Create a random periodic autocovariance function
sim_parAcvf.RdSelect randomly a periodic autoregression model and return the periodic autocovariances associated with it.
Arguments
- period
the period, a positive integer.
- order
the AR order, a vector of non-negative integers.
- sigma2
the variances of the innovations, a numeric vector of length
period(todo: or one?).
Details
Uses sim_parCoef() to generate a random PAR model.
Value
an object of class "matrix". In addition, the specification of the
model is in attribute "model" which is a list with the
following components:
- ar
a matrix, the coefficients of the PAR model,
- sigma2
numeric, the innovation variances,
- order
the PAR order.
References
Boshnakov GN, Iqelan BM (2009). “Generation of time series models with given spectral properties.” J. Time Series Anal., 30(3), 349--368. ISSN 0143-9782, doi: 10.1111/j.1467-9892.2009.00617.x .
Examples
sim_parAcvf(2, 5)
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 9.358814 2.522674 2.5124571 0.856207 -2.40770958 -0.8544942
#> [2,] 2.112913 1.884455 0.7005551 2.289959 -0.07141546 -0.2990444
#> attr(,"model")
#> attr(,"model")$ar
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 1 2.4817868 -0.1287243 0.4691656 -1.1946248 1.00237503
#> [2,] 1 0.2076349 -0.1122449 0.3412125 -0.5485619 0.06778367
#>
#> attr(,"model")$sigma2
#> [1] 1 1
#>
#> attr(,"model")$order
#> [1] 5
#>
sim_parAcvf(3, 5)
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 5.549885 -6.570274 4.887329 -2.372852 2.032531 -6.390012
#> [2,] 12.945914 3.088179 -5.663175 -5.053098 -4.313226 8.962977
#> [3,] 14.090953 -2.984629 5.917724 -9.868204 8.222589 -3.435384
#> attr(,"model")
#> attr(,"model")$ar
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 1 -0.2301267 0.3685835 -0.4352324 -0.08414653 -0.05865233
#> [2,] 1 2.4366551 0.3492087 -1.2693042 1.38636587 0.66546053
#> [3,] 1 -0.3805371 -0.3151011 -0.3951479 0.76598366 -1.05435211
#>
#> attr(,"model")$sigma2
#> [1] 1 1 1
#>
#> attr(,"model")$order
#> [1] 5
#>
res <- sim_parAcvf(2, 6)
res
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 292.9796 33.0503 140.31049 -94.47060 -146.7802 -117.26143 -265.28835
#> [2,] 63.8744 131.4541 28.53415 88.76269 -35.7699 -45.78448 -58.83145
#> attr(,"model")
#> attr(,"model")$ar
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 1 -4.5725434 2.3809656 1.22061700 -0.8770059 -2.4880512 0.73933919
#> [2,] 1 0.3318615 0.5358023 -0.07277562 -0.5674673 0.1295568 0.06706686
#>
#> attr(,"model")$sigma2
#> [1] 1 1
#>
#> attr(,"model")$order
#> [1] 6
#>
slMatrix(res)[3, 4, type = "tt"]
#> [,1]
#> [1,] 131.4541
res <- sim_parAcvf(2, 4)
attr(res, "model")
#> $ar
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 1 0.04749011 0.1370366 0.001487516 -0.01430092
#> [2,] 1 -2.69264664 0.4206360 -0.366223772 -0.06669012
#>
#> $sigma2
#> [1] 1 1
#>
#> $order
#> [1] 4
#>
acv <- res[ , ] # drop attributes
acv[2, 1 + 0]
#> [1] 10.72522
acv[2, 1 + 1]
#> [1] -2.67572
slMatrix(acv)[2, 0]
#> [1] 10.72522
slMatrix(acv)[2, 1]
#> [1] -2.67572
slMatrix(acv)[3, 4, type = "tt"]
#> [,1]
#> [1,] -2.67572
slMatrix(acv)[1:2, 1:2, type = "tt"]
#> [,1] [,2]
#> [1,] 1.011482 -2.67572
#> [2,] -2.675720 10.72522
slMatrix(acv)[1:4, 1:4, type = "tt"]
#> [,1] [,2] [,3] [,4]
#> [1,] 1.01148176 -2.6757202 0.01162881 -1.538695
#> [2,] -2.67572020 10.7252169 0.17168811 4.714611
#> [3,] 0.01162881 0.1716881 1.01148176 -2.675720
#> [4,] -1.53869505 4.7146112 -2.67572020 10.725217
## TODO: need method for autocorrelation()
## pc.acrf(acv)
## TODO: these need changing, after the change of the return values of sim_parAcvf
## pc.fcoeffs(acv, 2)
## pc.fcoeffs(acv, 3)
## pc.fcoeffs(acv, 4)
pcts:::calc_predictionCoefficients(acv, c(2, 2))
#> [,1] [,2] [,3]
#> [1,] 1 -0.05551134 -0.1583436
#> [2,] 1 2.72737196 -0.4832414
pcts:::calc_predictionCoefficients(acv, c(3, 3))
#> [,1] [,2] [,3] [,4]
#> [1,] 1 -0.0501526 -0.1435260 -0.003781037
#> [2,] 1 2.6934964 -0.3261654 0.627441294
pcts:::calc_predictionCoefficients(acv, c(4, 4))
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 1 -0.04749011 -0.1370366 -0.001487516 0.01430092
#> [2,] 1 2.69264664 -0.4206360 0.366223772 0.06669012