluation, and forecasting. Several useful extensions of the basic STAR model, which concern multiple regimes, time-varying non-linear properties, and models for vector time series, are also reviewed.     

Fuzzy Autoregressive Rules: Towards Linguistic Time Series Modeling

Fuzzy rule–based models, a key element in soft computing (SC), have arisen as an alternative for time series analysis and modeling. One difference with preexisting models is their interpretability in terms of human language. Their interactions with other components have also contributed to a huge development in their identification and estimation procedures. In this article, we present fuzzy rule–based models, their links with some regime-switching autoregressive models, and how the use of soft computing concepts can help the practitioner to solve and gain a deeper insight into a given problem. An example on a realized volatility series is presented to show the forecasting abilities of a fuzzy rule–based model.     

Business Cycle Asymmetries

Tests for business cycle asymmetries are developed for Markov-switching autoregressive models. The tests of deepness, steepness, and sharpness are Wald statistics, which have standard asymptotics. For the standard two-regime model of expansions and contractions, deepness is shown to imply sharpness (and vice versa), whereas the process is always nonsteep. Two and three-state models of U.S. GNP growth are used to illustrate the approach, along with models of U.S. investment and consumption growth. The robustness of the tests to model misspecification, and the effects of regime-dependent heteroscedasticity, are investigated.