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This vignette shows how to use the built-in pm10 dataset
with tsqn.
library(tsqn)
#> Loading required package: robustbase
#> Loading required package: MASS
#> Loading required package: fracdiff
data("pm10")
dim(pm10)
#> [1] 1826 8
head(pm10)
#> Laranjeiras Carapina Camburi Sua VixCentro Ibes VVCentro Cariacica
#> 1 24.0000 14.5833 16.1250 20.6667 18.0833 15.5417 21.3333 31.1667
#> 2 21.7917 14.5000 22.5000 26.5417 21.5417 17.4167 17.5417 32.6250
#> 3 31.7083 19.3333 28.2917 29.0417 28.2917 28.9167 39.8333 50.5417
#> 4 24.5833 22.9583 21.3750 20.8750 23.7917 19.2917 26.9583 38.1250
#> 5 34.5417 19.5000 28.9583 31.9583 31.1667 21.3333 37.9167 46.7083
#> 6 37.0000 17.1667 26.1250 29.0833 33.3333 23.4167 38.2917 40.4167The complete dataset has 1826 observations for 8 monitoring stations. For faster examples in this vignette, we use the first 365 observations.
pm10_subset <- as.matrix(pm10[1:365, ])
qn_cor <- corMatQn(pm10_subset)
qn_cov <- covMatQn(pm10_subset)
round(qn_cor, 3)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
#> [1,] 1.000 0.571 0.584 0.604 0.499 0.687 0.399 0.557
#> [2,] 0.571 1.000 0.720 0.654 0.667 0.705 0.431 0.757
#> [3,] 0.584 0.720 1.000 0.643 0.654 0.655 0.431 0.631
#> [4,] 0.604 0.654 0.643 1.000 0.759 0.689 0.476 0.630
#> [5,] 0.499 0.667 0.654 0.759 1.000 0.547 0.583 0.714
#> [6,] 0.687 0.705 0.655 0.689 0.547 1.000 0.301 0.709
#> [7,] 0.399 0.431 0.431 0.476 0.583 0.301 1.000 0.375
#> [8,] 0.557 0.757 0.631 0.630 0.714 0.709 0.375 1.000
round(qn_cov, 1)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
#> [1,] 114.0 39.7 49.5 49.8 39.0 66.7 55.2 83.1
#> [2,] 39.7 39.2 33.8 31.9 28.9 40.3 36.8 64.1
#> [3,] 49.5 33.8 57.0 38.0 33.5 44.7 42.9 62.3
#> [4,] 49.8 31.9 38.0 55.6 40.2 46.8 48.8 65.7
#> [5,] 39.0 28.9 33.5 40.2 49.0 34.6 52.6 66.3
#> [6,] 66.7 40.3 44.7 46.8 34.6 78.1 35.0 85.9
#> [7,] 55.2 36.8 42.9 48.8 52.6 35.0 136.7 69.2
#> [8,] 83.1 64.1 62.3 65.7 66.3 85.9 69.2 168.5Robust ACF and robust spectral analysis for one station:
vix <- pm10_subset[, "VixCentro"]
acf_qn <- robacf(vix, lag.max = 24, type = "correlation", plot = FALSE)
head(acf_qn$acf[, 1, 1], 10)
#> [1] 1.000000000 0.272263665 0.009576851 0.095893596 0.055512722
#> [6] -0.102051424 -0.075357148 0.036692338 -0.037377451 -0.009397082
per_qn <- PerQn(vix)
length(per_qn)
#> [1] 363
head(per_qn, 10)
#> [1] 10.8263433 9.2346587 9.9512860 14.0949867 19.2784413 21.1307737
#> [7] 16.9945525 8.6261808 1.4026843 0.4378287
GPH_estimate(vix, method = "GPH-Qn")
#> $method
#> [1] "Qn"
#>
#> $d
#> [1] 0.04464066
#>
#> $sd.reg
#> [1] 0.06856734
#>
#> [[4]]
#> [1] 0.7
For comparison, the classical (standard) ACF is:
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