persigest function

Periodic standard deviations

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".

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

Arguments

• x: input time series.

• T_t: period of the computed standard deviation.

• alpha: 1-alpha is confidence interval containment probability using the chi-square distribution.

• missval: notation for missing values.

• datastr: string name of data for printing.

• ...: other arguments used in the plot: typeci, typepstd, pchci, pchpstd, colci, colpstd, pp;

  typeci / typepstd, pchci / pchpstd, colci / colpstd 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 parameters are fixed to typeci = "o", typepstd = "b", pchci = 10, pchpstd = 15, colci = "red", colpstd = "blue", pp = 1.

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 c("$\\sigma(t)\n$", "$\\equiv \\sigma$") 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.

Returns

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.

References

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

Author(s)

Harry Hurd

See Also

permest

Examples

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