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