About the %logconcdensity function

[g_defi]

Dear Tom,

I am currently trying to replicate the paper of Haldrup and Nielsen (2006), Journal of Econometrics 135. It deals with estimation of Markov Switching process with long memory. Authors use a concentrated likelihood function and I have some difficulties with the implementation of the %logconcdensity function. So I am looking for an example that uses this instruction. Thanks for your help.

Best regards.

[TomDoan]

Dear Tom,

I am currently trying to replicate the paper of Haldrup and Nielsen (2006), Journal of Econometrics 135. It deals with estimation of Markov Switching process with long memory. Authors use a concentrated likelihood function and I have some difficulties with the implementation of the %logconcdensity function. So I am looking for an example that uses this instruction. Thanks for your help.

Best regards.

They are using the concentrated likelihood function because the residuals aren't a closed form expression because of the presence of fractional differencing. However, you can still use NLLS as long as you use a START option to filter the data first (given the regime-dependent settings of D and MU). The FIGARCH.RPF example from Baillie, Bollerslev and Mikkelson(1996), does something similar for using MAXIMIZE.

However, note that their concentrated likelihood function isn't correct given the assumptions. They are allowing for regime-specific variances. Minimizing the total sum of squared residuals would be OK if there were no parameters which were common to the regimes. (The log likelihood wouldn't be correct, but the point estimates would be). However, the mu's are shared because of the lags in the fractional difference so the estimation needs to take the heteroscedasticity into account.

[g_defi]

Many thanks for replying me so quickly and for your comments.