permest {perARMA}

Periodic Mean Estimation

Description

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".

Usage

permest(x, T_t, alpha, missval, datastr,...)

Arguments

x

input time series.

T_t

period of the computed mean.

alpha

1-alpha is confidence interval containment probability using the t-distribution.

missval

notation for missing values.

datastr

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.

Details

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.

Value

procedure returns:

pmean

periodic mean values.

lower, upper

bounds of the confidence intervals.

xr

series with missing values replaced by periodic mean values.

xd

series after removing periodic mean.

pmpv

p-value for a one-way ANOVA test for equality of means.

Author(s)

Harry Hurd

References

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.

See Also

persigest

Examples

data(arosa)
dev.set(which=1)
permest(t(arosa),12, 0.05, NaN,'arosa')