Continuous Time Random Exceedances

Fits a Continuous Time Random Exceedance model to bursty time series. CTREs model the distribution of threshold crossing times of extreme events. Fits are made by interactive visual assessment of "stability plots" using a shiny app.

References

"Peaks Over Threshold for Bursty Time Series", Katharina Hees, Smarak Nayak, Peter Straka. https://arxiv.org/abs/1802.05218

See also

Useful links:

• https://unsw-math.github.io/CTRE/

• Report bugs at https://github.com/strakaps/CTRE/issues

Author

Maintainer: Peter Straka straka.ps@unsw.edu.au

Authors:

• Katharina Hees heeskatharina@gmail.com

Examples

library(CTRE)
if (FALSE) {
runCTREshiny()
}

ctre_mod <- ctre(flares)
ctre_mod
#> 'ctre' object with 2488 timestamps and magnitudes.
#> Timestamps:
#>  POSIXct[1:2488], format: "1982-01-01 00:55:00" "1982-01-01 16:43:15" "1982-01-01 22:13:16" ...
#> Magnitudes:
#>  int [1:2488] 2404 94 60 53 107 5363 61 262 85 83 ...
length(ctre_mod)
#> [1] 2488
ctre_mod <- thin(ctre_mod, k = 500)
ctre_mod
#> 'ctre' object with 500 timestamps and magnitudes.
#> Timestamps:
#>  POSIXct[1:500], format: "1982-01-01 00:55:00" "1982-01-02 06:09:42" "1982-01-03 00:11:51" ...
#> Magnitudes:
#>  int [1:500] 2404 5363 262 421 2309 655 685 935 984 9763 ...
magnitudes(ctre_mod)
#>   [1]   2404   5363    262    421   2309    655    685    935    984   9763
#>  [11]    228    822   1006    375   1819   1428    419    540    365   4864
#>  [21]   1756    784    489   1610    494    223    806    546   1617    230
#>  [31]   7230    218    228   1143   1606    298    236    406    374    623
#>  [41]   2057    562   1193    326    275   4600  31095    429    386   1043
#>  [51]    430    653    448    232    580    460    819   1427    378    531
#>  [61]   1083    233    426    449    479   5966   4691    408   4521    229
#>  [71]    257    431    245    314    233    340    304   1896    277   1019
#>  [81]    347    352   1728   1312    531    248   1028    255    326    418
#>  [91]    408    751    260    256    213   1481    501   2833    289   1481
#> [101]   1482    220    235    243    279    371    342   1063    303    430
#> [111]    284    261    780    575    281   4635   5029   1121    320    331
#> [121]    227   1123    470  18903    375    459    367    358   1498   3248
#> [131]   7677    244   8452    225    245    266    352    359    776    659
#> [141]   3645    240    510    534    267    310    359   2061    261    277
#> [151]    407   3610    281    781    217    410   3194   1411 213791   1198
#> [161]   3590    443    493    291    258    251    213    709   1209   1497
#> [171]  18017    470   2843  20434    392  10152    460   1121    247    466
#> [181]    472    386    368   2681  60593    495    267    385    218   1517
#> [191]    528   1032    278    316    479    708    830   2239    324    367
#> [201]   1456    489   2174    583    440    647    392    906    457    893
#> [211]    405   2300    357    229   2619   1359    224    261   1223    590
#> [221]    857    410    232    279    332    582  25304   3478    726  33320
#> [231]  20609    782    220   9983    878    297   2228  13904   1170    579
#> [241]    277    378   1520   2609    324    596    414    423    965   1037
#> [251]  13670    979   5750   6122    216    794  20700    339    360   1708
#> [261]    414    286    367    268   1041    454    781    463   1276   7791
#> [271]   8678    385    263    224    216    283    280    370    331    213
#> [281]    256    230    377    246    878    893    276 155330   3277    262
#> [291]    574    451  57078   1283   1200    524   1145   5979   6260   1369
#> [301]    637   8609   3360    603    303    789    354    557    337    813
#> [311]    550    270    824    573    233    974    302    698    290   5290
#> [321]    241    316    220   1686    439  58007    929   2195    587    479
#> [331]    243    231    623    490    471    554   2178    548   1968    717
#> [341]  21000    308    358    666    295    303    383   8174   4487    246
#> [351]    718    243    340    230    567    265   7638   1000    912   2134
#> [361]    666   3374    282   3520    569    278    239    270    711    359
#> [371]    699    240    394   8504    437   1226    247    283    311   1516
#> [381]    294    446    610    535    259    359    393   1012    391    381
#> [391]    216    223    311    475    869    311   2052    394    351   1278
#> [401]    415    243    214    285    227   1899    487   1046    829    826
#> [411]   1108    214    237   2417   2309    496   2152    393   3269    265
#> [421]   1409   9983   1798    286    547    292   3734    412   3715    217
#> [431]    264    321   2201    404    572    363   4200    266    240  22747
#> [441]    441   1889   9400   2875    228    687    230    263    327    626
#> [451]    261    293    426   1600    240    234    332    427  23654    312
#> [461]    290   2454    269    259    469   2936    323   3311   1187    480
#> [471]    518  12464   2807    250  81391   5165   8678    269    448   3596
#> [481]    430    907 108043    408   1882  19095    413    228    380    304
#> [491]    534   1193    341    460    375    228   2287  38120   6891    423
time(ctre_mod)
#>   [1] "1982-01-01 00:55:00 UTC" "1982-01-02 06:09:42 UTC"
#>   [3] "1982-01-03 00:11:51 UTC" "1982-01-07 19:37:40 UTC"
#>   [5] "1982-01-08 02:01:20 UTC" "1982-01-08 14:27:01 UTC"
#>   [7] "1982-01-11 01:25:36 UTC" "1982-01-24 01:52:35 UTC"
#>   [9] "1982-01-24 19:36:20 UTC" "1982-01-28 07:13:20 UTC"
#>  [11] "1982-01-29 03:12:40 UTC" "1982-01-30 00:45:10 UTC"
#>  [13] "1982-01-30 12:04:50 UTC" "1982-01-31 07:06:00 UTC"
#>  [15] "1982-01-31 13:15:35 UTC" "1982-02-01 00:30:35 UTC"
#>  [17] "1982-02-01 14:18:45 UTC" "1982-02-02 15:47:40 UTC"
#>  [19] "1982-02-02 18:51:55 UTC" "1982-02-03 01:12:26 UTC"
#>  [21] "1982-02-03 03:14:25 UTC" "1982-02-03 13:15:30 UTC"
#>  [23] "1982-02-03 18:51:50 UTC" "1982-02-03 20:20:55 UTC"
#>  [25] "1982-02-03 20:41:35 UTC" "1982-02-04 13:41:05 UTC"
#>  [27] "1982-02-04 15:38:55 UTC" "1982-02-04 18:56:05 UTC"
#>  [29] "1982-02-05 01:09:35 UTC" "1982-02-05 03:06:50 UTC"
#>  [31] "1982-02-05 09:03:45 UTC" "1982-02-05 11:53:00 UTC"
#>  [33] "1982-02-06 04:25:00 UTC" "1982-02-06 12:23:50 UTC"
#>  [35] "1982-02-06 13:31:15 UTC" "1982-02-06 16:40:20 UTC"
#>  [37] "1982-02-06 18:17:25 UTC" "1982-02-06 19:48:15 UTC"
#>  [39] "1982-02-07 10:36:50 UTC" "1982-02-07 11:36:45 UTC"
#>  [41] "1982-02-07 20:57:50 UTC" "1982-02-08 01:44:50 UTC"
#>  [43] "1982-02-08 02:41:15 UTC" "1982-02-08 06:47:55 UTC"
#>  [45] "1982-02-08 07:12:45 UTC" "1982-02-08 08:04:00 UTC"
#>  [47] "1982-02-08 12:49:55 UTC" "1982-02-08 21:20:40 UTC"
#>  [49] "1982-02-09 01:39:55 UTC" "1982-02-09 03:35:25 UTC"
#>  [51] "1982-02-09 04:40:10 UTC" "1982-02-09 07:10:25 UTC"
#>  [53] "1982-02-09 09:25:30 UTC" "1982-02-09 11:06:50 UTC"
#>  [55] "1982-02-09 14:11:00 UTC" "1982-02-10 03:07:45 UTC"
#>  [57] "1982-02-10 09:44:05 UTC" "1982-02-10 18:43:40 UTC"
#>  [59] "1982-02-10 22:16:10 UTC" "1982-02-11 12:09:45 UTC"
#>  [61] "1982-02-11 13:44:40 UTC" "1982-02-11 18:32:45 UTC"
#>  [63] "1982-02-11 20:30:55 UTC" "1982-02-11 23:51:15 UTC"
#>  [65] "1982-02-12 05:48:40 UTC" "1982-02-12 21:30:15 UTC"
#>  [67] "1982-02-12 21:54:45 UTC" "1982-02-13 23:26:05 UTC"
#>  [69] "1982-02-14 03:43:15 UTC" "1982-02-14 04:07:25 UTC"
#>  [71] "1982-02-14 23:10:50 UTC" "1982-02-16 18:59:25 UTC"
#>  [73] "1982-02-17 09:55:55 UTC" "1982-02-17 19:43:20 UTC"
#>  [75] "1982-02-17 23:32:00 UTC" "1982-02-18 03:20:45 UTC"
#>  [77] "1982-02-18 04:44:00 UTC" "1982-02-18 09:02:59 UTC"
#>  [79] "1982-02-18 13:02:29 UTC" "1982-02-18 23:31:55 UTC"
#>  [81] "1982-02-19 04:51:45 UTC" "1982-02-19 13:36:49 UTC"
#>  [83] "1982-02-20 09:19:35 UTC" "1982-02-20 17:23:43 UTC"
#>  [85] "1982-02-23 03:12:42 UTC" "1982-02-24 05:09:05 UTC"
#>  [87] "1982-02-25 21:51:25 UTC" "1982-02-26 15:16:50 UTC"
#>  [89] "1982-02-26 17:35:30 UTC" "1982-03-01 02:35:54 UTC"
#>  [91] "1982-03-01 19:24:08 UTC" "1982-03-01 22:28:44 UTC"
#>  [93] "1982-03-02 00:39:56 UTC" "1982-03-03 01:24:24 UTC"
#>  [95] "1982-03-04 14:20:40 UTC" "1982-03-05 02:41:26 UTC"
#>  [97] "1982-03-05 06:40:52 UTC" "1982-03-07 02:46:24 UTC"
#>  [99] "1982-03-07 04:05:40 UTC" "1982-03-07 13:51:40 UTC"
#> [101] "1982-03-08 19:56:58 UTC" "1982-03-16 01:56:10 UTC"
#> [103] "1982-03-17 14:24:27 UTC" "1982-03-18 12:30:40 UTC"
#> [105] "1982-03-18 13:54:58 UTC" "1982-03-19 04:35:35 UTC"
#> [107] "1982-03-21 07:44:20 UTC" "1982-03-22 05:55:31 UTC"
#> [109] "1982-03-22 16:24:07 UTC" "1982-03-23 05:16:09 UTC"
#> [111] "1982-03-23 07:14:54 UTC" "1982-03-23 12:58:19 UTC"
#> [113] "1982-03-24 04:57:30 UTC" "1982-03-24 06:54:51 UTC"
#> [115] "1982-03-24 20:34:15 UTC" "1982-03-26 05:46:55 UTC"
#> [117] "1982-03-27 14:13:45 UTC" "1982-03-27 15:18:00 UTC"
#> [119] "1982-03-28 03:58:25 UTC" "1982-03-28 04:30:00 UTC"
#> [121] "1982-03-28 05:54:19 UTC" "1982-03-29 09:05:20 UTC"
#> [123] "1982-03-29 19:39:45 UTC" "1982-03-30 05:21:10 UTC"
#> [125] "1982-03-30 08:34:10 UTC" "1982-03-30 14:17:32 UTC"
#> [127] "1982-03-30 20:58:20 UTC" "1982-03-31 03:12:10 UTC"
#> [129] "1982-03-31 06:11:00 UTC" "1982-03-31 08:33:05 UTC"
#> [131] "1982-03-31 22:21:52 UTC" "1982-04-01 23:49:35 UTC"
#> [133] "1982-04-02 09:01:20 UTC" "1982-04-03 12:27:19 UTC"
#> [135] "1982-04-11 03:31:30 UTC" "1982-04-12 12:49:39 UTC"
#> [137] "1982-04-12 16:06:45 UTC" "1982-04-16 14:16:02 UTC"
#> [139] "1982-04-16 21:20:45 UTC" "1982-04-19 10:19:14 UTC"
#> [141] "1982-04-19 18:10:21 UTC" "1982-04-22 12:43:55 UTC"
#> [143] "1982-05-06 16:58:53 UTC" "1982-05-11 03:21:07 UTC"
#> [145] "1982-05-17 23:19:04 UTC" "1982-05-22 00:37:43 UTC"
#> [147] "1982-05-23 02:43:25 UTC" "1982-05-23 18:42:14 UTC"
#> [149] "1982-05-28 16:08:24 UTC" "1982-05-29 20:21:44 UTC"
#> [151] "1982-05-29 20:55:36 UTC" "1982-05-29 21:49:24 UTC"
#> [153] "1982-05-30 09:49:29 UTC" "1982-05-31 03:03:35 UTC"
#> [155] "1982-06-02 16:50:01 UTC" "1982-06-02 22:55:11 UTC"
#> [157] "1982-06-03 03:22:04 UTC" "1982-06-03 08:30:10 UTC"
#> [159] "1982-06-03 11:40:32 UTC" "1982-06-03 21:28:08 UTC"
#> [161] "1982-06-04 00:11:31 UTC" "1982-06-04 02:59:03 UTC"
#> [163] "1982-06-04 06:31:35 UTC" "1982-06-04 08:05:54 UTC"
#> [165] "1982-06-04 08:33:48 UTC" "1982-06-04 13:11:50 UTC"
#> [167] "1982-06-04 13:17:47 UTC" "1982-06-04 14:28:29 UTC"
#> [169] "1982-06-04 14:47:00 UTC" "1982-06-04 19:12:16 UTC"
#> [171] "1982-06-05 01:24:26 UTC" "1982-06-05 02:45:40 UTC"
#> [173] "1982-06-05 03:06:36 UTC" "1982-06-05 06:13:31 UTC"
#> [175] "1982-06-05 11:13:29 UTC" "1982-06-05 15:19:25 UTC"
#> [177] "1982-06-05 15:49:30 UTC" "1982-06-05 15:52:14 UTC"
#> [179] "1982-06-05 17:20:39 UTC" "1982-06-05 20:04:28 UTC"
#> [181] "1982-06-05 20:44:16 UTC" "1982-06-05 23:18:16 UTC"
#> [183] "1982-06-06 03:05:37 UTC" "1982-06-06 14:19:41 UTC"
#> [185] "1982-06-06 16:38:57 UTC" "1982-06-06 18:14:06 UTC"
#> [187] "1982-06-06 21:58:37 UTC" "1982-06-07 13:37:30 UTC"
#> [189] "1982-06-08 12:13:54 UTC" "1982-06-08 20:00:32 UTC"
#> [191] "1982-06-09 11:34:53 UTC" "1982-06-09 22:20:52 UTC"
#> [193] "1982-06-09 22:32:34 UTC" "1982-06-09 22:42:25 UTC"
#> [195] "1982-06-10 02:14:09 UTC" "1982-06-11 06:39:11 UTC"
#> [197] "1982-06-11 11:08:55 UTC" "1982-06-11 23:28:33 UTC"
#> [199] "1982-06-12 01:49:55 UTC" "1982-06-12 02:28:11 UTC"
#> [201] "1982-06-12 02:45:22 UTC" "1982-06-12 05:45:45 UTC"
#> [203] "1982-06-12 11:10:24 UTC" "1982-06-12 15:10:20 UTC"
#> [205] "1982-06-12 15:35:51 UTC" "1982-06-12 17:36:14 UTC"
#> [207] "1982-06-12 18:17:58 UTC" "1982-06-12 18:46:34 UTC"
#> [209] "1982-06-12 20:15:49 UTC" "1982-06-13 10:20:16 UTC"
#> [211] "1982-06-13 17:00:43 UTC" "1982-06-13 18:15:30 UTC"
#> [213] "1982-06-13 19:41:59 UTC" "1982-06-13 20:03:41 UTC"
#> [215] "1982-06-13 21:29:45 UTC" "1982-06-13 23:10:19 UTC"
#> [217] "1982-06-14 00:26:57 UTC" "1982-06-14 03:38:41 UTC"
#> [219] "1982-06-14 04:22:52 UTC" "1982-06-14 09:14:36 UTC"
#> [221] "1982-06-14 13:06:48 UTC" "1982-06-14 14:39:26 UTC"
#> [223] "1982-06-14 15:32:26 UTC" "1982-06-14 16:28:08 UTC"
#> [225] "1982-06-14 17:05:56 UTC" "1982-06-14 18:14:42 UTC"
#> [227] "1982-06-15 00:30:10 UTC" "1982-06-15 02:17:46 UTC"
#> [229] "1982-06-15 08:10:16 UTC" "1982-06-15 10:17:42 UTC"
#> [231] "1982-06-15 15:08:18 UTC" "1982-06-15 20:57:20 UTC"
#> [233] "1982-06-16 01:58:11 UTC" "1982-06-16 02:07:29 UTC"
#> [235] "1982-06-16 20:28:00 UTC" "1982-06-16 23:35:33 UTC"
#> [237] "1982-06-17 02:45:27 UTC" "1982-06-17 10:48:19 UTC"
#> [239] "1982-06-17 13:07:18 UTC" "1982-06-17 18:35:13 UTC"
#> [241] "1982-06-17 20:27:01 UTC" "1982-06-18 09:45:36 UTC"
#> [243] "1982-06-18 11:01:54 UTC" "1982-06-18 15:11:46 UTC"
#> [245] "1982-06-18 21:36:42 UTC" "1982-06-19 00:46:36 UTC"
#> [247] "1982-06-19 07:49:36 UTC" "1982-06-19 11:02:59 UTC"
#> [249] "1982-06-19 17:16:47 UTC" "1982-06-19 19:48:08 UTC"
#> [251] "1982-06-20 01:12:55 UTC" "1982-06-20 01:59:22 UTC"
#> [253] "1982-06-20 03:59:33 UTC" "1982-06-20 11:59:40 UTC"
#> [255] "1982-06-20 22:33:52 UTC" "1982-06-21 16:10:14 UTC"
#> [257] "1982-06-21 22:46:02 UTC" "1982-06-22 05:29:50 UTC"
#> [259] "1982-06-22 14:21:28 UTC" "1982-06-23 00:05:13 UTC"
#> [261] "1982-06-23 06:34:42 UTC" "1982-06-23 10:03:24 UTC"
#> [263] "1982-06-23 18:56:40 UTC" "1982-06-23 19:02:43 UTC"
#> [265] "1982-06-23 23:29:03 UTC" "1982-06-24 04:10:36 UTC"
#> [267] "1982-06-24 04:44:06 UTC" "1982-06-25 10:45:41 UTC"
#> [269] "1982-06-25 19:43:28 UTC" "1982-06-25 21:31:08 UTC"
#> [271] "1982-06-26 00:42:57 UTC" "1982-06-26 02:05:49 UTC"
#> [273] "1982-06-26 19:25:00 UTC" "1982-06-27 10:20:21 UTC"
#> [275] "1982-07-03 17:40:28 UTC" "1982-07-07 04:07:51 UTC"
#> [277] "1982-07-07 04:14:43 UTC" "1982-07-08 02:22:07 UTC"
#> [279] "1982-07-08 04:11:49 UTC" "1982-07-08 07:25:06 UTC"
#> [281] "1982-07-08 07:28:35 UTC" "1982-07-08 14:09:04 UTC"
#> [283] "1982-07-08 15:37:21 UTC" "1982-07-08 20:30:13 UTC"
#> [285] "1982-07-09 00:15:44 UTC" "1982-07-09 05:55:56 UTC"
#> [287] "1982-07-09 07:13:06 UTC" "1982-07-09 07:24:58 UTC"
#> [289] "1982-07-09 10:45:32 UTC" "1982-07-09 15:28:36 UTC"
#> [291] "1982-07-09 16:17:53 UTC" "1982-07-09 20:13:22 UTC"
#> [293] "1982-07-09 21:05:38 UTC" "1982-07-09 22:39:10 UTC"
#> [295] "1982-07-09 23:03:01 UTC" "1982-07-10 00:35:56 UTC"
#> [297] "1982-07-10 01:35:22 UTC" "1982-07-10 01:58:04 UTC"
#> [299] "1982-07-10 03:15:50 UTC" "1982-07-10 04:07:46 UTC"
#> [301] "1982-07-10 07:05:40 UTC" "1982-07-10 08:25:26 UTC"
#> [303] "1982-07-10 10:06:16 UTC" "1982-07-10 11:58:38 UTC"
#> [305] "1982-07-10 15:09:24 UTC" "1982-07-10 16:41:32 UTC"
#> [307] "1982-07-10 20:01:47 UTC" "1982-07-10 20:49:13 UTC"
#> [309] "1982-07-10 21:06:32 UTC" "1982-07-10 21:35:27 UTC"
#> [311] "1982-07-11 02:05:40 UTC" "1982-07-11 03:27:58 UTC"
#> [313] "1982-07-11 03:37:38 UTC" "1982-07-11 04:43:31 UTC"
#> [315] "1982-07-11 06:14:58 UTC" "1982-07-11 06:36:35 UTC"
#> [317] "1982-07-11 07:00:21 UTC" "1982-07-11 08:10:48 UTC"
#> [319] "1982-07-11 11:28:48 UTC" "1982-07-11 14:01:29 UTC"
#> [321] "1982-07-11 18:48:46 UTC" "1982-07-11 22:11:07 UTC"
#> [323] "1982-07-11 23:31:31 UTC" "1982-07-12 03:10:05 UTC"
#> [325] "1982-07-12 06:07:06 UTC" "1982-07-12 09:32:36 UTC"
#> [327] "1982-07-12 15:30:56 UTC" "1982-07-12 20:39:52 UTC"
#> [329] "1982-07-14 10:41:45 UTC" "1982-07-14 14:53:12 UTC"
#> [331] "1982-07-14 20:08:37 UTC" "1982-07-14 21:33:32 UTC"
#> [333] "1982-07-15 02:18:09 UTC" "1982-07-15 03:33:03 UTC"
#> [335] "1982-07-15 15:25:44 UTC" "1982-07-16 00:22:38 UTC"
#> [337] "1982-07-16 03:20:46 UTC" "1982-07-16 15:20:27 UTC"
#> [339] "1982-07-16 22:20:06 UTC" "1982-07-16 23:52:47 UTC"
#> [341] "1982-07-17 02:02:13 UTC" "1982-07-17 10:04:19 UTC"
#> [343] "1982-07-17 20:30:01 UTC" "1982-07-17 22:04:06 UTC"
#> [345] "1982-07-18 13:00:09 UTC" "1982-07-18 22:24:15 UTC"
#> [347] "1982-07-19 00:18:37 UTC" "1982-07-19 00:57:02 UTC"
#> [349] "1982-07-19 04:16:02 UTC" "1982-07-19 12:48:03 UTC"
#> [351] "1982-07-19 12:50:32 UTC" "1982-07-19 14:24:34 UTC"
#> [353] "1982-07-19 16:08:57 UTC" "1982-07-19 18:41:26 UTC"
#> [355] "1982-07-19 20:13:52 UTC" "1982-07-20 02:33:46 UTC"
#> [357] "1982-07-20 04:11:27 UTC" "1982-07-20 21:52:59 UTC"
#> [359] "1982-07-20 23:06:13 UTC" "1982-07-21 01:14:18 UTC"
#> [361] "1982-07-21 16:41:14 UTC" "1982-07-21 18:12:52 UTC"
#> [363] "1982-07-21 18:40:24 UTC" "1982-07-22 05:11:29 UTC"
#> [365] "1982-07-22 16:39:55 UTC" "1982-08-03 13:00:58 UTC"
#> [367] "1982-08-04 23:40:45 UTC" "1982-08-05 03:42:18 UTC"
#> [369] "1982-08-05 11:38:44 UTC" "1982-08-05 15:59:49 UTC"
#> [371] "1982-08-06 11:20:03 UTC" "1982-08-06 23:25:07 UTC"
#> [373] "1982-08-07 21:40:59 UTC" "1982-08-08 02:01:48 UTC"
#> [375] "1982-08-08 02:46:21 UTC" "1982-08-09 02:04:29 UTC"
#> [377] "1982-08-09 06:46:50 UTC" "1982-08-10 05:25:09 UTC"
#> [379] "1982-08-10 13:16:12 UTC" "1982-08-11 11:38:09 UTC"
#> [381] "1982-08-13 13:42:36 UTC" "1982-08-13 22:55:37 UTC"
#> [383] "1982-08-14 02:40:35 UTC" "1982-08-14 05:09:38 UTC"
#> [385] "1982-08-16 02:03:15 UTC" "1982-08-19 04:11:15 UTC"
#> [387] "1982-08-26 22:56:30 UTC" "1982-08-27 03:23:51 UTC"
#> [389] "1982-08-27 05:46:31 UTC" "1982-08-28 22:58:13 UTC"
#> [391] "1982-08-31 05:53:18 UTC" "1982-08-31 17:21:15 UTC"
#> [393] "1982-09-01 08:45:58 UTC" "1982-09-01 16:19:51 UTC"
#> [395] "1982-09-10 08:26:21 UTC" "1982-09-18 16:39:24 UTC"
#> [397] "1982-09-28 23:30:53 UTC" "1982-09-29 15:18:12 UTC"
#> [399] "1982-10-04 07:50:10 UTC" "1982-10-06 23:01:36 UTC"
#> [401] "1982-10-14 00:14:36 UTC" "1982-10-14 01:52:30 UTC"
#> [403] "1982-10-15 20:35:50 UTC" "1982-10-19 11:33:26 UTC"
#> [405] "1982-10-24 15:03:46 UTC" "1982-10-24 15:08:19 UTC"
#> [407] "1982-10-25 22:49:32 UTC" "1982-10-26 00:25:20 UTC"
#> [409] "1982-10-27 03:03:24 UTC" "1982-10-27 04:09:01 UTC"
#> [411] "1982-10-27 04:27:46 UTC" "1982-10-27 20:17:26 UTC"
#> [413] "1982-11-03 00:48:46 UTC" "1982-11-04 03:29:59 UTC"
#> [415] "1982-11-12 14:17:46 UTC" "1982-11-15 16:14:22 UTC"
#> [417] "1982-11-17 13:57:56 UTC" "1982-11-19 05:28:42 UTC"
#> [419] "1982-11-20 10:10:06 UTC" "1982-11-21 10:19:42 UTC"
#> [421] "1982-11-21 14:16:11 UTC" "1982-11-22 12:22:12 UTC"
#> [423] "1982-11-22 14:44:06 UTC" "1982-11-22 17:02:00 UTC"
#> [425] "1982-11-22 17:59:45 UTC" "1982-11-22 23:29:11 UTC"
#> [427] "1982-11-23 03:17:21 UTC" "1982-11-23 04:27:33 UTC"
#> [429] "1982-11-23 08:05:50 UTC" "1982-11-23 09:20:27 UTC"
#> [431] "1982-11-23 11:11:08 UTC" "1982-11-23 11:17:58 UTC"
#> [433] "1982-11-23 13:44:56 UTC" "1982-11-23 14:31:28 UTC"
#> [435] "1982-11-23 16:52:27 UTC" "1982-11-24 19:39:18 UTC"
#> [437] "1982-11-25 04:13:28 UTC" "1982-11-25 13:03:45 UTC"
#> [439] "1982-11-25 17:47:36 UTC" "1982-11-26 02:17:52 UTC"
#> [441] "1982-11-26 05:15:47 UTC" "1982-11-26 15:06:06 UTC"
#> [443] "1982-11-26 16:10:21 UTC" "1982-11-29 21:36:57 UTC"
#> [445] "1982-11-30 00:44:56 UTC" "1982-11-30 04:11:22 UTC"
#> [447] "1982-12-02 00:03:20 UTC" "1982-12-02 21:08:57 UTC"
#> [449] "1982-12-03 01:11:22 UTC" "1982-12-04 09:12:17 UTC"
#> [451] "1982-12-04 09:25:45 UTC" "1982-12-05 22:45:02 UTC"
#> [453] "1982-12-06 00:20:29 UTC" "1982-12-06 21:05:00 UTC"
#> [455] "1982-12-06 23:59:22 UTC" "1982-12-07 02:18:55 UTC"
#> [457] "1982-12-07 17:46:58 UTC" "1982-12-07 18:06:24 UTC"
#> [459] "1982-12-07 23:35:30 UTC" "1982-12-08 03:01:14 UTC"
#> [461] "1982-12-08 11:10:11 UTC" "1982-12-08 13:48:20 UTC"
#> [463] "1982-12-09 09:35:21 UTC" "1982-12-09 17:33:30 UTC"
#> [465] "1982-12-09 18:59:39 UTC" "1982-12-09 21:42:33 UTC"
#> [467] "1982-12-10 01:15:26 UTC" "1982-12-10 02:36:12 UTC"
#> [469] "1982-12-10 03:56:03 UTC" "1982-12-10 18:15:40 UTC"
#> [471] "1982-12-11 05:43:48 UTC" "1982-12-13 03:20:52 UTC"
#> [473] "1982-12-13 08:02:43 UTC" "1982-12-15 10:55:08 UTC"
#> [475] "1982-12-15 16:26:19 UTC" "1982-12-15 21:43:50 UTC"
#> [477] "1982-12-16 14:51:59 UTC" "1982-12-16 19:23:49 UTC"
#> [479] "1982-12-17 00:02:59 UTC" "1982-12-17 01:44:24 UTC"
#> [481] "1982-12-17 05:19:06 UTC" "1982-12-17 10:00:26 UTC"
#> [483] "1982-12-17 18:54:40 UTC" "1982-12-17 21:03:52 UTC"
#> [485] "1982-12-18 03:50:13 UTC" "1982-12-18 08:17:31 UTC"
#> [487] "1982-12-19 01:33:23 UTC" "1982-12-19 01:42:51 UTC"
#> [489] "1982-12-19 09:48:17 UTC" "1982-12-19 15:49:28 UTC"
#> [491] "1982-12-19 20:18:56 UTC" "1982-12-21 02:11:35 UTC"
#> [493] "1982-12-26 10:39:42 UTC" "1982-12-26 15:06:08 UTC"
#> [495] "1982-12-27 05:23:44 UTC" "1982-12-27 11:36:45 UTC"
#> [497] "1982-12-28 15:56:52 UTC" "1982-12-29 06:43:00 UTC"
#> [499] "1982-12-30 01:41:15 UTC" "1982-12-30 18:42:51 UTC"
interarrival(ctre_mod)
#>   [1]  1754.700000  1082.150000  6925.816667   383.666667   745.683333
#>   [6]  3538.583333 18746.983333  1063.750000  5017.000000  1199.333333
#>  [11]  1292.500000   679.666667  1141.166667   369.583333   675.000000
#>  [16]   828.166667  1528.916667   184.250000   380.516667   121.983333
#>  [21]   601.083333   336.333333    89.083333    20.666667  1019.500000
#>  [26]   117.833333   197.166667   373.500000   117.250000   356.916667
#>  [31]   169.250000   992.000000   478.833333    67.416667   189.083333
#>  [36]    97.083333    90.833333   888.583333    59.916667   561.083333
#>  [41]   287.000000    56.416667   246.666667    24.833333    51.250000
#>  [46]   285.916667   510.750000   259.250000   115.500000    64.750000
#>  [51]   150.250000   135.083333   101.333333   184.166667   776.750000
#>  [56]   396.333333   539.583333   212.500000   833.583333    94.916667
#>  [61]   288.083333   118.166667   200.333333   357.416667   941.583333
#>  [66]    24.500000  1531.333333   257.166667    24.166667  1143.416667
#>  [71]  2628.583333   896.500000   587.416667   228.666667   228.750000
#>  [76]    83.250000   258.983333   239.500000   629.433333   319.833333
#>  [81]   525.066667  1182.766667   484.133333  3468.983333  1556.383333
#>  [86]  2442.333333  1045.416667   138.666667  3420.400000  1008.233333
#>  [91]   184.600000   131.200000  1484.466667  2216.266667   740.766667
#>  [96]   239.433333  2645.533333    79.266667   586.000000  1805.300000
#> [101] 10439.200000  2188.283333  1326.216667    84.300000   880.616667
#> [106]  3068.750000  1331.183333   628.600000   772.033333   118.750000
#> [111]   343.416667   959.183333   117.350000   819.400000  1992.666667
#> [116]  1946.833333    64.250000   760.416667    31.583333    84.316667
#> [121]  1631.016667   634.416667   581.416667   193.000000   343.366667
#> [126]   400.800000   373.833333   178.833333   142.083333   828.783333
#> [131]  1527.716667   551.750000  1645.983333 10984.183333  1998.150000
#> [136]   197.100000  5649.283333   424.716667  3658.483333   471.116667
#> [141]  3993.566667 20414.966667  6382.233333  9837.950000  5838.650000
#> [146]  1565.700000   958.816667  7046.166667  1693.333333    33.866667
#> [151]    53.800000   720.083333  1034.100000  3706.433333   365.166667
#> [156]   266.883333   308.100000   190.366667   587.600000   163.383333
#> [161]   167.533333   212.533333    94.316667    27.900000   278.033333
#> [166]     5.950000    70.700000    18.516667   265.266667   372.166667
#> [171]    81.233333    20.933333   186.916667   299.966667   245.933333
#> [176]    30.083333     2.733333    88.416667   163.816667    39.800000
#> [181]   154.000000   227.350000   674.066667   139.266667    95.150000
#> [186]   224.516667   938.883333  1356.400000   466.633333   934.350000
#> [191]   645.983333    11.700000     9.850000   211.733333  1705.033333
#> [196]   269.733333   739.633333   141.366667    38.266667    17.183333
#> [201]   180.383333   324.650000   239.933333    25.516667   120.383333
#> [206]    41.733333    28.600000    89.250000   844.450000   400.450000
#> [211]    74.783333    86.483333    21.700000    86.066667   100.566667
#> [216]    76.633333   191.733333    44.183333   291.733333   232.200000
#> [221]    92.633333    53.000000    55.700000    37.800000    68.766667
#> [226]   375.466667   107.600000   352.500000   127.433333   290.600000
#> [231]   349.033333   300.850000     9.300000  1100.516667   187.550000
#> [236]   189.900000   482.866667   138.983333   327.916667   111.800000
#> [241]   798.583333    76.300000   249.866667   384.933333   189.900000
#> [246]   423.000000   193.383333   373.800000   151.350000   324.783333
#> [251]    46.450000   120.183333   480.116667   634.200000  1056.366667
#> [256]   395.800000   403.800000   531.633333   583.750000   389.483333
#> [261]   208.700000   533.266667     6.050000   266.333333   281.550000
#> [266]    33.500000  1801.583333   537.783333   107.666667   191.816667
#> [271]    82.866667  1039.183333   895.350000  9080.116667  4947.383333
#> [276]     6.866667  1327.400000   109.700000   193.283333     3.483333
#> [281]   400.483333    88.283333   292.866667   225.516667   340.200000
#> [286]    77.166667    11.866667   200.566667   283.066667    49.283333
#> [291]   235.483333    52.266667    93.533333    23.850000    92.916667
#> [296]    59.433333    22.700000    77.766667    51.933333   177.900000
#> [301]    79.766667   100.833333   112.366667   190.766667    92.133333
#> [306]   200.250000    47.433333    17.316667    28.916667   270.216667
#> [311]    82.300000     9.666667    65.883333    91.450000    21.616667
#> [316]    23.766667    70.450000   198.000000   152.683333   287.283333
#> [321]   202.350000    80.400000   218.566667   177.016667   205.500000
#> [326]   358.333333   308.933333  2281.883333   251.450000   315.416667
#> [331]    84.916667   284.616667    74.900000   712.683333   536.900000
#> [336]   178.133333   719.683333   419.650000    92.683333   129.433333
#> [341]   482.100000   625.700000    94.083333   896.050000   564.100000
#> [346]   114.366667    38.416667   199.000000   512.016667     2.483333
#> [351]    94.033333   104.383333   152.483333    92.433333   379.900000
#> [356]    97.683333  1061.533333    73.233333   128.083333   926.933333
#> [361]    91.633333    27.533333   631.083333   688.433333 17061.050000
#> [366]  2079.783333   241.550000   476.433333   261.083333  1160.233333
#> [371]   725.066667  1335.866667   260.816667    44.550000  1398.133333
#> [376]   282.350000  1358.316667   471.050000  1341.950000  3004.450000
#> [381]   553.016667   224.966667   149.050000  2693.616667  4448.000000
#> [386] 11205.250000   267.350000   142.666667  2471.700000  3295.083333
#> [391]   687.950000   924.716667   453.883333 12486.500000 12013.050000
#> [396] 14811.483333   947.316667  6751.966667  3791.433333 10153.000000
#> [401]    97.900000  2563.333333  5217.600000  7410.333333     4.550000
#> [406]  1901.216667    95.800000  1598.066667    65.616667    18.750000
#> [411]   949.666667  8911.333333  1601.216667 12167.783333  4436.600000
#> [416]  2743.566667  2370.766667  1721.400000  1449.600000   236.483333
#> [421]  1326.016667   141.900000   137.900000    57.750000   329.433333
#> [426]   228.166667    70.200000   218.283333    74.616667   110.683333
#> [431]     6.833333   146.966667    46.533333   140.983333  1606.850000
#> [436]   514.166667   530.283333   283.850000   510.266667   177.916667
#> [441]   590.316667    64.250000  4646.600000   187.983333   206.433333
#> [446]  2631.966667  1265.616667   242.416667  1920.916667    13.466667
#> [451]  2239.283333    95.450000  1244.516667   174.366667   139.550000
#> [456]   928.050000    19.433333   329.100000   205.733333   488.950000
#> [461]   158.150000  1187.016667   478.150000    86.150000   162.900000
#> [466]   212.883333    80.766667    79.850000   859.616667   688.133333
#> [471]  2737.066667   281.850000  3052.416667   331.183333   317.516667
#> [476]  1028.150000   271.833333   279.166667   101.416667   214.700000
#> [481]   281.333333   534.233333   129.200000   406.350000   267.300000
#> [486]  1035.866667     9.466667   485.433333   361.183333   269.466667
#> [491]  1792.650000  7708.116667   266.433333   857.600000   373.016667
#> [496]  1700.116667   886.133333  1138.250000  1021.600000
MLestimates(ctre_mod, tail = 0.8, scale = 3E7)
#> Computing Mittag-Leffler estimates for all thresholds.
library(magrittr)
ctre_mod %>% interarrival() %>% mlqqplot(tail = 0.8, log = 'xy')
acf(ctre_mod)
empcopula(ctre_mod)