How to estimate parameters by ML

[Jaine Myers]

Hi everyone,

I am trying to estimate rho, sigma and lambda using ML command. I have two timeseries data LN and TMP, and want to fit LN to a random walk process and TMP to an AR(1) process.
LN_{t} = LN_{t-1} +\sigma*sqrt(1-\lambda)*u_{t} where u_{t}~N(0,1), and
TMP{t} =\rho*TMP{t-1} +\sigma*sqrt(\lambda)*\eta_{t} where eta_{t}~N(0,1)

I constructed the following code, but it results in the message "could not find feasible values r(491);". Is there something wrong with my code, or is it simply that it cannot find the optimal values for rho, sigma, and lambda? Thank you for any comments.

program define loglik_combined
    args lnf rho sigma lambda

    // RW process
    tempvar dmu
    gen double `dmu' = LN -L.LN
    quietly replace `lnf' = ln(normalden(`dmu'/(`sigma'*sqrt(1-`lambda')), 0, 1)) - ln(`sigma'*sqrt(1-`lambda'))

    // AR(1) process
    tempvar dx
    gen double `dx' = TMP - `rho' * L.TMP
    quietly replace `lnf' = `lnf' + ln(normalden(`dx'/(`sigma'*sqrt(`lambda')), 0, 1)) - ln(`sigma'*sqrt(`lambda'))
end


constraint define 1 `rho' < 1


ml model lf loglik_combined (rho: ) (sigma: ) (lambda: )
ml search, repeat(500)
ml init 0.5 2 0.4, copy
ml maximize, difficult tolerance(1e-6) ltolerance(1e-7) constraints(1)

[Jaine Myers]

I've just noticed that
gen double `dmu'
gen double `dx'
The commands are not working properly. The temporary variables dmu and dx are missing. How can I fix this?