Variances of sample periodic autocorrelations

Computes the variances of sample periodic autocorrelations from periodic white noise.

Usage

pcacf_pwn_var(nepoch, period, lag, season)

Arguments

lag

desired lags, a vector of positive integers.

season

desired seasons.

nepoch

number of epochs.

period

number of seasons.

Details

These are given by McLeod (1994), see the reference, eq. (4.3).

Value

A matrix whose (i,j)th entry contains the variance of the autocorrelation coefficient for season season[i] and lag lag[j].

References

McLeod AI (1994). “Diagnostic checking of periodic autoregression models with application.” Journal of Time Series Analysis, 15(2), 221--233.

Author

Georgi N. Boshnakov

Examples

pcacf_pwn_var(79, 12, 0:16, 1:12)
#>             [,1]       [,2]       [,3]       [,4]       [,5]       [,6]
#>  [1,] 0.01234568 0.01249800 0.01249800 0.01249800 0.01249800 0.01249800
#>  [2,] 0.01234568 0.01265823 0.01249800 0.01249800 0.01249800 0.01249800
#>  [3,] 0.01234568 0.01265823 0.01265823 0.01249800 0.01249800 0.01249800
#>  [4,] 0.01234568 0.01265823 0.01265823 0.01265823 0.01249800 0.01249800
#>  [5,] 0.01234568 0.01265823 0.01265823 0.01265823 0.01265823 0.01249800
#>  [6,] 0.01234568 0.01265823 0.01265823 0.01265823 0.01265823 0.01265823
#>  [7,] 0.01234568 0.01265823 0.01265823 0.01265823 0.01265823 0.01265823
#>  [8,] 0.01234568 0.01265823 0.01265823 0.01265823 0.01265823 0.01265823
#>  [9,] 0.01234568 0.01265823 0.01265823 0.01265823 0.01265823 0.01265823
#> [10,] 0.01234568 0.01265823 0.01265823 0.01265823 0.01265823 0.01265823
#> [11,] 0.01234568 0.01265823 0.01265823 0.01265823 0.01265823 0.01265823
#> [12,] 0.01234568 0.01265823 0.01265823 0.01265823 0.01265823 0.01265823
#>             [,7]       [,8]       [,9]      [,10]      [,11]      [,12]
#>  [1,] 0.01249800 0.01249800 0.01249800 0.01249800 0.01249800 0.01249800
#>  [2,] 0.01249800 0.01249800 0.01249800 0.01249800 0.01249800 0.01249800
#>  [3,] 0.01249800 0.01249800 0.01249800 0.01249800 0.01249800 0.01249800
#>  [4,] 0.01249800 0.01249800 0.01249800 0.01249800 0.01249800 0.01249800
#>  [5,] 0.01249800 0.01249800 0.01249800 0.01249800 0.01249800 0.01249800
#>  [6,] 0.01249800 0.01249800 0.01249800 0.01249800 0.01249800 0.01249800
#>  [7,] 0.01265823 0.01249800 0.01249800 0.01249800 0.01249800 0.01249800
#>  [8,] 0.01265823 0.01265823 0.01249800 0.01249800 0.01249800 0.01249800
#>  [9,] 0.01265823 0.01265823 0.01265823 0.01249800 0.01249800 0.01249800
#> [10,] 0.01265823 0.01265823 0.01265823 0.01265823 0.01249800 0.01249800
#> [11,] 0.01265823 0.01265823 0.01265823 0.01265823 0.01265823 0.01249800
#> [12,] 0.01265823 0.01265823 0.01265823 0.01265823 0.01265823 0.01265823
#>           [,13]      [,14]      [,15]      [,16]      [,17]
#>  [1,] 0.0121894 0.01233777 0.01233777 0.01233777 0.01233777
#>  [2,] 0.0121894 0.01249800 0.01233777 0.01233777 0.01233777
#>  [3,] 0.0121894 0.01249800 0.01249800 0.01233777 0.01233777
#>  [4,] 0.0121894 0.01249800 0.01249800 0.01249800 0.01233777
#>  [5,] 0.0121894 0.01249800 0.01249800 0.01249800 0.01249800
#>  [6,] 0.0121894 0.01249800 0.01249800 0.01249800 0.01249800
#>  [7,] 0.0121894 0.01249800 0.01249800 0.01249800 0.01249800
#>  [8,] 0.0121894 0.01249800 0.01249800 0.01249800 0.01249800
#>  [9,] 0.0121894 0.01249800 0.01249800 0.01249800 0.01249800
#> [10,] 0.0121894 0.01249800 0.01249800 0.01249800 0.01249800
#> [11,] 0.0121894 0.01249800 0.01249800 0.01249800 0.01249800
#> [12,] 0.0121894 0.01249800 0.01249800 0.01249800 0.01249800