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: [EMAIL PROTECTED] <mailto:[EMAIL PROTECTED]> ________________________________ Fra: ¨Tariq Khan [mailto:[EMAIL PROTECTED] Sendt: to 01-12-2005 13:12 Til: R-help@stat.math.ethz.ch; [EMAIL PROTECTED] 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
