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")
}
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 -3.8245