[Gretl-users] ML Estimation/Estimate Behavior

Dear forum,    in "Chaing, Wang (2013): Volatility contagion: A range-based volatility approach" the authors specify a 'new' model for volatility forecasting. Simply put,    eps ~ logNormal(-0.5*sigma^2, sigma^2) volatility[t] = lambda[t] * eps[t] lambda[t] = c + a*volatility[t-1] + b*lambda[t-1]     I try to estimate the (1,1) specification of the model with   <hansl> scalar c_ = 0.1 scalar rng = 0.1 scalar err = 0.2 scalar sigma = 0.36   mle ll = -0.5*ln(2 * pi) - 0.5 * ln( sigma ^ 2 ) - ln(sqrtPark) - 0.5 * ( (( ln(sqrtPark) - ln(lambda) - sigma^2/2)^2 ) / sigma ^ 2 )       series lambda = mean(sqrtPark)     series lambda = c_ + rng * sqrtPark(-1) + err * lambda(-1)       params sigma c_ rng err end mle --robust   </hansl>     Estimation results are the following and everything seems all right   Model 6: ML, using observations 2007-12-11:2013-06-17 (T = 1440) ll = -0.5*ln(2 * pi) - 0.5 * ln( sigma ^ 2 ) - ln(sqrtPark) - 0.5 * ( (( ln(sqrtPark) - ln(lambda) - sigma^2/2)^2 ) / sigma ^ 2 ) Standard errors based on Hessian                    estimate       std. error          z          p-value    -----------------------------------------------------------------------------------------   sigma      0.360439      0.00671545     53.67    0.0000       ***   c_           7.26934e-05  2.98068e-05    2.439    0.0147       **   rng          0.0930949     0.0121914      7.636     2.24e-014  ***   err           0.881256      0.0163204       54.00    0.0000       ***   Log-likelihood       6803.599   Akaike criterion    −13599.20 Schwarz criterion   −13578.11   Hannan-Quinn        −13591.32 However, when I produce in-sample fits, this model's fit is "biased". A comparison of in-sample fits of a similar model (with eps[t] being exponentially distributed) can be found at https://dl.dropboxusercontent.com/u/84870456/gretl.png . The blue line is simply "way below" the green one. The green one is nearly the same in-sample fit as the one from a HAR model (i.e. the green line is a verified good fit).The red line is the target variable.  To solve the riddle I estimated this model in Julia and got completely opposite results. Julia gets different estimates and the resulting in-sample fit is "way above" what it should be. A comparison of in-sample fits from julia can befound at  https://dl.dropboxusercontent.com/u/84870456/julie.JPG . My question would thus be whether you have any idea why this model behaves so wierdly. Specifications with exponentially or weibull distributed eps[t] run and fit just fine in both softwares.Any hint is much appreciated, Daniel