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Re: st: -arima- vs. -sspace-
From
Jorge Eduardo Pérez Pérez <[email protected]>
To
"[email protected]" <[email protected]>
Subject
Re: st: -arima- vs. -sspace-
Date
Mon, 26 Mar 2012 11:00:36 -0400
Dear Mr. Gates.
Thank you for your suggestions. I will try them out.
______________________
Jorge Eduardo Pérez Pérez
On Fri, Mar 23, 2012 at 5:39 PM, Richard Gates <[email protected]> wrote:
> Jorge Eduardo Pérez Pérez wrote:
> >
> > I have been fitting arima models using the state space representation
> > and the -sspace- command instead of using -arima-. I am doing this
> > because I need the filtered state estimates for other purposes. I have
> > found that in some cases, -arima- achieves convergence while -sspace-
> > does not, even using the same optimization technique. See an example
> > below for an ARIMA(2,0,0). I have a couple of questions.
> >
> > 1. Why does this happen? I know that -arima- has its own
> > implementation of the Kalman Filter coded in the Stata matrix
> > language, while sspace is coded in mata and uses the mata optimization
> > routines. Can anyone point out the differences between the two
> > implementations? I would expect that a model that converges using
> > -arima-, would also converge using the -sspace- routines that are much
> > more up to date.
> > 2. How do I get -sspace- to achieve the same results as -arima-?
>
> Try scaling your data. -sspace- estimates the variance and -arima- the
> standard deviation.
>
> When you have a nonconvergent problem, use the -iterate()- option
> to terminate the optimization at a point where it looks like it is
> having trouble and take a look at the estimates.
>
>
>
> . do arima2
>
> . clear
>
> . * Input database
> . input dlym
>
> dlym
> 1. .0076563
> 2. .0095813
> 3. .007427
> ...
> (omitted)
>
> 44. -.0007679
> 45. .000582
> 46. .0012176
> 47. .0005591
> 48. -.0000923
> 49. .0030711
> 50. .0041749
> 51. .0029995
> 52. .0018442
> 53. end
>
> . * Declare time series
> . gen t=_n
>
> . tsset t
> time variable: t, 1 to 52
> delta: 1 unit
>
> . replace dlym = 1000*dlym
> (52 real changes made)
>
> . * Estimate arima
> . arima dlym, arima(2,0,0) nocons
>
> (setting optimization to BHHH)
> Iteration 0: log likelihood = -132.81204
> Iteration 1: log likelihood = -132.79176
> Iteration 2: log likelihood = -132.78632
> Iteration 3: log likelihood = -132.7844
> Iteration 4: log likelihood = -132.78369
> (switching optimization to BFGS)
> Iteration 5: log likelihood = -132.78337
> Iteration 6: log likelihood = -132.78305
> Iteration 7: log likelihood = -132.78304
>
> ARIMA regression
>
> Sample: 1 - 52 Number of obs = 52
> Wald chi2(2) = 193.17
> Log likelihood = -132.783 Prob > chi2 = 0.0000
>
> ------------------------------------------------------------------------------
> | OPG
> dlym | Coef. Std. Err. z P>|z| [95% Conf. Interval]
> -------------+----------------------------------------------------------------
> ARMA |
> ar |
> L1. | 1.098012 .1706826 6.43 0.000 .7634798 1.432543
> L2. | -.2922192 .1466112 -1.99 0.046 -.5795718 -.0048666
> -------------+----------------------------------------------------------------
> /sigma | 3.066515 .1590157 19.28 0.000 2.75485 3.37818
> ------------------------------------------------------------------------------
> Note: The test of the variance against zero is one sided, and the two-sided
> confidence interval is truncated at zero.
>
> .
> . *Estimate via sspace
> . constraint 1 [dy]e.dy=1
>
> . constraint 2 [dlym]dy=1
>
> . constraint 3 [et]e.dy=1
>
> . constraint 4 [ldy]l.dy=1
>
> .
> . sspace (dy l.dy l.ldy e.dy, state noconstant) ///
> > (ldy l.dy, state noconstant ) ///
> > (et e.dy, state noconstant) ///
> > (dlym dy, noconstant), ///
> > covstate(diagonal) constraints(1/4) tech(bhhh 4 nr) ///
> > iterate(15)
> searching for initial values ...........
> (setting technique to bhhh)
> Iteration 0: log likelihood = -133.26724
> Iteration 1: log likelihood = -133.08202
> Iteration 2: log likelihood = -132.96335
> Iteration 3: log likelihood = -132.89188
> (switching technique to nr)
> Iteration 4: log likelihood = -132.84706
> Iteration 5: log likelihood = -132.78316
> Iteration 6: log likelihood = -132.78304
> Iteration 7: log likelihood = -132.78304
> Refining estimates:
> Iteration 0: log likelihood = -132.78304
> Iteration 1: log likelihood = -132.78304
>
> State-space model
>
> Sample: 1 - 52 Number of obs = 52
> Wald chi2(2) = 163.02
> Log likelihood = -132.78304 Prob > chi2 = 0.0000
> ( 1) [dy]e.dy = 1
> ( 2) [dlym]dy = 1
> ( 3) [et]e.dy = 1
> ( 4) [ldy]L.dy = 1
> ------------------------------------------------------------------------------
> | OIM
> dlym | Coef. Std. Err. z P>|z| [95% Conf. Interval]
> -------------+----------------------------------------------------------------
> dy |
> dy |
> L1. | 1.098088 .1304214 8.42 0.000 .8424671 1.35371
> |
> ldy |
> L1. | -.2922904 .1330764 -2.20 0.028 -.5531154 -.0314655
> e.dy | 1 (constrained)
> -------------+----------------------------------------------------------------
> ldy |
> dy |
> L1. | 1 (constrained)
> -------------+----------------------------------------------------------------
> et |
> e.dy | 1 (constrained)
> -------------+----------------------------------------------------------------
> dlym |
> dy | 1 (constrained)
> -------------+----------------------------------------------------------------
> Variance |
> dy | 9.403747 1.845373 5.10 0.000 5.786882 13.02061
> ------------------------------------------------------------------------------
> Note: Tests of variances against zero are one sided, and the two-sided confidence
> intervals are truncated at zero.
>
> I hope this is what you need.
>
> -Rich
> [email protected]
> *
> * For searches and help try:
> * http://www.stata.com/help.cgi?search
> * http://www.stata.com/support/statalist/faq
> * http://www.ats.ucla.edu/stat/stata/
>
>
*
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