## How to use maximum likelihood to estimate parameters in an equation, not a regression

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xh550
Posts: 2
Joined: Mon Jul 17, 2017 11:47 am

### How to use maximum likelihood to estimate parameters in an equation, not a regression

basically, my problem is to use the daily market return data to get the monthly conditional variance.

The monthly conditional variance is the sum of weighted squared demeaned daily return within 250 days ( trading days in one year), multiplying 22 (trading days in one month). The weight of squared demeaned daily return is decided by a function, and the literature says we need to use maximum likelihood to get the parameters in the weight function.

However, I try to use the log likelihood function estimation in Eviews. but it seems that the Eviews only can estimate a regression but not a equation by maximum likelihood. In the meantime, it also requires us to get the log likelihood function of the original regression. However, I do not know how to figure out the log likelihood function of my equation.

Please find more detail on the relevant literature. See
Ghysel, E.,Santa-Clara,P.,Valkanov,R.,2005. there is a -returntradeoff after all. Journal of Financial Economics76,509–548.

I also attach the image of two equations. The first equation is to get the monthly volatility by sum of weighted squared demeaned daily return within 250 days multiplying 22. The second equation needs to be estimated by maximum likelihood function to get the weight. Wd represents weight, K1 and K2 are parameters we need to estimate,
Attachments
The equation I need to use maximum likelihood to estimate the weight of demean-ed daily return square
equation.png (11.29 KiB) Viewed 571 times
function to get the monthly continual volatility
Conditional volatility.png (8.48 KiB) Viewed 571 times

xh550
Posts: 2
Joined: Mon Jul 17, 2017 11:47 am

### Re: How to use maximum likelihood to estimate parameters in an equation, not a regression

sorry, the image is in wrong order

startz
Non-normality and collinearity are NOT problems!
Posts: 3299
Joined: Wed Sep 17, 2008 2:25 pm

### Re: How to use maximum likelihood to estimate parameters in an equation, not a regression

Start by reading the extensive documentation on the log-likelihood object.