Level shift estimation

[ag_2018]

Hi,
I was wondering if anyone can help me coding the empirical example given in the following paper:

Harris, D., Kew, H., & Taylor, A. R. (2020). Level shift estimation in the presence of non-stationary volatility with an application to the unit root testing problem. Journal of Econometrics, 219: 354-388.

I have attached the US data they use for their estimation. In particular, I am having some trouble estimating equation 3.8 in the paper; and table 5 and 6.

Any help would be most appreciated!

[TomDoan]

3.8 (in fact, the whole analysis) is very similar to the NPREG.RPF example, except that it uses time as the explanatory variable in the non-parametric fit on the squared residuals.

[ag_2018]

Thanks Tom.
I am finding the estimation difficult and was hoping if you/someone could help in the calculation of the series 'sigma(t)' in 3.8. Not sure how to carry out the kernel smoothing. Any pointers would be much appreciated!
Table 5 is the variance profile calculation due to Cavaliere and Taylor (2008) which is to determine whether there is non-stationary unconditional volatility; separate estimation altogether.
Many thanks in advance!

[TomDoan]

This does an example of the calculation of the WLS estimator for a single example. The calculation of the time-varying variance is the same regardless of the regression---the bandwidth depends only upon the number of data points.

[ag_2018]

Thanks Tom! Much appreciated.