Solved – Fitting a time-varying coefficient DLM

dlmdynamic-regressionrregressiontime series

I want to fit a DLM with time-varying coefficients, i.e. an extension to the usual linear regression,

$y_t = \theta_1 + \theta_2x_2$.

I have a predictor ($x_2$) and a response variable ($y_t$), marine & inland annual fish catches respectively from 1950 – 2011. I want the DLM regression model to follow,

$y_t = \theta_{t,1} + \theta_{t,2}x_t$

where the system evolution equation is

$\theta_t = G_t \theta_{t-1}$

from page 43 of Dynamic Linear Models With R by Petris et al.

Some coding here,

fishdata <- read.csv("http://dl.dropbox.com/s/4w0utkqdhqribl4/fishdata.csv", header=T)
x <- fishdata$marinefao
    y <- fishdata$inlandfao

lmodel <- lm(y ~ x)
summary(lmodel)
plot(x, y)
abline(lmodel)

Clearly time-varying coefficients of the regression model are more appropriate here. I follow his example from pages 121 – 125 and want to apply this to my own data. This is the coding from the example

############ PAGE 123
require(dlm)

capm <- read.table("http://shazam.econ.ubc.ca/intro/P.txt", header=T)
capm.ts <- ts(capm, start = c(1978, 1), frequency = 12)
colnames(capm)
plot(capm.ts)
IBM <- capm.ts[, "IBM"]  - capm.ts[, "RKFREE"]
x <- capm.ts[, "MARKET"] - capm.ts[, "RKFREE"]
x
plot(x)
outLM <- lm(IBM ~ x)
outLM$coef
    acf(outLM$res)
qqnorm(outLM$res)
    sig <- var(outLM$res)
sig

mod <- dlmModReg(x,dV = sig, m0 = c(0, 1.5), C0 = diag(c(1e+07, 1)))
outF <- dlmFilter(IBM, mod)
outF$m
    plot(outF$m)
outF$m[ 1 + length(IBM), ]

########## PAGES 124-125
buildCapm <- function(u){
  dlmModReg(x, dV = exp(u[1]), dW = exp(u[2:3]))
}

outMLE <- dlmMLE(IBM, parm = rep(0,3), buildCapm)
exp(outMLE$par)
    outMLE
    outMLE$value
mod <- buildCapm(outMLE$par)
    outS <- dlmSmooth(IBM, mod)
    plot(dropFirst(outS$s))
outS$s

I want to be able to plot the smoothing estimates plot(dropFirst(outS$s)) for my own data, which I'm having trouble executing.

UPDATE

I can now produce these plots but I don't think they are correct.

fishdata <- read.csv("http://dl.dropbox.com/s/4w0utkqdhqribl4/fishdata.csv", header=T)
x <- as.numeric(fishdata$marinefao)
    y <- as.numeric(fishdata$inlandfao)
xts <- ts(x, start=c(1950,1), frequency=1)
xts
yts <- ts(y, start=c(1950,1), frequency=1)
yts

lmodel <- lm(yts ~ xts)
#################################################
require(dlm)
    buildCapm <- function(u){
  dlmModReg(xts, dV = exp(u[1]), dW = exp(u[2:3]))
}

outMLE <- dlmMLE(yts, parm = rep(0,3), buildCapm)
exp(outMLE$par)
        outMLE$value
mod <- buildCapm(outMLE$par)
        outS <- dlmSmooth(yts, mod)
        plot(dropFirst(outS$s))

> summary(outS$s); lmodel$coef
       V1              V2       
 Min.   :87.67   Min.   :1.445  
 1st Qu.:87.67   1st Qu.:1.924  
 Median :87.67   Median :3.803  
 Mean   :87.67   Mean   :4.084  
 3rd Qu.:87.67   3rd Qu.:6.244  
 Max.   :87.67   Max.   :7.853  
 (Intercept)          xts 
273858.30308      1.22505

The intercept smoothing estimate (V1) is far from the lm regression coefficient. I assume they should be nearer to each other.

Best Answer

What is exactly your problem?

The only pitfall I found is that, apparently, 

fishdata <- read.csv("http://dl.dropbox.com/s/4w0utkqdhqribl4,
                     fishdata.csv", header=T)

reads data as integers. I had to convert them to float,

x <- as.numeric(fishdata$marinefao)
y <- as.numeric(fishdata$inlandfao)

before I could invoke the dlm* functions.

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