peracf {perARMA}

Periodic ACF function

Description

Function 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.

Usage

peracf(x, T_t, tau, missval, datastr,...)

Arguments

x

input time series, at the begining missing values in x will be treat as zeros and periodic mean will be computed, then missing values will be replaced by periodic mean.

T_t

period of PC-T structure.

tau

vector of lag values for which estimation is made.

missval

notation for missing values (denoted as NaN).

datastr

string name of data for printing.

...

other arguments, that are connected with the plots:
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".

Details

Function 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.

Value

tables of values for each specified lag \tau:

rho(t, tau)

estimated correlation coefficients.

lower

lower bands of confidence intervals.

upper

upper bands of confidence intervals.

nsamp

number of samples used in each estimation.

Above values are also returned as matrices.

Author(s)

Harry Hurd

References

Hurd, H. L., Miamee, A. G., (2007), Periodically Correlated Random Sequences: Spectral Theory and Practice, Wiley InterScience.

See Also

Bcoeff, perpacf

Examples

data(volumes)
dev.set(which=1)
peracf(t(volumes),24,seq(1,12),NaN,'volumes')