UCM smooth trend

[Riccardo Trezzi]

Hello,

I'm trying to estimate a simple unobserved component model with smooth trend on quarterly data of US PCE (core) inflation.
If I estimate the model via "ucm", I type the following: ucm pce_exfe, model(strend)
The model is expected to estimate a *smooth* trend (an I(2) series). However, I get what you see in the image below (which is essentially a random walk).

I also tried to estimate the model via the "sspace" command. This is what I wrote:

constraint 1 [trend]L.trend = 1
constraint 2 [trend]L.slope = 1
constraint 3 [slope]L.slope = 1
constraint 4 [pce_exfe]trend= 1
sspace (trend L.trend L.slope, state noerror noconstant) ///
(slope L.slope, state noconstant) ///
(pce_exfe trend, noconstant), ///
constraints(1 2 3 4) covstate(diagonal) method(kdiffuse) difficult
predict trend
twoway (line pce_exfe time) (line trend time)

However, I got similar results.

The point is that the "smooth trend" model should be of the form:
y(t) = mu(t) + epsilon(t)
mu(t) = mu(t-1) + beta(t-1)
beta(t) = beta(t-1) + eta(t)

Such trend should be *smooth* by construction being an I(2) series. But no matter how you estimate it in STATA, you do not get something smooth (at least on these data).

Am I doing anything wrong?

Many thanks for your help!
Best,
R.

[Riccardo Trezzi]

Hi guys, any idea about the above? Thanks!

[Justin Niakamal]

I'm not familiar with unobserved components models, but Stata does have ucm. If you're looking for a smoothed series, you can just use tssmooth ma. Example below using quarterly core PCE

import delimited using "https://fred.stlouisfed.org/series/BPCCRO1Q156NBEA/downloaddata/BPCCRO1Q156NBEA.csv", clear 

gen quarter = qofd(date(date, "YMD"))
format quarter %tq

tsset quarter, quarterly 

ucm value, cycle(1)  model(strend) technique(bfgs)
predict strend, trend

tssmooth ma smoothed = value, window(4 1 4) 

tsline smoothed strend value

[Riccardo Trezzi]

Hi Justin,
Thanks for your reply.
However, the problem here is that you have smoothed the series it self with a moving average.
The ucm command (used with model(strend)) should produce a smooth trend similar to the centered moving average. But as well in your code, ucm results in a trend which is *not* smooth.