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st: state space model (Hessian is not negative semidefinite)


From   杂事 <[email protected]>
To   [email protected]
Subject   st: state space model (Hessian is not negative semidefinite)
Date   Tue, 25 Mar 2014 21:31:14 +0100

Dear Statalist,

I attempt to build the following state space model with sspace in STATA:
1. Measurement equation  :  P(i,t)=m(i,t) + t(i,t)
2. State 1 equation                : m(i,t+1) = m(i,t) + w(i,t+1)
3. State 2 equation                : t(i,t+1)=x(i)*t(i,t) + e(i,t+1)

What I coded in STATA for the model above: 
constraint define 1 [ar] L.ar = 1
constraint define 2 [point]trend = 1
constraint define 3 [point]ar=1
sspace  (trend L.trend, state noconstant) ///
              (ar L.ar, state noconstant) ///
	      (point ar trend, noerror noconstant), ///
	      covstate(diagonal)
	      constraints(1/3) 

The Stata Error Message is: 
optimization terminated because of numerical instability: Hessian is not negative semidefinite

My questions are:
1.Did I do anything wrong in the code? 
2.If not, why would such message occur? Is there a solution to it? 
    I guess I can not estimate the standard error if the Hessian is inaccurate by its inverse.  
3.Does sspace function have special requirement on the timeseries data ("point" in my case)? 

Thanks very much for your help!
Kind regards,
Dan
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