On Tue, 21 Feb 2012, Dan Běsoň wrote: > I am trying to write a script for MLE estimation of a CARR model, similar > to GARCH. It is a MEM model in daily ranges of some instrument, i,e, > > Eq. 1: lRng = lambda * epsilon # epsilon is exponentially distributed > here, giving the shape of LL > Eq. 2: lambda = a + b*Rng(-1) + c*lambda(-1) > > I tried the following code but the algorithm never converges. What should I > improve? > scalar a = 0.1 > scalar b = 0.4 > scalar c = 0.4 > > mle ll = -ln(lambda) + Rng/lambda Improve here: use the correct loglikelihood! mle ll = -ln(lambda) - Rng/lambda > series lambda = mean(Rng) > series lambda = a + b*Rng(-1) + c*lambda(-1) > > params a b c > end mle You may also have to constrain all the parameter values to be positive, if I'm reading the CARR literature correctly. In which case you could, for example, express lambda as exp(a) + exp(b)*Rng(-1) + exp(c)*lambda(-1).