From: Claus Dethlefsen / Aalborg Sygehus <aas.claus.dethlefsen_at_nja.dk>

Date: Fri 02 Dec 2005 - 03:32:01 EST

Claus Dethlefsen, Msc, PhD

Statistiker ved Kardiovaskulært Forskningscenter

ss <- ssm(y ~ tvar(x), time = 1:nrow(dfrm), family=gaussian(link="identity"),

R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Fri Dec 02 04:06:28 2005

Date: Fri 02 Dec 2005 - 03:32:01 EST

Dear Tariq Khan

The initial conditions m0 and C0 can be specified according to your needs. If you are a Bayesian (as in West&Harrison 1997), you will use m0 and C0 to express your prior information. If you use a vague prior, you will give a high weight to your observations in the beginning, and the influence of the prior will die out fast.

The values of m0 and C0 could also stem from several time-series and express a random effect of the level of the individual series.

Finally, you may estimate m0 and C0 using maximum likelihood estimation. This is not done in sspir (but the log-likelihood value is provided from a run of the filter).

One crude way of specifying m0 and C0 would be to use the estimates from a static model, i.e.

ss$ss$m0[1:2,] <- coef(lm(y~x,data=dfrm))
ss$ss$C0[1:2,1:2] <- summary(lm(y~x,data=dfrm))$cov.unscaled
smooth.params3 <- kfs(ss)$m

ts.plot(t(smooth.params3))

Note that the 'kfs' function is a shortcut for using smoother(kfilter()).

Note also, that your variance parameters are both set to unity. Again, you may discuss how to set these either by previous knowledge or by maximum likelihood estimation. It is set using

ss$ss$phi[1] <- 2 # observational variance ss$ss$phi[2] <- .5# variance of the beta-parameter

Hope this helps,

Claus

Claus Dethlefsen, Msc, PhD

Statistiker ved Kardiovaskulært Forskningscenter

Forskningens Hus

Aalborg Sygehus

Sdr. Skovvej 15

9000 Aalborg

Tlf: 9932 6863

email: aas.claus.dethlefsen@nja.dk <mailto:aas.claus.dethlefsen@nja.dk>

Fra: ¨Tariq Khan [mailto:tariq.khan@gmail.com]
Sendt: to 01-12-2005 13:12

Til: R-help@stat.math.ethz.ch; R-sig-finance@stat.math.ethz.ch
Cc: Claus Dethlefsen / Aalborg Sygehus

Emne: Kalman Smoothing - time-variant parameters (sspir)

Dear R-brains,

I'm rather new to state-space models and would benefit from the extra confidence in using the excellent package sspir.

In a one-factor model, If I am trying to do a simple regression where I assume the intercept is constant and the 'Beta' is changing, how do I do that? How do i Initialize the filter (i.e. what is appropriate to set m0, and C0 for the example below)?

The model I want is: y = alpha + beta + err1; beta_(t+1) = beta_t + err2

I thought of the following:

library(mvtnorm) # (1)

library(sspir)

# Let's get some data so we can all try this at home
dfrm <- data.frame(

y = c(0.02,0.04,-0.03,0.02,0,0.01,0.04,0.03,-0.01,0.04,-0.01,0.05,0.04, 0.03,0.01,-0.01,-0.01,-0.03,0.02,-0.04,-0.05,-0.02,-0.04,0,0.02,0, -0.01,-0.01,0.01,0.09,0.03,0.03,0.05,0.04,-0.01,0.05,0.03,0.01, 0.04,0.01,-0.01,-0.02,-0.01,-0.01, 0.06,0.03,0.02,0.03,0.03,0.04, 0.03,0.04,-0.02,-0.03,0.04,0.03,0.05,0.02,0.03,-0.1), x = c(-0.03,-0.01,0.07,-0.03,-0.07,0.05,0.02,-0.05,-0.04,)

-0.02,-0.19,0.07,0.09,0.01,0.01,0,0.05,0,-0.02,-0.09,

-0.12,-0.01,-0.13,0.04,0.04,-0.07,-0.05,-0.03,-0.01,0.11,0.06,0.03,0.06,0.06,-0.01,0.07,0.01,

0,0.07,0.04,-0.02,0,-0.03,0.04,-0.04,-0.01,0.03,0.02,0.05,0.04, 0.05,0.03,0,-0.04,0.05,0.05,0.06,0.02,0.04,-0.06)

ss <- ssm(y ~ tvar(x), time = 1:nrow(dfrm), family=gaussian(link="identity"),

data=dfrm)

smooth.params <- smoother(kfilter(ss$ss))$m

(1) I read in http://ww.math.aau.dk/~mbn/Teaching/MarkovE05/Lecture3.pdf that this is requred as there is a bug in sspir.

To what should I set ss$ss$m0 and ss$ss$C0? (I did notice that smoother() replaces these, but it still matters what I initialize it to in the first place)

Many thanks!

Tariq Khan

R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Fri Dec 02 04:06:28 2005

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