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Re: st: RE: State Space Model


From   Joshua Shindell <jshindell@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: RE: State Space Model
Date   Wed, 21 Apr 2010 10:01:15 -0400

Robert,

Thank you very much for your prompt reply.

I am convinced the Kalman filter approach is the correct one for my
application.  My problem is that I am having difficulty specifying a
"State-Space Model with Stochastically Varying Coefficients" as
described in Section 13.8 of Hamilton (1994).  Specifically, I am
trying to estimate a linear model with time varying coefficients Page
400 of Hamilton (1994), but I am unable to correctly structure the
sspace command to perform the estimation.  Additionally, the sspace
section of the manual states that "sspace estimates linear state-space
models with time-invariant coefficient matrices."  Am I attempting to
do something that this procedure does not allow?

Best,

Joshua A. Shindell

2010/4/21 Robert A Yaffee <bob.yaffee@nyu.edu>:
> Joshua,
>   In the literature, the State space model was originally predicated on the Kalman filter, with a first-order Markov (ar(1)) transition equation, to project the mean, while using another part of it filtered the variance.  Notwithstanding the capability of handling a nonstationary local random walk with noise, the Kalman filter was originally formulated with its
> transition equation in that form. Later versions of it (the extended Kalman
> Filter, for example) have sought to extend it to nonlinear functions.  MCMC versions suggested by Genshiro Kitigawa JASA Sept 1998 and as early as 1996) have endeavored to handle nonGaussian frontiers. Andrew Harvey (1989) Forecasting Structural time series models and the Kalman filter is a good source for this information(Cambridge Univ Press), and later on in his book, he discusses ways of how this can be applied to other kinds of models, whether they are ARIMA(0,1,1) or poisson, binomial, or multinomial models.
>     The Kalman filter is very flexible and accurate.
>          Cheers,
>                 Robert
>
> Robert A. Yaffee, Ph.D.
> Research Professor
> Silver School of Social Work
> New York University
>
> Biosketch: http://homepages.nyu.edu/~ray1/Biosketch2009.pdf
>
> CV:  http://homepages.nyu.edu/~ray1/vita.pdf
>
> ----- Original Message -----
> From: Joshua Shindell <jshindell@gmail.com>
> Date: Tuesday, April 20, 2010 11:26 am
> Subject: Re: st: RE: State Space Model
> To: statalist@hsphsun2.harvard.edu
>
>
>> Thank you for the suggestion.
>>
>> After looking over the help files, the problem I am having is the
>> syntax of how to specify the state equation so that the time series of
>> the B(t) values, the sensitivites time series, is modeled as an ar(1)
>> process.
>>
>> Thank you,
>>
>> Joshua A. Shindell
>>
>> On Tue, Apr 20, 2010 at 10:30 AM, Nick Cox <n.j.cox@durham.ac.uk> wrote:
>> > . search state space
>> >
>> > Keyword search
>> >
>> >        Keywords:  state space
>> >          Search:  (1) Official help files, FAQs, Examples, SJs, and
>> STBs
>> >
>> > Search of official help files, FAQs, Examples, SJs, and STBs
>> >
>> >
>> > [TS]    time series . . . . . . . . . . . Introduction to
>> time-series commands
>> >        (help time)
>> >
>> > [TS]    arima . . . . . . .  ARIMA, ARMAX, and other dynamic
>> regression models
>> >        (help arima)
>> >
>> > [TS]    sspace  . . . . . . . . . . . . . . . . . . . . . .
>> State-space models
>> >        (help sspace)
>> >
>> > If one of these is not the answer, you might need to spell out why.
>> >
>> > Nick
>> > n.j.cox@durham.ac.uk
>> >
>> > Joshua Shindell
>> >
>> > I am looking to estimate a state space model of the following form:
>> >
>> > Y(t)  = X(t)B(t) + e(t)    -  Observation Equation
>> >
>> > B(t) = Z*B(t-1) + u(t)    -  State Equation
>> >
>> > I am unable to specify the state equation as a function of the
>> previous periods.
>> >
>> > To understand the context of what I am trying to do, I am trying to
>> > estimate stock Beta coeffiecients with a stochastic parameter
>> > regression model using a Kalman filter, as outlined in Applied
>> > Quantitative Methods for Trading and Investment, by Christian L.
>> > Dunis, Jason Laws, Patrick Naďm, 2005; Chapter 7, pp 223-237.
>> >
>> >
>> > *
>> > *   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/
>> >
>>
>> *
>> *   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/
>
> *
> *   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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