Volume 14, Issue 1

This paper deals with a detailed analysis of the first-order diagonal bilinear time series model, first proposed in Granger and Andersen (1978. An Introduction to Bilinear Time Series Models . Göttingen: Vandenhoeck & Ruprecht). This model allows for sequences of “outliers” in the data. We show that the model has a variety of features that we can observe in practice, while we also document that the bilinear features show up in just a limited number of observations. When the moment restrictions are close, parameter estimation becomes difficult. When the parameters are further away from the moment restrictions, parameter estimation is easy. Yet, in those latter cases, approximative linear models appear to generate equally accurate fit and forecasts. In sum, in cases of proper inference on a bilinear model, the model is barely relevant for forecasting.

Unknown parameters, including regression coefficients, in state space models can be estimated by maximum likelihood. An alternative approach is to augment the state vector to include regression coefficients. However, the state estimator obtained by the Kalman filter is numerically different from the maximum likelihood estimator. We address the discrepancy by a novel method based on proper distributions returned by the ordinary Kalman filter without dependency on diffuse initialization. We prove that maximizing a low-dimensional objective function that combines the likelihood, the filtering mean and variance can reproduce the high-dimensional maximum likelihood results.

The QR.break package provides methods for detecting, estimating, and conducting inference on multiple structural breaks in linear quantile regression models, based on one or multiple quantiles and applicable to both time series and repeated cross-sectional data. The main function, rq.break() , returns testing and estimation results based on user specifications of the quantiles of interest, the maximum number of breaks allowed, and the minimum length of a single regime. This note outlines the underlying methods and explains how to use the main function with two datasets: a time series dataset on U.S. real GDP growth rates and a repeated cross-sectional dataset on youth drinking and driving behavior. Both datasets are included in the package available on CRAN.

The estimation of Quantile Regression with Selection (QRS) requires the estimation of the entire quantile process several times to estimate the parameters that model self-selection. Moreover, closed-form expressions of the asymptotic variance are too cumbersome, making the bootstrap more convenient to perform inference. I propose streamlined algorithms for the QRS estimator that significantly reduce computation time through preprocessing techniques and quantile grid reduction for the estimation of the parameters. I show the optimization enhancements and how they can improve the precision of the estimates without sacrificing computational efficiency with some simulations.