2. Plot each station time series
op <- par(mfrow = c(4, 2), mar = c(3, 3, 2, 1))
for (st in colnames(pm10)) {
plot(pm10[, st], type = "l", xlab = "Time index", ylab = "PM10", main = st, col = "#1B6CA8")
}
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acfMPeriod estimates autocorrelation and autocovariance
by reversing periodogram diagonalization through harmonic regressions.
This workflow follows the requested order on the bundled PM10
dataset.
library(acfMPeriod)
#> Loading required package: MASS
pm10_candidates <- c(
system.file("extdata", "pm10data.csv", package = "acfMPeriod"),
file.path("inst", "extdata", "pm10data.csv"),
file.path("..", "inst", "extdata", "pm10data.csv")
)
pm10_candidates <- pm10_candidates[nzchar(pm10_candidates)]
pm10_path <- pm10_candidates[file.exists(pm10_candidates)][1]
stopifnot(length(pm10_path) == 1L, nzchar(pm10_path))
pm10 <- as.matrix(read.csv(pm10_path, check.names = FALSE))
uni_stations <- c("Laranjeiras", "Cariacica")
multi_stations <- c("Laranjeiras", "Cariacica", "Carapina", "Camburi")
x_multi <- pm10[, multi_stations, drop = FALSE]
lag_max <- 12L
# PerACF/MPerACF return lags 0:(lag.max - 1), so lag.max + 1 includes lag 12.
lag_max_reg <- lag_max + 1L
dim(pm10)
#> [1] 1826 8
colnames(pm10)
#> [1] "Laranjeiras" "Carapina" "Camburi" "Sua" "VixCentro"
#> [6] "Ibes" "VVCentro" "Cariacica"
head(pm10, 3)
#> 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
summary(pm10[, uni_stations, drop = FALSE])
#> Laranjeiras Cariacica
#> Min. : 6.083 Min. : 8.917
#> 1st Qu.:24.500 1st Qu.: 36.135
#> Median :31.271 Median : 43.333
#> Mean :32.256 Mean : 44.161
#> 3rd Qu.:38.073 3rd Qu.: 50.792
#> Max. :86.458 Max. :106.333lag_values <- function(obj, i = 1, j = 1, max_lag = 12) {
lag_vec <- as.numeric(obj$lag[, i, j])
keep <- lag_vec <= max_lag
data.frame(
lag = lag_vec[keep],
value = as.numeric(obj$acf[keep, i, j])
)
}
compare_three <- function(reg_standard, reg_robust, stats_standard, i = 1, j = 1, max_lag = 12) {
x_std <- lag_values(reg_standard, i = i, j = j, max_lag = max_lag)
x_rob <- lag_values(reg_robust, i = i, j = j, max_lag = max_lag)
x_sta <- lag_values(stats_standard, i = i, j = j, max_lag = max_lag)
out <- data.frame(
lag = x_std$lag,
reg_standard = x_std$value,
reg_robust = x_rob$value,
stats_standard = x_sta$value
)
out$diff_reg_stats <- out$reg_standard - out$stats_standard
out$diff_rob_reg <- out$reg_robust - out$reg_standard
out$diff_rob_stats <- out$reg_robust - out$stats_standard
out
}
pair_indices <- rbind(
cbind(seq_along(multi_stations), seq_along(multi_stations)),
t(utils::combn(seq_along(multi_stations), 2))
)
pair_labels <- apply(pair_indices, 1, function(idx) {
paste(multi_stations[idx[1]], "vs", multi_stations[idx[2]])
})op <- par(mfrow = c(4, 2), mar = c(3, 3, 2, 1))
for (st in colnames(pm10)) {
plot(pm10[, st], type = "l", xlab = "Time index", ylab = "PM10", main = st, col = "#1B6CA8")
}
rob_cor_lag0 <- CovCorMPer(x_multi, type = "correlation")
rob_cov_lag0 <- CovCorMPer(x_multi, type = "covariance")
round(rob_cor_lag0, 4)
#> [,1] [,2] [,3] [,4]
#> [1,] 1.0000 0.4228 0.3856 0.5567
#> [2,] 0.4228 1.0000 0.6768 0.5201
#> [3,] 0.3856 0.6768 1.0000 0.5327
#> [4,] 0.5567 0.5201 0.5327 1.0000
round(rob_cov_lag0, 4)
#> [,1] [,2] [,3] [,4]
#> [1,] 121.2045 57.9476 28.5814 47.5982
#> [2,] 57.9476 154.9985 56.7283 50.2937
#> [3,] 28.5814 56.7283 45.3198 27.8541
#> [4,] 47.5982 50.2937 27.8541 60.3190rob_uni_acf <- setNames(
lapply(uni_stations, function(st) {
MPerACF(pm10[, st], lag.max = lag_max_reg, type = "correlation", plot = FALSE)
}),
uni_stations
)
rob_uni_acovf <- setNames(
lapply(uni_stations, function(st) {
MPerACF(pm10[, st], lag.max = lag_max_reg, type = "covariance", plot = FALSE)
}),
uni_stations
)
rob_multi_acf <- MPerACF(x_multi, lag.max = lag_max_reg, type = "correlation", plot = FALSE)
rob_multi_acovf <- MPerACF(x_multi, lag.max = lag_max_reg, type = "covariance", plot = FALSE)
c(
total_observations = nrow(pm10),
laranjeiras_n_used = rob_uni_acf[["Laranjeiras"]]$n.used,
cariacica_n_used = rob_uni_acf[["Cariacica"]]$n.used,
multivariate_n_used = rob_multi_acf$n.used
)
#> total_observations laranjeiras_n_used cariacica_n_used multivariate_n_used
#> 1826 1826 1826 1826rob_uni_acf_values <- setNames(
lapply(uni_stations, function(st) {
round(lag_values(rob_uni_acf[[st]], max_lag = lag_max), 4)
}),
uni_stations
)
rob_uni_acovf_values <- setNames(
lapply(uni_stations, function(st) {
round(lag_values(rob_uni_acovf[[st]], max_lag = lag_max), 4)
}),
uni_stations
)
rob_uni_acf_values
#> $Laranjeiras
#> lag value
#> 1 0 1.0000
#> 2 1 0.5924
#> 3 2 0.3411
#> 4 3 0.2257
#> 5 4 0.1731
#> 6 5 0.1301
#> 7 6 0.1227
#> 8 7 0.1673
#> 9 8 0.1486
#> 10 9 0.1172
#> 11 10 0.1045
#> 12 11 0.0958
#> 13 12 0.0873
#>
#> $Cariacica
#> lag value
#> 1 0 1.0000
#> 2 1 0.3498
#> 3 2 0.1182
#> 4 3 0.0733
#> 5 4 0.0579
#> 6 5 0.0350
#> 7 6 0.1284
#> 8 7 0.2686
#> 9 8 0.1427
#> 10 9 0.0672
#> 11 10 0.0534
#> 12 11 0.0736
#> 13 12 0.0404
rob_uni_acovf_values
#> $Laranjeiras
#> lag value
#> 1 0 121.2045
#> 2 1 71.8049
#> 3 2 41.3404
#> 4 3 27.3523
#> 5 4 20.9803
#> 6 5 15.7645
#> 7 6 14.8702
#> 8 7 20.2835
#> 9 8 18.0117
#> 10 9 14.2022
#> 11 10 12.6675
#> 12 11 11.6108
#> 13 12 10.5868
#>
#> $Cariacica
#> lag value
#> 1 0 154.9985
#> 2 1 54.2239
#> 3 2 18.3232
#> 4 3 11.3554
#> 5 4 8.9803
#> 6 5 5.4191
#> 7 6 19.8959
#> 8 7 41.6297
#> 9 8 22.1161
#> 10 9 10.4201
#> 11 10 8.2815
#> 12 11 11.4145
#> 13 12 6.2635rob_multi_acf_values <- setNames(
lapply(seq_len(nrow(pair_indices)), function(k) {
i <- pair_indices[k, 1]
j <- pair_indices[k, 2]
round(lag_values(rob_multi_acf, i = i, j = j, max_lag = lag_max), 4)
}),
pair_labels
)
rob_multi_acovf_values <- setNames(
lapply(seq_len(nrow(pair_indices)), function(k) {
i <- pair_indices[k, 1]
j <- pair_indices[k, 2]
round(lag_values(rob_multi_acovf, i = i, j = j, max_lag = lag_max), 4)
}),
pair_labels
)
rob_multi_acf_values
#> $`Laranjeiras vs Laranjeiras`
#> lag value
#> 1 0 1.0000
#> 2 1 0.5924
#> 3 2 0.3411
#> 4 3 0.2257
#> 5 4 0.1731
#> 6 5 0.1301
#> 7 6 0.1227
#> 8 7 0.1673
#> 9 8 0.1486
#> 10 9 0.1172
#> 11 10 0.1045
#> 12 11 0.0958
#> 13 12 0.0873
#>
#> $`Cariacica vs Cariacica`
#> lag value
#> 1 0 1.0000
#> 2 1 0.3498
#> 3 2 0.1182
#> 4 3 0.0733
#> 5 4 0.0579
#> 6 5 0.0350
#> 7 6 0.1284
#> 8 7 0.2686
#> 9 8 0.1427
#> 10 9 0.0672
#> 11 10 0.0534
#> 12 11 0.0736
#> 13 12 0.0404
#>
#> $`Carapina vs Carapina`
#> lag value
#> 1 0 1.0000
#> 2 1 0.4057
#> 3 2 0.2070
#> 4 3 0.1638
#> 5 4 0.1527
#> 6 5 0.1498
#> 7 6 0.1541
#> 8 7 0.1867
#> 9 8 0.1750
#> 10 9 0.1602
#> 11 10 0.1522
#> 12 11 0.1584
#> 13 12 0.0980
#>
#> $`Camburi vs Camburi`
#> lag value
#> 1 0 1.0000
#> 2 1 0.3880
#> 3 2 0.1458
#> 4 3 0.0758
#> 5 4 0.0577
#> 6 5 0.0363
#> 7 6 0.1273
#> 8 7 0.2092
#> 9 8 0.1356
#> 10 9 0.0297
#> 11 10 0.0035
#> 12 11 0.0359
#> 13 12 0.0504
#>
#> $`Laranjeiras vs Cariacica`
#> lag value
#> 1 0 0.4228
#> 2 1 0.2088
#> 3 2 0.0741
#> 4 3 0.0250
#> 5 4 -0.0019
#> 6 5 -0.0202
#> 7 6 0.0077
#> 8 7 0.0898
#> 9 8 0.0493
#> 10 9 0.0075
#> 11 10 0.0135
#> 12 11 0.0233
#> 13 12 0.0003
#>
#> $`Laranjeiras vs Carapina`
#> lag value
#> 1 0 0.3856
#> 2 1 0.1975
#> 3 2 0.0841
#> 4 3 0.0533
#> 5 4 0.0506
#> 6 5 0.0213
#> 7 6 0.0287
#> 8 7 0.0760
#> 9 8 0.0705
#> 10 9 0.0556
#> 11 10 0.0439
#> 12 11 0.0693
#> 13 12 0.0638
#>
#> $`Laranjeiras vs Camburi`
#> lag value
#> 1 0 0.5567
#> 2 1 0.3446
#> 3 2 0.1628
#> 4 3 0.1039
#> 5 4 0.0720
#> 6 5 0.0405
#> 7 6 0.0725
#> 8 7 0.1184
#> 9 8 0.0867
#> 10 9 0.0407
#> 11 10 0.0247
#> 12 11 0.0481
#> 13 12 0.0411
#>
#> $`Cariacica vs Carapina`
#> lag value
#> 1 0 0.6768
#> 2 1 0.2879
#> 3 2 0.1251
#> 4 3 0.0804
#> 5 4 0.0707
#> 6 5 0.0551
#> 7 6 0.0837
#> 8 7 0.1615
#> 9 8 0.1174
#> 10 9 0.0884
#> 11 10 0.0751
#> 12 11 0.1001
#> 13 12 0.0542
#>
#> $`Cariacica vs Camburi`
#> lag value
#> 1 0 0.5201
#> 2 1 0.2502
#> 3 2 0.0909
#> 4 3 0.0473
#> 5 4 0.0255
#> 6 5 0.0054
#> 7 6 0.0786
#> 8 7 0.1717
#> 9 8 0.0956
#> 10 9 0.0181
#> 11 10 0.0240
#> 12 11 0.0460
#> 13 12 0.0221
#>
#> $`Carapina vs Camburi`
#> lag value
#> 1 0 0.5327
#> 2 1 0.2613
#> 3 2 0.1187
#> 4 3 0.0740
#> 5 4 0.0716
#> 6 5 0.0468
#> 7 6 0.0878
#> 8 7 0.1434
#> 9 8 0.1051
#> 10 9 0.0750
#> 11 10 0.0820
#> 12 11 0.0913
#> 13 12 0.0721
rob_multi_acovf_values
#> $`Laranjeiras vs Laranjeiras`
#> lag value
#> 1 0 121.2045
#> 2 1 71.8049
#> 3 2 41.3404
#> 4 3 27.3523
#> 5 4 20.9803
#> 6 5 15.7645
#> 7 6 14.8702
#> 8 7 20.2835
#> 9 8 18.0117
#> 10 9 14.2022
#> 11 10 12.6675
#> 12 11 11.6108
#> 13 12 10.5868
#>
#> $`Cariacica vs Cariacica`
#> lag value
#> 1 0 154.9985
#> 2 1 54.2239
#> 3 2 18.3232
#> 4 3 11.3554
#> 5 4 8.9803
#> 6 5 5.4191
#> 7 6 19.8959
#> 8 7 41.6297
#> 9 8 22.1161
#> 10 9 10.4201
#> 11 10 8.2815
#> 12 11 11.4145
#> 13 12 6.2635
#>
#> $`Carapina vs Carapina`
#> lag value
#> 1 0 45.3198
#> 2 1 18.3842
#> 3 2 9.3829
#> 4 3 7.4220
#> 5 4 6.9181
#> 6 5 6.7871
#> 7 6 6.9822
#> 8 7 8.4631
#> 9 8 7.9311
#> 10 9 7.2606
#> 11 10 6.8960
#> 12 11 7.1783
#> 13 12 4.4396
#>
#> $`Camburi vs Camburi`
#> lag value
#> 1 0 60.3190
#> 2 1 23.4016
#> 3 2 8.7948
#> 4 3 4.5709
#> 5 4 3.4802
#> 6 5 2.1888
#> 7 6 7.6760
#> 8 7 12.6203
#> 9 8 8.1808
#> 10 9 1.7893
#> 11 10 0.2117
#> 12 11 2.1681
#> 13 12 3.0390
#>
#> $`Laranjeiras vs Cariacica`
#> lag value
#> 1 0 57.9476
#> 2 1 28.6152
#> 3 2 10.1595
#> 4 3 3.4325
#> 5 4 -0.2588
#> 6 5 -2.7644
#> 7 6 1.0609
#> 8 7 12.3061
#> 9 8 6.7619
#> 10 9 1.0225
#> 11 10 1.8458
#> 12 11 3.1934
#> 13 12 0.0444
#>
#> $`Laranjeiras vs Carapina`
#> lag value
#> 1 0 28.5814
#> 2 1 14.6358
#> 3 2 6.2293
#> 4 3 3.9527
#> 5 4 3.7469
#> 6 5 1.5780
#> 7 6 2.1294
#> 8 7 5.6294
#> 9 8 5.2282
#> 10 9 4.1200
#> 11 10 3.2500
#> 12 11 5.1378
#> 13 12 4.7301
#>
#> $`Laranjeiras vs Camburi`
#> lag value
#> 1 0 47.5982
#> 2 1 29.4662
#> 3 2 13.9184
#> 4 3 8.8878
#> 5 4 6.1575
#> 6 5 3.4654
#> 7 6 6.1962
#> 8 7 10.1236
#> 9 8 7.4122
#> 10 9 3.4841
#> 11 10 2.1116
#> 12 11 4.1118
#> 13 12 3.5149
#>
#> $`Cariacica vs Carapina`
#> lag value
#> 1 0 56.7283
#> 2 1 24.1323
#> 3 2 10.4820
#> 4 3 6.7364
#> 5 4 5.9227
#> 6 5 4.6202
#> 7 6 7.0153
#> 8 7 13.5343
#> 9 8 9.8410
#> 10 9 7.4099
#> 11 10 6.2922
#> 12 11 8.3866
#> 13 12 4.5466
#>
#> $`Cariacica vs Camburi`
#> lag value
#> 1 0 50.2937
#> 2 1 24.1934
#> 3 2 8.7894
#> 4 3 4.5696
#> 5 4 2.4629
#> 6 5 0.5176
#> 7 6 7.6024
#> 8 7 16.6021
#> 9 8 9.2406
#> 10 9 1.7496
#> 11 10 2.3215
#> 12 11 4.4509
#> 13 12 2.1397
#>
#> $`Carapina vs Camburi`
#> lag value
#> 1 0 27.8541
#> 2 1 13.6600
#> 3 2 6.2072
#> 4 3 3.8671
#> 5 4 3.7412
#> 6 5 2.4448
#> 7 6 4.5894
#> 8 7 7.4998
#> 9 8 5.4952
#> 10 9 3.9237
#> 11 10 4.2875
#> 12 11 4.7735
#> 13 12 3.7682stats::acf and to regression-based ACF
(standard and robust)std_uni_acf <- setNames(
lapply(uni_stations, function(st) {
PerACF(pm10[, st], lag.max = lag_max_reg, type = "correlation", plot = FALSE)
}),
uni_stations
)
std_uni_acovf <- setNames(
lapply(uni_stations, function(st) {
PerACF(pm10[, st], lag.max = lag_max_reg, type = "covariance", plot = FALSE)
}),
uni_stations
)
stats_uni_acf <- setNames(
lapply(uni_stations, function(st) {
stats::acf(pm10[, st], lag.max = lag_max, type = "correlation", plot = FALSE, demean = TRUE)
}),
uni_stations
)
stats_uni_acovf <- setNames(
lapply(uni_stations, function(st) {
stats::acf(pm10[, st], lag.max = lag_max, type = "covariance", plot = FALSE, demean = TRUE)
}),
uni_stations
)
std_multi_acf <- PerACF(x_multi, lag.max = lag_max_reg, type = "correlation", plot = FALSE)
std_multi_acovf <- PerACF(x_multi, lag.max = lag_max_reg, type = "covariance", plot = FALSE)
stats_multi_acf <- stats::acf(x_multi, lag.max = lag_max, type = "correlation", plot = FALSE, demean = TRUE)
stats_multi_acovf <- stats::acf(x_multi, lag.max = lag_max, type = "covariance", plot = FALSE, demean = TRUE)uni_compare_acf <- setNames(
lapply(uni_stations, function(st) {
round(compare_three(
reg_standard = std_uni_acf[[st]],
reg_robust = rob_uni_acf[[st]],
stats_standard = stats_uni_acf[[st]],
max_lag = lag_max
), 4)
}),
uni_stations
)
uni_compare_acovf <- setNames(
lapply(uni_stations, function(st) {
round(compare_three(
reg_standard = std_uni_acovf[[st]],
reg_robust = rob_uni_acovf[[st]],
stats_standard = stats_uni_acovf[[st]],
max_lag = lag_max
), 4)
}),
uni_stations
)
uni_compare_acf
#> $Laranjeiras
#> lag reg_standard reg_robust stats_standard diff_reg_stats diff_rob_reg
#> 1 0 1.0000 1.0000 1.0000 0.0000 0.0000
#> 2 1 0.6006 0.5924 0.6007 -0.0001 -0.0082
#> 3 2 0.3488 0.3411 0.3494 -0.0006 -0.0077
#> 4 3 0.2314 0.2257 0.2318 -0.0004 -0.0057
#> 5 4 0.1900 0.1731 0.1897 0.0003 -0.0169
#> 6 5 0.1419 0.1301 0.1422 -0.0004 -0.0118
#> 7 6 0.1311 0.1227 0.1315 -0.0004 -0.0084
#> 8 7 0.1698 0.1673 0.1699 -0.0001 -0.0024
#> 9 8 0.1664 0.1486 0.1668 -0.0004 -0.0178
#> 10 9 0.1310 0.1172 0.1310 0.0000 -0.0138
#> 11 10 0.1222 0.1045 0.1219 0.0003 -0.0177
#> 12 11 0.1013 0.0958 0.1010 0.0003 -0.0055
#> 13 12 0.0921 0.0873 0.0904 0.0017 -0.0047
#> diff_rob_stats
#> 1 0.0000
#> 2 -0.0082
#> 3 -0.0083
#> 4 -0.0061
#> 5 -0.0166
#> 6 -0.0121
#> 7 -0.0088
#> 8 -0.0026
#> 9 -0.0182
#> 10 -0.0139
#> 11 -0.0174
#> 12 -0.0052
#> 13 -0.0030
#>
#> $Cariacica
#> lag reg_standard reg_robust stats_standard diff_reg_stats diff_rob_reg
#> 1 0 1.0000 1.0000 1.0000 0e+00 0.0000
#> 2 1 0.4022 0.3498 0.4018 4e-04 -0.0523
#> 3 2 0.1465 0.1182 0.1461 3e-04 -0.0282
#> 4 3 0.1166 0.0733 0.1164 2e-04 -0.0433
#> 5 4 0.1033 0.0579 0.1026 8e-04 -0.0454
#> 6 5 0.0615 0.0350 0.0615 0e+00 -0.0265
#> 7 6 0.1432 0.1284 0.1429 3e-04 -0.0148
#> 8 7 0.3070 0.2686 0.3062 8e-04 -0.0384
#> 9 8 0.1690 0.1427 0.1686 4e-04 -0.0263
#> 10 9 0.0750 0.0672 0.0743 7e-04 -0.0078
#> 11 10 0.0799 0.0534 0.0798 1e-04 -0.0264
#> 12 11 0.0885 0.0736 0.0891 -5e-04 -0.0149
#> 13 12 0.0408 0.0404 0.0412 -5e-04 -0.0004
#> diff_rob_stats
#> 1 0.0000
#> 2 -0.0520
#> 3 -0.0279
#> 4 -0.0431
#> 5 -0.0446
#> 6 -0.0266
#> 7 -0.0146
#> 8 -0.0376
#> 9 -0.0259
#> 10 -0.0071
#> 11 -0.0264
#> 12 -0.0154
#> 13 -0.0008
uni_compare_acovf
#> $Laranjeiras
#> lag reg_standard reg_robust stats_standard diff_reg_stats diff_rob_reg
#> 1 0 127.3392 121.2045 127.3392 0.0000 -6.1346
#> 2 1 76.4775 71.8049 76.4880 -0.0105 -4.6726
#> 3 2 44.4171 41.3404 44.4894 -0.0723 -3.0767
#> 4 3 29.4625 27.3523 29.5185 -0.0560 -2.1102
#> 5 4 24.1885 20.9803 24.1504 0.0381 -3.2082
#> 6 5 18.0634 15.7645 18.1093 -0.0459 -2.2989
#> 7 6 16.6904 14.8702 16.7457 -0.0554 -1.8201
#> 8 7 21.6207 20.2835 21.6393 -0.0187 -1.3372
#> 9 8 21.1855 18.0117 21.2367 -0.0512 -3.1738
#> 10 9 16.6832 14.2022 16.6876 -0.0044 -2.4810
#> 11 10 15.5596 12.6675 15.5197 0.0398 -2.8921
#> 12 11 12.9007 11.6108 12.8596 0.0411 -1.2899
#> 13 12 11.7253 10.5868 11.5086 0.2167 -1.1385
#> diff_rob_stats
#> 1 -6.1346
#> 2 -4.6832
#> 3 -3.1490
#> 4 -2.1661
#> 5 -3.1701
#> 6 -2.3448
#> 7 -1.8755
#> 8 -1.3558
#> 9 -3.2250
#> 10 -2.4854
#> 11 -2.8523
#> 12 -1.2488
#> 13 -0.9218
#>
#> $Cariacica
#> lag reg_standard reg_robust stats_standard diff_reg_stats diff_rob_reg
#> 1 0 172.1221 154.9985 172.1221 0.0000 -17.1236
#> 2 1 69.2234 54.2239 69.1594 0.0640 -14.9995
#> 3 2 25.2096 18.3232 25.1537 0.0559 -6.8864
#> 4 3 20.0670 11.3554 20.0344 0.0326 -8.7116
#> 5 4 17.7864 8.9803 17.6562 0.1302 -8.8060
#> 6 5 10.5847 5.4191 10.5881 -0.0034 -5.1655
#> 7 6 24.6476 19.8959 24.5988 0.0488 -4.7517
#> 8 7 52.8391 41.6297 52.6983 0.1408 -11.2094
#> 9 8 29.0864 22.1161 29.0151 0.0714 -6.9704
#> 10 9 12.9137 10.4201 12.7916 0.1221 -2.4936
#> 11 10 13.7473 8.2815 13.7372 0.0101 -5.4658
#> 12 11 15.2409 11.4145 15.3289 -0.0880 -3.8264
#> 13 12 7.0196 6.2635 7.0972 -0.0776 -0.7561
#> diff_rob_stats
#> 1 -17.1236
#> 2 -14.9355
#> 3 -6.8305
#> 4 -8.6790
#> 5 -8.6759
#> 6 -5.1690
#> 7 -4.7029
#> 8 -11.0685
#> 9 -6.8990
#> 10 -2.3715
#> 11 -5.4557
#> 12 -3.9144
#> 13 -0.8338multi_compare_acf <- setNames(
lapply(seq_len(nrow(pair_indices)), function(k) {
i <- pair_indices[k, 1]
j <- pair_indices[k, 2]
round(compare_three(
reg_standard = std_multi_acf,
reg_robust = rob_multi_acf,
stats_standard = stats_multi_acf,
i = i,
j = j,
max_lag = lag_max
), 4)
}),
pair_labels
)
multi_compare_acovf <- setNames(
lapply(seq_len(nrow(pair_indices)), function(k) {
i <- pair_indices[k, 1]
j <- pair_indices[k, 2]
round(compare_three(
reg_standard = std_multi_acovf,
reg_robust = rob_multi_acovf,
stats_standard = stats_multi_acovf,
i = i,
j = j,
max_lag = lag_max
), 4)
}),
pair_labels
)
multi_compare_acf
#> $`Laranjeiras vs Laranjeiras`
#> lag reg_standard reg_robust stats_standard diff_reg_stats diff_rob_reg
#> 1 0 1.0000 1.0000 1.0000 0.0000 0.0000
#> 2 1 0.6006 0.5924 0.6007 -0.0001 -0.0082
#> 3 2 0.3488 0.3411 0.3494 -0.0006 -0.0077
#> 4 3 0.2314 0.2257 0.2318 -0.0004 -0.0057
#> 5 4 0.1900 0.1731 0.1897 0.0003 -0.0169
#> 6 5 0.1419 0.1301 0.1422 -0.0004 -0.0118
#> 7 6 0.1311 0.1227 0.1315 -0.0004 -0.0084
#> 8 7 0.1698 0.1673 0.1699 -0.0001 -0.0024
#> 9 8 0.1664 0.1486 0.1668 -0.0004 -0.0178
#> 10 9 0.1310 0.1172 0.1310 0.0000 -0.0138
#> 11 10 0.1222 0.1045 0.1219 0.0003 -0.0177
#> 12 11 0.1013 0.0958 0.1010 0.0003 -0.0055
#> 13 12 0.0921 0.0873 0.0904 0.0017 -0.0047
#> diff_rob_stats
#> 1 0.0000
#> 2 -0.0082
#> 3 -0.0083
#> 4 -0.0061
#> 5 -0.0166
#> 6 -0.0121
#> 7 -0.0088
#> 8 -0.0026
#> 9 -0.0182
#> 10 -0.0139
#> 11 -0.0174
#> 12 -0.0052
#> 13 -0.0030
#>
#> $`Cariacica vs Cariacica`
#> lag reg_standard reg_robust stats_standard diff_reg_stats diff_rob_reg
#> 1 0 1.0000 1.0000 1.0000 0e+00 0.0000
#> 2 1 0.4022 0.3498 0.4018 4e-04 -0.0523
#> 3 2 0.1465 0.1182 0.1461 3e-04 -0.0282
#> 4 3 0.1166 0.0733 0.1164 2e-04 -0.0433
#> 5 4 0.1033 0.0579 0.1026 8e-04 -0.0454
#> 6 5 0.0615 0.0350 0.0615 0e+00 -0.0265
#> 7 6 0.1432 0.1284 0.1429 3e-04 -0.0148
#> 8 7 0.3070 0.2686 0.3062 8e-04 -0.0384
#> 9 8 0.1690 0.1427 0.1686 4e-04 -0.0263
#> 10 9 0.0750 0.0672 0.0743 7e-04 -0.0078
#> 11 10 0.0799 0.0534 0.0798 1e-04 -0.0264
#> 12 11 0.0885 0.0736 0.0891 -5e-04 -0.0149
#> 13 12 0.0408 0.0404 0.0412 -5e-04 -0.0004
#> diff_rob_stats
#> 1 0.0000
#> 2 -0.0520
#> 3 -0.0279
#> 4 -0.0431
#> 5 -0.0446
#> 6 -0.0266
#> 7 -0.0146
#> 8 -0.0376
#> 9 -0.0259
#> 10 -0.0071
#> 11 -0.0264
#> 12 -0.0154
#> 13 -0.0008
#>
#> $`Carapina vs Carapina`
#> lag reg_standard reg_robust stats_standard diff_reg_stats diff_rob_reg
#> 1 0 1.0000 1.0000 1.0000 0.0000 0.0000
#> 2 1 0.4524 0.4057 0.4520 0.0004 -0.0467
#> 3 2 0.2558 0.2070 0.2560 -0.0002 -0.0488
#> 4 3 0.1902 0.1638 0.1899 0.0003 -0.0264
#> 5 4 0.2037 0.1527 0.2025 0.0012 -0.0511
#> 6 5 0.1998 0.1498 0.1981 0.0017 -0.0501
#> 7 6 0.2201 0.1541 0.2188 0.0013 -0.0661
#> 8 7 0.2327 0.1867 0.2313 0.0015 -0.0460
#> 9 8 0.1922 0.1750 0.1896 0.0026 -0.0172
#> 10 9 0.1730 0.1602 0.1700 0.0030 -0.0128
#> 11 10 0.1603 0.1522 0.1577 0.0026 -0.0081
#> 12 11 0.1839 0.1584 0.1808 0.0031 -0.0256
#> 13 12 0.1114 0.0980 0.1088 0.0026 -0.0134
#> diff_rob_stats
#> 1 0.0000
#> 2 -0.0463
#> 3 -0.0490
#> 4 -0.0262
#> 5 -0.0498
#> 6 -0.0484
#> 7 -0.0648
#> 8 -0.0445
#> 9 -0.0146
#> 10 -0.0098
#> 11 -0.0055
#> 12 -0.0224
#> 13 -0.0108
#>
#> $`Camburi vs Camburi`
#> lag reg_standard reg_robust stats_standard diff_reg_stats diff_rob_reg
#> 1 0 1.0000 1.0000 1.0000 0.0000 0.0000
#> 2 1 0.4316 0.3880 0.4309 0.0007 -0.0436
#> 3 2 0.1691 0.1458 0.1689 0.0002 -0.0233
#> 4 3 0.0914 0.0758 0.0909 0.0005 -0.0156
#> 5 4 0.0690 0.0577 0.0672 0.0018 -0.0113
#> 6 5 0.0409 0.0363 0.0391 0.0019 -0.0047
#> 7 6 0.1325 0.1273 0.1307 0.0017 -0.0052
#> 8 7 0.2194 0.2092 0.2168 0.0026 -0.0101
#> 9 8 0.1558 0.1356 0.1518 0.0040 -0.0202
#> 10 9 0.0353 0.0297 0.0324 0.0029 -0.0056
#> 11 10 -0.0062 0.0035 -0.0083 0.0020 0.0097
#> 12 11 0.0326 0.0359 0.0298 0.0027 0.0034
#> 13 12 0.0512 0.0504 0.0473 0.0039 -0.0008
#> diff_rob_stats
#> 1 0.0000
#> 2 -0.0429
#> 3 -0.0231
#> 4 -0.0151
#> 5 -0.0095
#> 6 -0.0028
#> 7 -0.0035
#> 8 -0.0075
#> 9 -0.0162
#> 10 -0.0027
#> 11 0.0118
#> 12 0.0061
#> 13 0.0031
#>
#> $`Laranjeiras vs Cariacica`
#> lag reg_standard reg_robust stats_standard diff_reg_stats diff_rob_reg
#> 1 0 0.4161 0.4228 0.4214 -0.0053 0.0067
#> 2 1 0.2181 0.2088 0.2467 -0.0286 -0.0093
#> 3 2 0.0771 0.0741 0.1050 -0.0279 -0.0030
#> 4 3 0.0394 0.0250 0.0537 -0.0143 -0.0144
#> 5 4 0.0074 -0.0019 0.0264 -0.0190 -0.0093
#> 6 5 -0.0102 -0.0202 0.0042 -0.0144 -0.0100
#> 7 6 0.0162 0.0077 0.0248 -0.0086 -0.0085
#> 8 7 0.0874 0.0898 0.0995 -0.0121 0.0024
#> 9 8 0.0437 0.0493 0.0794 -0.0356 0.0056
#> 10 9 0.0048 0.0075 0.0356 -0.0308 0.0027
#> 11 10 0.0134 0.0135 0.0369 -0.0235 0.0000
#> 12 11 0.0211 0.0233 0.0399 -0.0188 0.0022
#> 13 12 -0.0053 0.0003 0.0181 -0.0234 0.0056
#> diff_rob_stats
#> 1 0.0014
#> 2 -0.0379
#> 3 -0.0309
#> 4 -0.0287
#> 5 -0.0282
#> 6 -0.0244
#> 7 -0.0171
#> 8 -0.0097
#> 9 -0.0300
#> 10 -0.0281
#> 11 -0.0234
#> 12 -0.0166
#> 13 -0.0178
#>
#> $`Laranjeiras vs Carapina`
#> lag reg_standard reg_robust stats_standard diff_reg_stats diff_rob_reg
#> 1 0 0.3684 0.3856 0.3534 0.0150 0.0172
#> 2 1 0.1968 0.1975 0.1718 0.0250 0.0007
#> 3 2 0.0801 0.0841 0.0677 0.0123 0.0040
#> 4 3 0.0510 0.0533 0.0401 0.0109 0.0023
#> 5 4 0.0536 0.0506 0.0434 0.0102 -0.0031
#> 6 5 0.0297 0.0213 0.0177 0.0120 -0.0084
#> 7 6 0.0264 0.0287 0.0150 0.0114 0.0023
#> 8 7 0.0675 0.0760 0.0548 0.0128 0.0084
#> 9 8 0.0707 0.0705 0.0626 0.0081 -0.0001
#> 10 9 0.0470 0.0556 0.0423 0.0047 0.0086
#> 11 10 0.0336 0.0439 0.0338 -0.0002 0.0103
#> 12 11 0.0585 0.0693 0.0374 0.0211 0.0108
#> 13 12 0.0423 0.0638 0.0302 0.0121 0.0215
#> diff_rob_stats
#> 1 0.0322
#> 2 0.0257
#> 3 0.0163
#> 4 0.0132
#> 5 0.0071
#> 6 0.0036
#> 7 0.0137
#> 8 0.0212
#> 9 0.0079
#> 10 0.0133
#> 11 0.0100
#> 12 0.0319
#> 13 0.0336
#>
#> $`Laranjeiras vs Camburi`
#> lag reg_standard reg_robust stats_standard diff_reg_stats diff_rob_reg
#> 1 0 0.5298 0.5567 0.5246 0.0052 0.0269
#> 2 1 0.3398 0.3446 0.3728 -0.0329 0.0048
#> 3 2 0.1641 0.1628 0.1767 -0.0125 -0.0013
#> 4 3 0.1030 0.1039 0.1165 -0.0135 0.0010
#> 5 4 0.0767 0.0720 0.0921 -0.0153 -0.0047
#> 6 5 0.0456 0.0405 0.0743 -0.0287 -0.0051
#> 7 6 0.0753 0.0725 0.0873 -0.0120 -0.0028
#> 8 7 0.1208 0.1184 0.1174 0.0034 -0.0024
#> 9 8 0.0856 0.0867 0.0865 -0.0009 0.0011
#> 10 9 0.0327 0.0407 0.0222 0.0104 0.0081
#> 11 10 0.0174 0.0247 0.0134 0.0040 0.0073
#> 12 11 0.0374 0.0481 0.0306 0.0068 0.0106
#> 13 12 0.0389 0.0411 0.0513 -0.0124 0.0022
#> diff_rob_stats
#> 1 0.0321
#> 2 -0.0282
#> 3 -0.0139
#> 4 -0.0125
#> 5 -0.0200
#> 6 -0.0337
#> 7 -0.0148
#> 8 0.0010
#> 9 0.0002
#> 10 0.0185
#> 11 0.0113
#> 12 0.0175
#> 13 -0.0102
#>
#> $`Cariacica vs Carapina`
#> lag reg_standard reg_robust stats_standard diff_reg_stats diff_rob_reg
#> 1 0 0.6903 0.6768 0.7022 -0.0119 -0.0134
#> 2 1 0.3331 0.2879 0.3147 0.0184 -0.0452
#> 3 2 0.1559 0.1251 0.1514 0.0044 -0.0308
#> 4 3 0.1064 0.0804 0.1323 -0.0259 -0.0261
#> 5 4 0.1046 0.0707 0.1286 -0.0241 -0.0339
#> 6 5 0.0877 0.0551 0.1108 -0.0231 -0.0326
#> 7 6 0.1238 0.0837 0.1445 -0.0208 -0.0401
#> 8 7 0.1976 0.1615 0.2146 -0.0169 -0.0362
#> 9 8 0.1389 0.1174 0.1254 0.0135 -0.0215
#> 10 9 0.1026 0.0884 0.0853 0.0173 -0.0142
#> 11 10 0.0960 0.0751 0.0814 0.0146 -0.0209
#> 12 11 0.1170 0.1001 0.1047 0.0123 -0.0170
#> 13 12 0.0490 0.0542 0.0586 -0.0097 0.0053
#> diff_rob_stats
#> 1 -0.0254
#> 2 -0.0268
#> 3 -0.0264
#> 4 -0.0519
#> 5 -0.0580
#> 6 -0.0557
#> 7 -0.0608
#> 8 -0.0531
#> 9 -0.0080
#> 10 0.0031
#> 11 -0.0064
#> 12 -0.0046
#> 13 -0.0044
#>
#> $`Cariacica vs Camburi`
#> lag reg_standard reg_robust stats_standard diff_reg_stats diff_rob_reg
#> 1 0 0.5523 0.5201 0.5564 -0.0041 -0.0322
#> 2 1 0.2917 0.2502 0.2512 0.0405 -0.0415
#> 3 2 0.1075 0.0909 0.0633 0.0442 -0.0166
#> 4 3 0.0639 0.0473 0.0640 -0.0001 -0.0167
#> 5 4 0.0501 0.0255 0.0734 -0.0233 -0.0246
#> 6 5 0.0181 0.0054 0.0515 -0.0334 -0.0128
#> 7 6 0.0858 0.0786 0.1004 -0.0146 -0.0072
#> 8 7 0.1894 0.1717 0.1713 0.0182 -0.0177
#> 9 8 0.1104 0.0956 0.0431 0.0673 -0.0149
#> 10 9 0.0351 0.0181 -0.0303 0.0654 -0.0170
#> 11 10 0.0304 0.0240 0.0044 0.0260 -0.0064
#> 12 11 0.0507 0.0460 0.0597 -0.0090 -0.0046
#> 13 12 0.0237 0.0221 0.0479 -0.0242 -0.0016
#> diff_rob_stats
#> 1 -0.0362
#> 2 -0.0010
#> 3 0.0276
#> 4 -0.0168
#> 5 -0.0479
#> 6 -0.0461
#> 7 -0.0217
#> 8 0.0005
#> 9 0.0524
#> 10 0.0484
#> 11 0.0196
#> 12 -0.0136
#> 13 -0.0258
#>
#> $`Carapina vs Camburi`
#> lag reg_standard reg_robust stats_standard diff_reg_stats diff_rob_reg
#> 1 0 0.5634 0.5327 0.5518 0.0116 -0.0306
#> 2 1 0.3072 0.2613 0.3164 -0.0092 -0.0460
#> 3 2 0.1416 0.1187 0.1297 0.0119 -0.0229
#> 4 3 0.0887 0.0740 0.0710 0.0177 -0.0148
#> 5 4 0.0904 0.0716 0.0836 0.0067 -0.0188
#> 6 5 0.0735 0.0468 0.0568 0.0167 -0.0267
#> 7 6 0.1151 0.0878 0.0850 0.0301 -0.0273
#> 8 7 0.1606 0.1434 0.1255 0.0351 -0.0171
#> 9 8 0.1314 0.1051 0.1036 0.0278 -0.0263
#> 10 9 0.0848 0.0750 0.0614 0.0234 -0.0097
#> 11 10 0.0877 0.0820 0.0625 0.0253 -0.0057
#> 12 11 0.0986 0.0913 0.0798 0.0188 -0.0073
#> 13 12 0.0696 0.0721 0.0425 0.0271 0.0024
#> diff_rob_stats
#> 1 -0.0190
#> 2 -0.0552
#> 3 -0.0110
#> 4 0.0030
#> 5 -0.0121
#> 6 -0.0101
#> 7 0.0027
#> 8 0.0180
#> 9 0.0015
#> 10 0.0136
#> 11 0.0196
#> 12 0.0115
#> 13 0.0295
multi_compare_acovf
#> $`Laranjeiras vs Laranjeiras`
#> lag reg_standard reg_robust stats_standard diff_reg_stats diff_rob_reg
#> 1 0 127.3392 121.2045 127.3392 0.0000 -6.1346
#> 2 1 76.4775 71.8049 76.4880 -0.0105 -4.6726
#> 3 2 44.4171 41.3404 44.4894 -0.0723 -3.0767
#> 4 3 29.4625 27.3523 29.5185 -0.0560 -2.1102
#> 5 4 24.1885 20.9803 24.1504 0.0381 -3.2082
#> 6 5 18.0634 15.7645 18.1093 -0.0459 -2.2989
#> 7 6 16.6904 14.8702 16.7457 -0.0554 -1.8201
#> 8 7 21.6207 20.2835 21.6393 -0.0187 -1.3372
#> 9 8 21.1855 18.0117 21.2367 -0.0512 -3.1738
#> 10 9 16.6832 14.2022 16.6876 -0.0044 -2.4810
#> 11 10 15.5596 12.6675 15.5197 0.0398 -2.8921
#> 12 11 12.9007 11.6108 12.8596 0.0411 -1.2899
#> 13 12 11.7253 10.5868 11.5086 0.2167 -1.1385
#> diff_rob_stats
#> 1 -6.1346
#> 2 -4.6832
#> 3 -3.1490
#> 4 -2.1661
#> 5 -3.1701
#> 6 -2.3448
#> 7 -1.8755
#> 8 -1.3558
#> 9 -3.2250
#> 10 -2.4854
#> 11 -2.8523
#> 12 -1.2488
#> 13 -0.9218
#>
#> $`Cariacica vs Cariacica`
#> lag reg_standard reg_robust stats_standard diff_reg_stats diff_rob_reg
#> 1 0 172.1221 154.9985 172.1221 0.0000 -17.1236
#> 2 1 69.2234 54.2239 69.1594 0.0640 -14.9995
#> 3 2 25.2096 18.3232 25.1537 0.0559 -6.8864
#> 4 3 20.0670 11.3554 20.0344 0.0326 -8.7116
#> 5 4 17.7864 8.9803 17.6562 0.1302 -8.8060
#> 6 5 10.5847 5.4191 10.5881 -0.0034 -5.1655
#> 7 6 24.6476 19.8959 24.5988 0.0488 -4.7517
#> 8 7 52.8391 41.6297 52.6983 0.1408 -11.2094
#> 9 8 29.0864 22.1161 29.0151 0.0714 -6.9704
#> 10 9 12.9137 10.4201 12.7916 0.1221 -2.4936
#> 11 10 13.7473 8.2815 13.7372 0.0101 -5.4658
#> 12 11 15.2409 11.4145 15.3289 -0.0880 -3.8264
#> 13 12 7.0196 6.2635 7.0972 -0.0776 -0.7561
#> diff_rob_stats
#> 1 -17.1236
#> 2 -14.9355
#> 3 -6.8305
#> 4 -8.6790
#> 5 -8.6759
#> 6 -5.1690
#> 7 -4.7029
#> 8 -11.0685
#> 9 -6.8990
#> 10 -2.3715
#> 11 -5.4557
#> 12 -3.9144
#> 13 -0.8338
#>
#> $`Carapina vs Carapina`
#> lag reg_standard reg_robust stats_standard diff_reg_stats diff_rob_reg
#> 1 0 58.7560 45.3198 58.7560 0.0000 -13.4362
#> 2 1 26.5806 18.3842 26.5568 0.0238 -8.1964
#> 3 2 15.0309 9.3829 15.0426 -0.0117 -5.6480
#> 4 3 11.1747 7.4220 11.1597 0.0149 -3.7527
#> 5 4 11.9704 6.9181 11.8972 0.0732 -5.0523
#> 6 5 11.7409 6.7871 11.6422 0.0987 -4.9538
#> 7 6 12.9338 6.9822 12.8583 0.0756 -5.9516
#> 8 7 13.6732 8.4631 13.5875 0.0856 -5.2101
#> 9 8 11.2907 7.9311 11.1392 0.1515 -3.3595
#> 10 9 10.1647 7.2606 9.9887 0.1759 -2.9041
#> 11 10 9.4175 6.8960 9.2654 0.1521 -2.5216
#> 12 11 10.8080 7.1783 10.6244 0.1835 -3.6297
#> 13 12 6.5431 4.4396 6.3904 0.1527 -2.1036
#> diff_rob_stats
#> 1 -13.4362
#> 2 -8.1727
#> 3 -5.6597
#> 4 -3.7377
#> 5 -4.9791
#> 6 -4.8551
#> 7 -5.8761
#> 8 -5.1245
#> 9 -3.2081
#> 10 -2.7281
#> 11 -2.3694
#> 12 -3.4461
#> 13 -1.9509
#>
#> $`Camburi vs Camburi`
#> lag reg_standard reg_robust stats_standard diff_reg_stats diff_rob_reg
#> 1 0 64.1435 60.3190 64.1435 0.0000 -3.8245
#> 2 1 27.6843 23.4016 27.6386 0.0458 -4.2827
#> 3 2 10.8453 8.7948 10.8319 0.0134 -2.0505
#> 4 3 5.8606 4.5709 5.8296 0.0310 -1.2897
#> 5 4 4.4257 3.4802 4.3132 0.1126 -0.9455
#> 6 5 2.6264 2.1888 2.5054 0.1209 -0.4376
#> 7 6 8.4961 7.6760 8.3841 0.1120 -0.8201
#> 8 7 14.0711 12.6203 13.9039 0.1671 -1.4508
#> 9 8 9.9945 8.1808 9.7394 0.2551 -1.8137
#> 10 9 2.2645 1.7893 2.0782 0.1863 -0.4753
#> 11 10 -0.3989 0.2117 -0.5298 0.1309 0.6106
#> 12 11 2.0893 2.1681 1.9130 0.1764 0.0788
#> 13 12 3.2850 3.0390 3.0351 0.2499 -0.2460
#> diff_rob_stats
#> 1 -3.8245
#> 2 -4.2369
#> 3 -2.0371
#> 4 -1.2587
#> 5 -0.8329
#> 6 -0.3167
#> 7 -0.7081
#> 8 -1.2837
#> 9 -1.5585
#> 10 -0.2889
#> 11 0.7415
#> 12 0.2552
#> 13 0.0039
#>
#> $`Laranjeiras vs Cariacica`
#> lag reg_standard reg_robust stats_standard diff_reg_stats diff_rob_reg
#> 1 0 61.6041 57.9476 62.3873 -0.7832 -3.6565
#> 2 1 32.2894 28.6152 36.5262 -4.2369 -3.6742
#> 3 2 11.4159 10.1595 15.5471 -4.1311 -1.2565
#> 4 3 5.8343 3.4325 7.9537 -2.1195 -2.4018
#> 5 4 1.0915 -0.2588 3.9027 -2.8112 -1.3503
#> 6 5 -1.5122 -2.7644 0.6193 -2.1316 -1.2521
#> 7 6 2.4048 1.0609 3.6783 -1.2735 -1.3439
#> 8 7 12.9400 12.3061 14.7259 -1.7858 -0.6339
#> 9 8 6.4731 6.7619 11.7488 -5.2757 0.2888
#> 10 9 0.7071 1.0225 5.2671 -4.5600 0.3154
#> 11 10 1.9865 1.8458 5.4623 -3.4758 -0.1407
#> 12 11 3.1226 3.1934 5.9029 -2.7802 0.0707
#> 13 12 -0.7841 0.0444 2.6767 -3.4608 0.8285
#> diff_rob_stats
#> 1 -4.4397
#> 2 -7.9110
#> 3 -5.3876
#> 4 -4.5213
#> 5 -4.1615
#> 6 -3.3837
#> 7 -2.6174
#> 8 -2.4198
#> 9 -4.9869
#> 10 -4.2447
#> 11 -3.6165
#> 12 -2.7095
#> 13 -2.6323
#>
#> $`Laranjeiras vs Carapina`
#> lag reg_standard reg_robust stats_standard diff_reg_stats diff_rob_reg
#> 1 0 31.8665 28.5814 30.5711 1.2954 -3.2851
#> 2 1 17.0229 14.6358 14.8604 2.1624 -2.3871
#> 3 2 6.9252 6.2293 5.8572 1.0680 -0.6958
#> 4 3 4.4129 3.9527 3.4684 0.9446 -0.4603
#> 5 4 4.6381 3.7469 3.7570 0.8811 -0.8912
#> 6 5 2.5714 1.5780 1.5340 1.0374 -0.9934
#> 7 6 2.2832 2.1294 1.2966 0.9867 -0.1538
#> 8 7 5.8404 5.6294 4.7363 1.1041 -0.2110
#> 9 8 6.1146 5.2282 5.4171 0.6975 -0.8865
#> 10 9 4.0646 4.1200 3.6554 0.4092 0.0554
#> 11 10 2.9044 3.2500 2.9239 -0.0195 0.3456
#> 12 11 5.0621 5.1378 3.2342 1.8279 0.0757
#> 13 12 3.6607 4.7301 2.6115 1.0492 1.0694
#> diff_rob_stats
#> 1 -1.9897
#> 2 -0.2246
#> 3 0.3721
#> 4 0.4843
#> 5 -0.0101
#> 6 0.0440
#> 7 0.8328
#> 8 0.8930
#> 9 -0.1889
#> 10 0.4646
#> 11 0.3261
#> 12 1.9036
#> 13 2.1186
#>
#> $`Laranjeiras vs Camburi`
#> lag reg_standard reg_robust stats_standard diff_reg_stats diff_rob_reg
#> 1 0 47.8793 47.5982 47.4131 0.4662 -0.2811
#> 2 1 30.7144 29.4662 33.6916 -2.9772 -1.2483
#> 3 2 14.8332 13.9184 15.9658 -1.1325 -0.9148
#> 4 3 9.3059 8.8878 10.5247 -1.2188 -0.4182
#> 5 4 6.9336 6.1575 8.3202 -1.3866 -0.7761
#> 6 5 4.1203 3.4654 6.7129 -2.5926 -0.6549
#> 7 6 6.8026 6.1962 7.8904 -1.0878 -0.6063
#> 8 7 10.9181 10.1236 10.6064 0.3117 -0.7945
#> 9 8 7.7324 7.4122 7.8155 -0.0831 -0.3202
#> 10 9 2.9532 3.4841 2.0093 0.9438 0.5309
#> 11 10 1.5737 2.1116 1.2152 0.3586 0.5378
#> 12 11 3.3846 4.1118 2.7672 0.6174 0.7272
#> 13 12 3.5179 3.5149 4.6342 -1.1163 -0.0030
#> diff_rob_stats
#> 1 0.1851
#> 2 -4.2255
#> 3 -2.0473
#> 4 -1.6370
#> 5 -2.1627
#> 6 -3.2475
#> 7 -1.6941
#> 8 -0.4828
#> 9 -0.4034
#> 10 1.4747
#> 11 0.8964
#> 12 1.3446
#> 13 -1.1193
#>
#> $`Cariacica vs Carapina`
#> lag reg_standard reg_robust stats_standard diff_reg_stats diff_rob_reg
#> 1 0 69.4191 56.7283 70.6164 -1.1974 -12.6908
#> 2 1 33.4991 24.1323 31.6511 1.8480 -9.3668
#> 3 2 15.6745 10.4820 15.2288 0.4457 -5.1925
#> 4 3 10.7049 6.7364 13.3048 -2.5999 -3.9685
#> 5 4 10.5165 5.9227 12.9366 -2.4201 -4.5937
#> 6 5 8.8172 4.6202 11.1419 -2.3247 -4.1970
#> 7 6 12.4475 7.0153 14.5351 -2.0876 -5.4322
#> 8 7 19.8756 13.5343 21.5774 -1.7018 -6.3413
#> 9 8 13.9712 9.8410 12.6089 1.3623 -4.1301
#> 10 9 10.3197 7.4099 8.5797 1.7399 -2.9098
#> 11 10 9.6562 6.2922 8.1900 1.4662 -3.3640
#> 12 11 11.7693 8.3866 10.5291 1.2402 -3.3828
#> 13 12 4.9227 4.5466 5.8939 -0.9712 -0.3761
#> diff_rob_stats
#> 1 -13.8881
#> 2 -7.5189
#> 3 -4.7468
#> 4 -6.5684
#> 5 -7.0138
#> 6 -6.5217
#> 7 -7.5198
#> 8 -8.0431
#> 9 -2.7679
#> 10 -1.1699
#> 11 -1.8978
#> 12 -2.1426
#> 13 -1.3473
#>
#> $`Cariacica vs Camburi`
#> lag reg_standard reg_robust stats_standard diff_reg_stats diff_rob_reg
#> 1 0 58.0352 50.2937 58.4613 -0.4260 -7.7416
#> 2 1 30.6491 24.1934 26.3953 4.2537 -6.4557
#> 3 2 11.2978 8.7894 6.6521 4.6457 -2.5084
#> 4 3 6.7170 4.5696 6.7268 -0.0098 -2.1474
#> 5 4 5.2641 2.4629 7.7094 -2.4453 -2.8011
#> 6 5 1.9042 0.5176 5.4109 -3.5067 -1.3866
#> 7 6 9.0170 7.6024 10.5468 -1.5298 -1.4145
#> 8 7 19.9037 16.6021 17.9939 1.9097 -3.3015
#> 9 8 11.6036 9.2406 4.5315 7.0722 -2.3630
#> 10 9 3.6867 1.7496 -3.1862 6.8729 -1.9371
#> 11 10 3.1978 2.3215 0.4608 2.7370 -0.8762
#> 12 11 5.3249 4.4509 6.2707 -0.9457 -0.8741
#> 13 12 2.4955 2.1397 5.0355 -2.5400 -0.3558
#> diff_rob_stats
#> 1 -8.1676
#> 2 -2.2019
#> 3 2.1372
#> 4 -2.1573
#> 5 -5.2465
#> 6 -4.8933
#> 7 -2.9444
#> 8 -1.3918
#> 9 4.7092
#> 10 4.9358
#> 11 1.8608
#> 12 -1.8198
#> 13 -2.8959
#>
#> $`Carapina vs Camburi`
#> lag reg_standard reg_robust stats_standard diff_reg_stats diff_rob_reg
#> 1 0 34.5844 27.8541 33.8744 0.7101 -6.7304
#> 2 1 18.8613 13.6600 19.4251 -0.5637 -5.2013
#> 3 2 8.6926 6.2072 7.9640 0.7285 -2.4854
#> 4 3 5.4476 3.8671 4.3594 1.0882 -1.5805
#> 5 4 5.5470 3.7412 5.1351 0.4119 -1.8059
#> 6 5 4.5112 2.4448 3.4888 1.0224 -2.0664
#> 7 6 7.0660 4.5894 5.2208 1.8452 -2.4766
#> 8 7 9.8565 7.4998 7.7027 2.1538 -2.3567
#> 9 8 8.0654 5.4952 6.3584 1.7070 -2.5702
#> 10 9 5.2044 3.9237 3.7697 1.4347 -1.2807
#> 11 10 5.3843 4.2875 3.8339 1.5504 -1.0967
#> 12 11 6.0543 4.7735 4.8977 1.1566 -1.2809
#> 13 12 4.2757 3.7682 2.6112 1.6646 -0.5076
#> diff_rob_stats
#> 1 -6.0203
#> 2 -5.7650
#> 3 -1.7568
#> 4 -0.4923
#> 5 -1.3940
#> 6 -1.0440
#> 7 -0.6314
#> 8 -0.2029
#> 9 -0.8632
#> 10 0.1540
#> 11 0.4536
#> 12 -0.1242
#> 13 1.1570lag0_cor_standard <- CovCorPer(x_multi, type = "correlation")
lag0_cor_robust <- CovCorMPer(x_multi, type = "correlation")
lag0_cor_stats <- stats_multi_acf$acf[1, , ]
lag0_cov_standard <- CovCorPer(x_multi, type = "covariance")
lag0_cov_robust <- CovCorMPer(x_multi, type = "covariance")
lag0_cov_stats <- stats_multi_acovf$acf[1, , ]
round(lag0_cor_standard, 4)
#> [,1] [,2] [,3] [,4]
#> [1,] 1.0000 0.4161 0.3684 0.5298
#> [2,] 0.4161 1.0000 0.6903 0.5523
#> [3,] 0.3684 0.6903 1.0000 0.5634
#> [4,] 0.5298 0.5523 0.5634 1.0000
round(lag0_cor_robust, 4)
#> [,1] [,2] [,3] [,4]
#> [1,] 1.0000 0.4228 0.3856 0.5567
#> [2,] 0.4228 1.0000 0.6768 0.5201
#> [3,] 0.3856 0.6768 1.0000 0.5327
#> [4,] 0.5567 0.5201 0.5327 1.0000
round(lag0_cor_stats, 4)
#> [,1] [,2] [,3] [,4]
#> [1,] 1.0000 0.4214 0.3534 0.5246
#> [2,] 0.4214 1.0000 0.7022 0.5564
#> [3,] 0.3534 0.7022 1.0000 0.5518
#> [4,] 0.5246 0.5564 0.5518 1.0000
round(lag0_cor_standard - lag0_cor_stats, 4)
#> [,1] [,2] [,3] [,4]
#> [1,] 0.0000 -0.0053 0.0150 0.0052
#> [2,] -0.0053 0.0000 -0.0119 -0.0041
#> [3,] 0.0150 -0.0119 0.0000 0.0116
#> [4,] 0.0052 -0.0041 0.0116 0.0000
round(lag0_cor_robust - lag0_cor_standard, 4)
#> [,1] [,2] [,3] [,4]
#> [1,] 0.0000 0.0067 0.0172 0.0269
#> [2,] 0.0067 0.0000 -0.0134 -0.0322
#> [3,] 0.0172 -0.0134 0.0000 -0.0306
#> [4,] 0.0269 -0.0322 -0.0306 0.0000
round(lag0_cov_standard, 4)
#> [,1] [,2] [,3] [,4]
#> [1,] 127.3392 61.6041 31.8665 47.8793
#> [2,] 61.6041 172.1221 69.4191 58.0352
#> [3,] 31.8665 69.4191 58.7560 34.5844
#> [4,] 47.8793 58.0352 34.5844 64.1435
round(lag0_cov_robust, 4)
#> [,1] [,2] [,3] [,4]
#> [1,] 121.2045 57.9476 28.5814 47.5982
#> [2,] 57.9476 154.9985 56.7283 50.2937
#> [3,] 28.5814 56.7283 45.3198 27.8541
#> [4,] 47.5982 50.2937 27.8541 60.3190
round(lag0_cov_stats, 4)
#> [,1] [,2] [,3] [,4]
#> [1,] 127.3392 62.3873 30.5711 47.4131
#> [2,] 62.3873 172.1221 70.6164 58.4613
#> [3,] 30.5711 70.6164 58.7560 33.8744
#> [4,] 47.4131 58.4613 33.8744 64.1435
round(lag0_cov_standard - lag0_cov_stats, 4)
#> [,1] [,2] [,3] [,4]
#> [1,] 0.0000 -0.7832 1.2954 0.4662
#> [2,] -0.7832 0.0000 -1.1974 -0.4260
#> [3,] 1.2954 -1.1974 0.0000 0.7101
#> [4,] 0.4662 -0.4260 0.7101 0.0000
round(lag0_cov_robust - lag0_cov_standard, 4)
#> [,1] [,2] [,3] [,4]
#> [1,] -6.1346 -3.6565 -3.2851 -0.2811
#> [2,] -3.6565 -17.1236 -12.6908 -7.7416
#> [3,] -3.2851 -12.6908 -13.4362 -6.7304
#> [4,] -0.2811 -7.7416 -6.7304 -3.8245These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.