Assuming that the period T is known, procedure permest plots and returns the estimated periodic
mean as a function of season. Missing data are permitted.
The confidence intervals for these values, based on the t-distribution, are also computed
and plotted. The de-meaned x is also returned with missing values
replaced by periodic mean values.
If at time t there is a missing value,
it is replaced with the periodic mean at (t mod T), provided the periodic mean exists (meaning there is at least one non-missing data for the
season (t mod T)). Otherwise the periodic mean at (t mod T) will be set to "Missing" and in the output vectors
xr and xd all the values whose times are congruent with (t mod T) will be set to "Missing".
permest(x, T_t, alpha, missval, datastr,...)procedure returns:
periodic mean values.
bounds of the confidence intervals.
series with missing values replaced by periodic mean values.
series after removing periodic mean.
p-value for a one-way ANOVA test for equality of means.
input time series.
period of the computed mean.
1-alpha is confidence interval containment probability using the t-distribution.
notation for missing values.
string name of data for printing.
other arguments used in the plot: typeci, typepmean, pchci, pchpmean, colci, colpmean, pp;
typeci / typepmean, pchci / pchpmean, colci / colpmean set the type, plot character and colors of confidence
intervals / periodic mean values on the plot,
pp should be positive to print and plot permest values.
By default these parameters are fixed to typeci = "o", typepmean = "b", pchci = 10, pchpmean = 15, colci = "red", colpmean = "blue", pp = 1.
Harry Hurd
The series may contain missing values (we suggest using NaN)
and the length of the series need not be
an integer multiple of the period. The program returns
and plots the periodic mean with 1-alpha confidence
intervals based on all non-missing values present for each
particular season. The p-value for a one-way
ANOVA test for equality of seasonal means is also computed.
Hurd, H. L., Miamee, A. G., (2007), Periodically Correlated Random Sequences:
Spectral Theory and Practice, Wiley InterScience.
Westfall, P. H., Young, S. S. (1993), Resampling-Based Multiple Testing: Examples and Methods
for p-Value Adjustment, Wiley Series in Probability and Statistics.
persigest
data(arosa)
dev.set(which=1)
permest(t(arosa),12, 0.05, NaN,'arosa')
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