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st: Threshold Autoregression


From   Christopher Hajzler <chajzler@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: Threshold Autoregression
Date   Sat, 27 Mar 2010 17:40:23 +1300

Dear Statalist,

Is anyone aware of previously written code/routines that can be used
to estimate a threshold autoregression (TAR) in Stata?  I am
specifically hoping to find code that will run the TAR model (or more
specifically, what is also referred to as self-exciting TAR, defining
the regimes in terms of threshold values of the lagged dependent
variable) over a grid of threshold values and ideally over alternative
lag lengths as well, but choosing the "best" threshold and lag length
(maximizing the likelihood function or otherwise).  If there is also a
way to conduct Tsay's test for testing the TAR alternative against the
AR null, that would be a bonus.

If not, I welcome any advice on where to start (I am not at all an
experienced programmer).  What I am looking at specifically are
relative price series across geographical locations, and I would like
to estimate an autoregressive process that is restricted to follow a
random walk when taking on values within a certain band, but which is
potentially mean-reverting outside of the band (which corresponds to
the thresholds to be estimated, for a total of 3 regimes).   So this
is ultimately a two-part problem: (i) estimating the TAR for given
thresholds and lag length, and (ii) setting up a loop that searches
over the grid of possible thresholds and lags for the best fit.  I
have a substantial number of relative price series, so the second part
is important since it would be very labour intensive to conduct a
manual grid search for each individual series.

I am not even sure if Stata is the ideal program for this sort of
task, but I hope it can work!  Thanks in advance for any advice.

Best wishes,
Chris
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