peracf, given an input time series and a specified period T, computes the periodic correlation coefficients for which
$ \rho(t+\tau,t)=\rho(t,\tau)$, where $t = 1,\ldots, T$
are seasons and $\tau$ is lag. For each
possible pair of $ t$ and $\tau $ confidence limits for
$\rho(t,\tau)$ are also computed using Fisher
transformation. Procedure peracf
provides also two important tests: $ \rho(t+\tau,t) \equiv \rho(\tau)$ and $\rho(t+\tau,t) \equiv 0$.
peracf(x, T, tau, missval, datastr,...)x will be treat as zeros and periodic mean will be computed,
then missing values will be replaced by periodic mean.
prttaus, plottaus, cialpha, typeci, typerho, pchci, pchrho, colci, colrho, where
prttaus is a set of lags for which correlation coefficients are printed; it is a subset of tau,
plottaus is a set of lags for plotting the correlation coefficients
(one plot per lag); it is a subset of tau,
cialpha threshold for confidence interval,
typeci/ typerho, pchci/ pchrho, colci/colrho
define the type, plot character and colors of confidence intervals/periodic correlation values.
By default these parameters are fixed to prttaus = seq(1,T/2), plottaus = seq(1,T/2), cialpha = 0.05, typeci = "b", typerho = "b", pchci = 10, pchrho = 15, colci = "blue", colrho = "red".
peracf uses three separate procedures:
rhoci() returns the upper and lower bands defining a $1 - \alpha$ confidence interval for the true values of
$ \rho(t, \tau)$,
rho.zero.test() tests whether the estimated correlation coefficients are equal to zeros, $ \rho(t+\tau,t) \equiv 0$.
rho.equal.test() tests whether the estimated correlation coefficients are equal to each other for all seasons in the period,
$ \rho(t+\tau,t) \equiv \rho(\tau)$.In the test $ \rho(t+\tau,t) \equiv \rho(\tau)$, rejection for some $\tau > 0$ indicates that series is properly PC and is not just an amplitude modulated stationary sequence. In other words, there exists a nonzero lag $\tau$ for which $ \rho(t+\tau,t)$ is properly periodic in $t$. In the test $\rho(t+\tau,t) \equiv 0$, the rejection for some $ \tau \neq 0$ indicates the sequence is not PC white noise.
Bcoeff, perpacf
data(volumes)
dev.set(which=1)
peracf(t(volumes),24,seq(1,12),NaN,'volumes')
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