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From |
"Brian P. Poi" <bpoi@stata.com> |

To |
statalist@hsphsun2.harvard.edu |

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

Date |
Thu, 11 Mar 2004 14:11:27 -0600 (CST) |

Earlier today John Hund wrote: > 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? Although there are probably exceptions, most time-series models would require you to use a type d0, d1, or d2 evaluator because it is not possible to write the log likelihood of a single observation without referring to prior values of some of the variables. In John's case, a type lf evaluator cannot be used because the term ln(Vt/Vt-1) depends on Vt-1, which is itself a function of the parameters. If John would like to send me his likelihood function, programs, and data privately, I would be more than happy to help him further. -- Brian Poi -- bpoi@stata.com * * 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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