Layman’s abstract for Canadian Journal of Statistics article on Functional-coefficient regression models with GARCH errors

Each week, we publish layman’s abstracts of new articles from our prestigious portfolio of journals in statistics. The aim is to highlight the latest research to a broader audience in an accessible format.
The article featured today is from The Canadian Journal of Statistics, with the full article now available to read here.
Yuan, Y., Bai, L. and Jiang, J. (2021), Functional-coefficient regression models with GARCH errors. Can J Statistics, 49: 939-964.
The celebrated GARCH models are widely used to model various heavily tailed financial data with nonlinearity and heteroscedasticity structures. In this paper, the authors propose a functional-coefficient regression model with GARCH errors to model these kinds of data. The proposed model contains many existing time series models as special examples. 
To deal with the effect of heteroscedasticity, they introduce a two-step approach to estimating the unknown coefficient functions and to forecasting the volatility by applying nonparametric smoothing techniques that require less assumptions than parametric modeling. This two-step method results in two estimators, unweighted and weighted. Since this procedure involves a smoothing parameter, the authors suggest a data-driven method for choosing it. Furthermore, they consider selection of the order of model. 
It is appealing that they develop some elegant mathematical theory of the proposed estimators: on one hand, the weighted estimator is proven to be more efficient than the unweighted one; on the other hand, it is shown that the coefficient functions can be estimated as if the volatility were known.  
In addition, they conduct extensive simulations to support their discovery. The proposed methodology is also successfully applied to analyze the monthly yields of the 3-month U.S. treasury bills and 3-year treasury notes. Their examples exhibit that the volatility can be more accurately forecasted with the weighted estimator than some previous procedures.  


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