Hello there,
I am currently trying to implement the Markov Switching Model from Calvet and Fisher (2004). I read some of their papers and think that this model is quite interesting to investigate it a little further. However, the estimation of parameters via maximum likelihood seems a little too complex for me.
I want to code this procedure in C later, but at first i really want to completely understand the methods they used. Therefore I tried to code the MLE in an Excel Spreadsheet. Unfortunately I made some mistakes, as I am getting weird parameter values when I try to maximize the likelihood function via Solver.
I attached the spreasheet I developed and I would be really grateful if anyone who is interested in this topic could have a look at it. The basic outline of the model can be found in the following paper up to page 57: MSM - Calvet/Fisher Paper
A brief summary of the formulas can also be found in good old Wikipedia: MSM - Wikipedia
As the model estimation grows exponentially with the volatility components k, i limited this number to 3 (again, my first step is to understand the model) and limitations for the other parameters are also specified in the attachment. The parameters that should be estimated are marked with a grey background as is the sum of the likelihood function. My supposition is that my transition matrix is incorrect (J15:Q22) and also the initial vector Pi0 (W28:AD28). The implementation is their binomial model - therefore m0 only can have two values (m0 and 2-m0).
I hope that someone will have a look at it and I think its definitely worth to give this multifractal model some attention. Thanks in advance to all those who are interested in this topic. Hopefully this is the start of a fruitful and ongoing discussion.
I am currently trying to implement the Markov Switching Model from Calvet and Fisher (2004). I read some of their papers and think that this model is quite interesting to investigate it a little further. However, the estimation of parameters via maximum likelihood seems a little too complex for me.
I want to code this procedure in C later, but at first i really want to completely understand the methods they used. Therefore I tried to code the MLE in an Excel Spreadsheet. Unfortunately I made some mistakes, as I am getting weird parameter values when I try to maximize the likelihood function via Solver.
I attached the spreasheet I developed and I would be really grateful if anyone who is interested in this topic could have a look at it. The basic outline of the model can be found in the following paper up to page 57: MSM - Calvet/Fisher Paper
A brief summary of the formulas can also be found in good old Wikipedia: MSM - Wikipedia
As the model estimation grows exponentially with the volatility components k, i limited this number to 3 (again, my first step is to understand the model) and limitations for the other parameters are also specified in the attachment. The parameters that should be estimated are marked with a grey background as is the sum of the likelihood function. My supposition is that my transition matrix is incorrect (J15:Q22) and also the initial vector Pi0 (W28:AD28). The implementation is their binomial model - therefore m0 only can have two values (m0 and 2-m0).
I hope that someone will have a look at it and I think its definitely worth to give this multifractal model some attention. Thanks in advance to all those who are interested in this topic. Hopefully this is the start of a fruitful and ongoing discussion.
