Errata Mondatta

never say

oops

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)
```

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]])
```

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 \(\pi_j(t \mid t-1)\).