# fig6_4

## PURPOSE

Local Regression and Likelihood, Figure 6.4.

## SYNOPSIS

This is a script file.

## DESCRIPTION

     Local Regression and Likelihood, Figure 6.4.
     Author: Catherine Loader

     Local smooth of CO2 dataset. Estimate the main trend,
     then use periodic smoothing of the residuals to estimate
     the annual effect. Add main trend and periodic components
     to get overall smooth.

     A periodic smooth is specified by 'style','a'.
     Note that year+month/12 scales the predictor to have a period
     of 1. The 'scale' argument to locfit() is period/(2*pi).

## CROSS-REFERENCE INFORMATION

This function calls:

- fitted Fitted values from a locfit object.
- locfit Smoothing noisy data using Local Regression and Likelihood.
- residuals Residuals (or a few other things) from a locfit() fit.

This function is called by:

- runbook

## SOURCE CODE

    0001 % Local Regression and Likelihood, Figure 6.4.
    0002 % Author: Catherine Loader
    0003 %
    0004 % Local smooth of CO2 dataset. Estimate the main trend,
    0005 % then use periodic smoothing of the residuals to estimate
    0006 % the annual effect. Add main trend and periodic components
    0007 % to get overall smooth.
    0008 %
    0009 % A periodic smooth is specified by 'style','a'.
    0010 % Note that year+month/12 scales the predictor to have a period
    0011 % of 1. The 'scale' argument to locfit() is period/(2*pi).
    0012
    0013 load co2;
    0014 fit1 = locfit(year+month/12,co2,'alpha',0.5,'deg',1);
    0015 res = residuals(fit1);
    0016 fit2 = locfit(year+month/12,res,'alpha',[0 2],'style','a','scale',1/(2*pi));
    0017 f1 = fitted(fit1);
    0018 f2 = fitted(fit2);
    0019 figure('Name','fig6_4: CO2 dataset local smoothing' );
    0020 plot(year+month/12,f1+f2);