# Chapter 8 Estimating Functions of GWN Model Parameters

Updated: May 9, 2021

In the previous chapter, we considered estimation of the parameters of the GWN model for asset returns and the construction of estimated standard errors and confidence intervals for the estimated parameters. In this chapter, we consider estimation of functions of the parameters of the GWN model, and the construction of estimated standard errors and confidence intervals for these estimates. This is an important topic as we are often more interested in a function of the GWN model parameters (e.g. $$\mathrm{VaR}_{\alpha}$$) than the GWN model parameters themselves. In order to do this, we introduce some new statistical tools including the analytic delta method and two computer intensive resampling methods called the jackknife and the bootstrap.

The R packages used in this chapter are boot, bootstrap, car, IntroCompFinR, and PerformanceAnalytics. Have these packages installed and loaded in R before replicating the chapter examples.

suppressPackageStartupMessages(library(boot))
suppressPackageStartupMessages(library(bootstrap))
suppressPackageStartupMessages(library(car))
suppressPackageStartupMessages(library(IntroCompFinR))
suppressPackageStartupMessages(library(PerformanceAnalytics))
options(digits=3)