Fourier seasonality terms (ch. 4 p. 61, ch. 5 p. 95)

Column pair j is sin(2 pi j t / m), cos(2 pi j t / m) for j = 1..k. The book calls these trigonometric seasonality.

Usage

morie_fourfeat(n, period, k, start = 0)

Arguments

n

number of rows

period

the seasonal period m

k

number of harmonic pairs

start

first time index

Value

list(rows, nrows, ncols, k, period, mean, sumsq)

Examples

morie_fourfeat(n = 24, period = 12, k = 2)
#> $rows
#>                [,1]          [,2]          [,3] [,4]
#>  [1,]  0.000000e+00  1.000000e+00  0.000000e+00  1.0
#>  [2,]  5.000000e-01  8.660254e-01  8.660254e-01  0.5
#>  [3,]  8.660254e-01  5.000000e-01  8.660254e-01 -0.5
#>  [4,]  1.000000e+00  6.123234e-17  1.224647e-16 -1.0
#>  [5,]  8.660254e-01 -5.000000e-01 -8.660254e-01 -0.5
#>  [6,]  5.000000e-01 -8.660254e-01 -8.660254e-01  0.5
#>  [7,]  1.224647e-16 -1.000000e+00 -2.449294e-16  1.0
#>  [8,] -5.000000e-01 -8.660254e-01  8.660254e-01  0.5
#>  [9,] -8.660254e-01 -5.000000e-01  8.660254e-01 -0.5
#> [10,] -1.000000e+00 -1.836970e-16  3.673940e-16 -1.0
#> [11,] -8.660254e-01  5.000000e-01 -8.660254e-01 -0.5
#> [12,] -5.000000e-01  8.660254e-01 -8.660254e-01  0.5
#> [13,] -2.449294e-16  1.000000e+00 -4.898587e-16  1.0
#> [14,]  5.000000e-01  8.660254e-01  8.660254e-01  0.5
#> [15,]  8.660254e-01  5.000000e-01  8.660254e-01 -0.5
#> [16,]  1.000000e+00  1.194340e-15  2.388680e-15 -1.0
#> [17,]  8.660254e-01 -5.000000e-01 -8.660254e-01 -0.5
#> [18,]  5.000000e-01 -8.660254e-01 -8.660254e-01  0.5
#> [19,]  3.673940e-16 -1.000000e+00 -7.347881e-16  1.0
#> [20,] -5.000000e-01 -8.660254e-01  8.660254e-01  0.5
#> [21,] -8.660254e-01 -5.000000e-01  8.660254e-01 -0.5
#> [22,] -1.000000e+00 -4.286264e-16  8.572528e-16 -1.0
#> [23,] -8.660254e-01  5.000000e-01 -8.660254e-01 -0.5
#> [24,] -5.000000e-01  8.660254e-01 -8.660254e-01  0.5
#> 
#> $nrows
#> [1] 24
#> 
#> $ncols
#> [1] 4
#> 
#> $k
#> [1] 2
#> 
#> $period
#> [1] 12
#> 
#> $mean
#> [1] -2.091268e-17
#> 
#> $sumsq
#> [1] 48
#>