Oracally Efficient Estimation of Functional-Coefficient Autoregressive Models

TL;DR

This paper introduces an efficient estimation method for functional-coefficient autoregressive models, combining spline and kernel techniques to handle nonlinear time series without suffering from the curse of dimensionality.

Contribution

It adapts the spline backfitted kernel method specifically for functional-coefficient autoregressive models, improving estimation efficiency.

Findings

The method reduces computational complexity.

It maintains asymptotic properties of kernel smoothing.

It effectively estimates nonlinear components in time series.

Abstract

Nonlinear autoregressive models are very useful for modeling many natural processes, however, the size of the class of these models is large. Functional-coefficient autoregressive models (FCAR) are useful structures for reducing the size of the class of these models. Although this structure reduces the class of nonlinear models, it is broad enough to include some common time series models as specific cases. A recent development in estimating nonlinear time series data is the spline backfitted kernel (SBK) method. This method combines the computational speed of splines with the asymptotic properties of kernel smoothing. To estimate a component function in the model, all other component functions are pre-estimated with splines and then the difference is taken of the observed time series and the pre-estimates. This difference is then used as pseudo-responses for which kernel smoothing is used to estimate the function of interest. By constructing the estimates in this way, the method does not suffer from the curse of dimensionality. In this paper, we adapt the SBK method to FCAR models.