Inference for a change-point problem under an OU setting with unequal and unknown volatilities

An Ornstein–Uhlenbeck (OU) process is employed as a versatile model to capture the mean-reverting and stochastic evolution of many variables in various fields of applications including finance and economics. Within the OU setting, we develop a new estimation method to determine the unknown change-point location under the assumption that the volatilities before and after the change point in a time series are unequal. Our method hinges on the concept of a weighted least sum of squared errors approach and enhanced by a fusion of an iterative algorithm. The consistency of the change-point estimator is established. This article highlights a numerical implementation on simulated and observed financial market data demonstrating the significant flexibility and accuracy of our proposed modelling and estimation method. The Canadian Journal of Statistics 48: 62–78; 2020 © 2019 Statistical Society of Canada     

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.     

The use of public transportation in urban areas: Toward a causal model

In this study, using the statistical models recently introduced by Goodman, we analyze the reasons why individuals choose the car or public transportation for the journey to work and draw out some of the implications of our analysis for public policy. Building on the work of Schnore, we develop a model in which both structural and individual variables are interrelated and show that the structural contexts within which individuals make decisions about their choice are crucial. We also show that, while status differentials are largely accounted for by income differences, male preferences for the automobile tend not to be due either to the structural variables or to income differences. Our findings suggest that present policies designed to induce people to shift to public transportation for the journey to work are not likely to be effective, since they do nothing to alter present cost differentials between the two modes.