persigest {perARMA} | R Documentation |
Periodic standard deviations
Description
Assuming that the period T
is known, procedure persigest
plots and returns the estimated periodic
standard deviation as a function of season. Missing data are permitted. The
confidence intervals for these values, based on the chi-square distribution, are also
computed and plotted. The de-meaned and normalized series
xn
is returned.
First, the periodic mean is computed using the method of permest
. If at time t
there is a missing value in the data, it is ignored
in the computation of periodic standard deviation. For any season (t mod T)
where all the data are missing, the periodic standard
deviation is set to "Missing"
and in the output vector xn
all the values whose times are congruent with (t mod T)
will be set to "Missing"
.
Usage
persigest(x, T_t, alpha, missval, datastr,...)
Arguments
x |
input time series. |
T_t |
period of the computed standard deviation. |
alpha |
|
missval |
notation for missing values. |
datastr |
string name of data for printing. |
... |
other arguments used in the plot: |
Details
The series may contain missing values (we suggest using NaN
)
and the length of the series may not be
an integer multiple of the period. The program returns and plots the
periodic standard deviations with 1-alpha
confidence
intervals based on all non-missing values present for each particular
season.
The p-value for Barttlet's test for homogenity of variance \sigma(t)
\equiv \sigma
is also computed.
Rejection of homogeneity
(based on the pspv
value) indicates a properly periodic variance,
but leaves open whether or
not series is simply the result of a stationary process subjected
to amplitude-scale modulation. To
resolve this R (t + \tau, t)
for some \tau \neq 0
need to be estimated.
Value
procedure returns:
pstd |
periodic standard deviations values. |
lower , upper |
bounds of the confidence intervals. |
xn |
series after removing periodic mean and divided by standard deviations |
pspv |
p-value for Bartlett's test for the homogeneity of variance. |
Author(s)
Harry Hurd
References
Hurd, H. L., Miamee, A. G., (2007), Periodically Correlated Random Sequences:
Spectral Theory and Practice, Wiley InterScience.
See Also
Examples
data(arosa)
dev.set(which=1)
persigest(t(arosa),12, 0.05, NaN,'arosa')