never say
oops
Chapter 1
Chapter 2
- Eq (2.38)-(2.39): To be more general, the time subscript should have
been \(t_i\) so the equations would read
\[
m_t = \sum_{i=1}^n w_i(t) x_{t_i}\, , \tag{2.38} \]
where
\[
w_i(t)= K\bigl(\tfrac{t-{t_i}}{b}\bigr) \Bigm/
\sum_{j=1}^n K\bigl(\tfrac{t-{t_j}}{b}\bigr) \tag{2.39}
\]
... and typically \(K(z)=\exp(-z^2/2)\) is used (no need for constants because the weights
are normalized).
So these two are the same:
par(mfrow=c(2,1), mar=c(2,2,0,0)+.5, mgp=c(1.6,.6,0)) plot(soi) # monthly data; frequency=12 and t = 1/12, 2/12, ... lines(ksmooth(time(soi), soi, kernel="normal", bandwidth=1), lwd=2, col=4) # SOI = ts(soi, frequency=1) # change to t = 1,2,... plot(SOI) lines(ksmooth(time(SOI), SOI, kernel="normal", bandwidth=12), lwd=2, col=4)
Chapter 3
Chapter 4
Chapter 5
- Example 5.1: I put this note on the R code page, but I thought I'd repeat it here.
In Example 5.1, we used fracdiff, but it's not a very good package.
We should have used another package such as arfima,
but unfortunately it didn't make it into
the revision:
library(arfima) summary(varve.fd <- arfima(log(varve))) # d.hat = 0.3728, se(d,hat) = 0.0273 # residual stuff innov = resid(varve.fd) plot.ts(innov[[1]]) acf(innov[[1]])
Chapter 6
- Property 6.7, equation (6.137): Left off the conditioning arguments ... the \(\pi_j(t)\)s in the numerator
and in the denominator should be \(\pi_j(t \mid t-1)\).
Chapter 7
Elsewhere