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From |
"John Hund" <jhund@tulane.edu> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
st: Is maximum likelihood lf method appropriate for lagged (time series) data? |

Date |
Thu, 11 Mar 2004 03:05:11 -0600 |

I am new to Stata and especially new to the maximum likelihood command in Stata, and I am trying to assess whether the lf method is possible for the likelihood function I need to maximize. The fundamental problem is to estimate the mean and standard deviation of an (unobserved) geometric diffusion process. The unobserved data is a nonlinear function of the observed data under a particular model; I can (and already have written a Stata function to) numerically invert the function to get observations to apply to the density. If the data was observed, the density would simply be the lognormal distribution; as it is, the density is the lognormal distribution multiplied by the Jacobian of the nonlinear transformation (which I have in closed form). I think that the lf method would work fine given that the transformation is a one-to-one mapping...but the likelihood of each individual observation depends on the observation previous to it. That is, the likelihood contains the ratio of two successive observations, since the diffusion process describes the change through time. Specifically, if the data at t is Vt, the likelihood incorporates the term: ln(Vt/Vt-1). I can't just transform the data before I hand it to the maximizer since I have to invert the data inside the maximization step (the transformation depends on the estimated parameters). I have tried to pass two sets of data into my program...the data and the lagged data, but haven't gotten it to work, and I'm not sure whether that has to do with my inexperience or if this incorporates a violation of the linear form restrictions. Does anyone have any experience with either fitting diffusions in Stata, or more generally, using the ml command to fit time-series models (where this sort of issue would naturally arise)? Is there a reference somewhere for writing Stata likelihoods for time-series maximization...nearly all of the examples I've seen are cross-sectional? Thanks in advance for your consideration... Cheers, John ==================================== John Hund Assistant Professor of Finance A. B. Freeman School of Business Tulane University New Orleans, LA 70118-5669 504.865.5551 * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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