GitHub

Declustering threshold exceedances

When the data are dependent, the exceedances may have a tendency to cluster. It is common to assume that the marginal distribution of each exceedance is the Generalized Pareto (see for example Chapter 5 of Coles , 2001). Various methods have been proposed for dealing with the problem of dependent exceedances. The most widely-adopted one consists in declustering the exceedances, which corresponds to a filtering of the exceedances to obtain a set of that are approximately independent. As summarized by Coles (2001), the declustering approach consists in:

  • identifying cluster of extreme values;
  • retrieving the cluster maxima;
  • assuming that each cluster maxima are independent;
  • fitting the GP distribution to the cluster maxima.

In Extremes.jl, two methods for identifying cluster of extreme values are implemented in the getcluster function: the runs method and the two thresholds method. The function returns a vector of Cluster type.

Data loading

Both methods for identifying the clusters are illustrated with the Wooster dataset studied by Coles (2001). This dataset consists in the daily temperature minimum recorded in Wooster, Ohio, from 1983 to 1988. The attention is restricted to the winter months (November to February) and to the negated series for using the model defined for maxima.

data = Extremes.dataset("wooster")
plot(data, x=:Date, y=:Temperature, Geom.point)
Date Jan 1, 1983 1984 1985 1986 1987 1988 Jan 1, 1983 Apr Jul Oct Jan 1984 Apr Jul Oct Jan 1985 Apr Jul Oct Jan 1986 Apr Jul Oct Jan 1987 Apr Jul Oct Jan 1988 Dec 24, 1983 31 Jan 7, 1984 14 21 28 Feb 4 11 18 25 Mar 3 10 17 24 31 Apr 7 14 21 28 May 5 12 19 26 Jun 2 9 16 23 30 Jul 7 14 21 28 Aug 4 11 18 25 Sep 1 8 15 22 29 Oct 6 13 20 27 Nov 3 10 17 24 Dec 1 8 15 22 29 Jan 5, 1985 12 19 26 Feb 2 9 16 23 Mar 2 9 16 23 30 Apr 6 13 20 27 May 4 11 18 25 Jun 1 8 15 22 29 Jul 6 13 20 27 Aug 3 10 17 24 31 Sep 7 14 21 28 Oct 5 12 19 26 Nov 2 9 16 23 30 Dec 7 14 21 28 Jan 4, 1986 11 18 25 Feb 1 8 15 22 Mar 1 8 15 22 29 Apr 5 12 19 26 May 3 10 17 24 31 Jun 7 14 21 28 Jul 5 12 19 26 Aug 2 9 16 23 30 Sep 6 13 20 27 Oct 4 11 18 25 Nov 1 8 15 22 29 Dec 6 13 20 27 Jan 3, 1987 10 17 24 31 Feb 7 14 21 28 Mar 7 14 21 28 Apr 4 11 18 25 May 2 9 16 23 30 Jun 6 13 20 27 Jul 4 11 18 25 Aug 1 8 15 22 29 Sep 5 12 19 26 Oct 3 10 17 24 31 Nov 7 14 21 28 Dec 5 12 19 26 Jan 2, 1988 Jan 1, 1983 1986 1989 1987-12-3126 1987-12-3012 1987-12-2918 1987-12-2831 1987-12-2725 1987-12-2626 1987-12-2535 1987-12-2429 1987-12-2332 1987-12-2221 1987-12-2128 1987-12-2036 1987-12-1930 1987-12-1826 1987-12-1726 1987-12-1627 1987-12-1530 1987-12-1428 1987-12-1331 1987-12-1232 1987-12-1129 1987-12-1032 1987-12-0943 1987-12-0834 1987-12-0726 1987-12-0621 1987-12-0527 1987-12-0427 1987-12-0329 1987-12-0228 1987-12-0130 1987-11-3036 1987-11-2939 1987-11-2841 1987-11-2735 1987-11-2638 1987-11-2542 1987-11-2439 1987-11-2324 1987-11-2213 1987-11-2116 1987-11-2022 1987-11-1930 1987-11-1838 1987-11-1753 1987-11-1639 1987-11-1529 1987-11-1437 1987-11-1334 1987-11-1225 1987-11-1125 1987-11-1028 1987-11-0936 1987-11-0845 1987-11-0739 1987-11-0629 1987-11-0531 1987-11-0456 1987-11-0355 1987-11-0249 1987-11-0145 1987-10-3140 1987-10-3032 1987-10-2938 1987-10-2830 1987-10-2736 1987-10-2625 1987-10-2530 1987-10-2435 1987-10-2340 1987-10-2230 1987-10-2132 1987-10-2040 1987-10-1932 1987-10-1839 1987-10-1746 1987-10-1635 1987-10-1532 1987-10-1426 1987-10-1328 1987-10-1231 1987-10-1132 1987-10-1042 1987-10-0931 1987-10-0835 1987-10-0742 1987-10-0644 1987-10-0540 1987-10-0430 1987-10-0336 1987-10-0246 1987-10-0141 1987-09-3043 1987-09-2957 1987-09-2849 1987-09-2743 1987-09-2633 1987-09-2540 1987-09-2447 1987-09-2348 1987-09-2249 1987-09-2151 1987-09-2050 1987-09-1957 1987-09-1864 1987-09-1766 1987-09-1663 1987-09-1551 1987-09-1453 1987-09-1360 1987-09-1262 1987-09-1162 1987-09-1054 1987-09-0958 1987-09-0862 1987-09-0760 1987-09-0662 1987-09-0559 1987-09-0443 1987-09-0343 1987-09-0247 1987-09-0147 1987-08-3153 1987-08-3048 1987-08-2955 1987-08-2861 1987-08-2753 1987-08-2655 1987-08-2548 1987-08-2450 1987-08-2355 1987-08-2265 1987-08-2156 1987-08-2055 1987-08-1959 1987-08-1855 1987-08-1767 1987-08-1663 1987-08-1560 1987-08-1465 1987-08-1365 1987-08-1259 1987-08-1156 1987-08-1058 1987-08-0970 1987-08-0863 1987-08-0756 1987-08-0658 1987-08-0562 1987-08-0465 1987-08-0369 1987-08-0269 1987-08-0168 1987-07-3166 1987-07-3063 1987-07-2959 1987-07-2853 1987-07-2757 1987-07-2671 1987-07-2572 1987-07-2463 1987-07-2369 1987-07-2269 1987-07-2170 1987-07-2070 1987-07-1963 1987-07-1857 1987-07-1754 1987-07-1657 1987-07-1553 1987-07-1458 1987-07-1371 1987-07-1267 1987-07-1168 1987-07-1070 1987-07-0972 1987-07-0871 1987-07-0769 1987-07-0667 1987-07-0556 1987-07-0461 1987-07-0365 1987-07-0264 1987-07-0164 1987-06-3064 1987-06-2958 1987-06-2851 1987-06-2753 1987-06-2661 1987-06-2561 1987-06-2458 1987-06-2361 1987-06-2268 1987-06-2170 1987-06-2070 1987-06-1965 1987-06-1854 1987-06-1757 1987-06-1657 1987-06-1561 1987-06-1461 1987-06-1366 1987-06-1251 1987-06-1145 1987-06-1041 1987-06-0946 1987-06-0866 1987-06-0761 1987-06-0654 1987-06-0547 1987-06-0453 1987-06-0366 1987-06-0265 1987-06-0166 1987-05-3163 1987-05-3066 1987-05-2965 1987-05-2863 1987-05-2765 1987-05-2662 1987-05-2548 1987-05-2449 1987-05-2357 1987-05-2265 1987-05-2158 1987-05-2061 1987-05-1962 1987-05-1858 1987-05-1747 1987-05-1636 1987-05-1543 1987-05-1455 1987-05-1337 1987-05-1243 1987-05-1157 1987-05-1059 1987-05-0939 1987-05-0837 1987-05-0740 1987-05-0633 1987-05-0533 1987-05-0438 1987-05-0345 1987-05-0245 1987-05-0134 1987-04-3034 1987-04-2939 1987-04-2838 1987-04-2738 1987-04-2640 1987-04-2537 1987-04-2441 1987-04-2351 1987-04-2248 1987-04-2151 1987-04-2048 1987-04-1943 1987-04-1841 1987-04-1748 1987-04-1647 1987-04-1550 1987-04-1449 1987-04-1345 1987-04-1246 1987-04-1144 1987-04-1034 1987-04-0928 1987-04-0831 1987-04-0739 1987-04-0637 1987-04-0533 1987-04-0428 1987-04-0327 1987-04-0230 1987-04-0121 1987-03-3122 1987-03-3029 1987-03-2937 1987-03-2840 1987-03-2734 1987-03-2640 1987-03-2540 1987-03-2436 1987-03-2334 1987-03-2227 1987-03-2128 1987-03-2026 1987-03-1933 1987-03-1825 1987-03-1719 1987-03-1623 1987-03-1529 1987-03-1427 1987-03-1321 1987-03-1225 1987-03-1116 1987-03-1014 1987-03-0919 1987-03-0835 1987-03-0740 1987-03-0628 1987-03-0525 1987-03-0420 1987-03-0327 1987-03-0236 1987-03-0136 1987-02-2835 1987-02-2732 1987-02-2625 1987-02-2520 1987-02-2426 1987-02-2331 1987-02-2232 1987-02-2120 1987-02-2014 1987-02-1912 1987-02-1821 1987-02-178 1987-02-167 1987-02-158 1987-02-1420 1987-02-1321 1987-02-1231 1987-02-1118 1987-02-1016 1987-02-0915 1987-02-0816 1987-02-0729 1987-02-0620 1987-02-0516 1987-02-0424 1987-02-0332 1987-02-0235 1987-02-0125 1987-01-3125 1987-01-3026 1987-01-2924 1987-01-2813 1987-01-270 1987-01-267 1987-01-251 1987-01-24-3 1987-01-23-1 1987-01-2223 1987-01-2115 1987-01-2023 1987-01-1924 1987-01-1828 1987-01-1719 1987-01-1622 1987-01-1531 1987-01-1435 1987-01-1325 1987-01-1227 1987-01-1128 1987-01-1028 1987-01-0925 1987-01-0827 1987-01-0732 1987-01-0613 1987-01-0513 1987-01-0417 1987-01-0323 1987-01-0230 1987-01-0126 1986-12-3130 1986-12-3026 1986-12-2921 1986-12-2825 1986-12-2728 1986-12-2629 1986-12-2531 1986-12-2426 1986-12-2319 1986-12-2217 1986-12-2123 1986-12-2027 1986-12-1928 1986-12-1830 1986-12-1732 1986-12-1625 1986-12-1527 1986-12-1415 1986-12-1315 1986-12-1219 1986-12-1117 1986-12-1017 1986-12-0939 1986-12-0837 1986-12-0731 1986-12-0622 1986-12-0523 1986-12-0424 1986-12-0333 1986-12-0232 1986-12-0130 1986-11-3033 1986-11-2936 1986-11-2831 1986-11-2731 1986-11-2628 1986-11-2522 1986-11-2427 1986-11-2330 1986-11-2231 1986-11-2133 1986-11-2030 1986-11-1927 1986-11-1832 1986-11-1734 1986-11-1634 1986-11-1515 1986-11-1411 1986-11-1316 1986-11-1228 1986-11-1133 1986-11-1026 1986-11-0943 1986-11-0849 1986-11-0740 1986-11-0642 1986-11-0537 1986-11-0439 1986-11-0324 1986-11-0244 1986-11-0149 1986-10-3133 1986-10-3035 1986-10-2947 1986-10-2848 1986-10-2750 1986-10-2650 1986-10-2550 1986-10-2452 1986-10-2352 1986-10-2239 1986-10-2136 1986-10-2028 1986-10-1927 1986-10-1831 1986-10-1740 1986-10-1634 1986-10-1537 1986-10-1437 1986-10-1359 1986-10-1251 1986-10-1136 1986-10-1032 1986-10-0942 1986-10-0842 1986-10-0732 1986-10-0639 1986-10-0551 1986-10-0461 1986-10-0364 1986-10-0264 1986-10-0163 1986-09-3068 1986-09-2969 1986-09-2866 1986-09-2763 1986-09-2665 1986-09-2567 1986-09-2466 1986-09-2367 1986-09-2255 1986-09-2158 1986-09-2065 1986-09-1962 1986-09-1852 1986-09-1736 1986-09-1641 1986-09-1552 1986-09-1451 1986-09-1345 1986-09-1264 1986-09-1165 1986-09-1049 1986-09-0936 1986-09-0835 1986-09-0742 1986-09-0648 1986-09-0555 1986-09-0466 1986-09-0356 1986-09-0253 1986-09-0148 1986-08-3143 1986-08-3041 1986-08-2940 1986-08-2844 1986-08-2751 1986-08-2667 1986-08-2545 1986-08-2451 1986-08-2364 1986-08-2260 1986-08-2162 1986-08-2062 1986-08-1957 1986-08-1863 1986-08-1764 1986-08-1667 1986-08-1567 1986-08-1461 1986-08-1349 1986-08-1243 1986-08-1149 1986-08-1064 1986-08-0962 1986-08-0864 1986-08-0764 1986-08-0658 1986-08-0553 1986-08-0452 1986-08-0359 1986-08-0261 1986-08-0162 1986-07-3156 1986-07-3059 1986-07-2964 1986-07-2860 1986-07-2761 1986-07-2665 1986-07-2564 1986-07-2459 1986-07-2356 1986-07-2258 1986-07-2163 1986-07-2069 1986-07-1974 1986-07-1874 1986-07-1771 1986-07-1667 1986-07-1557 1986-07-1460 1986-07-1371 1986-07-1269 1986-07-1165 1986-07-1055 1986-07-0961 1986-07-0866 1986-07-0768 1986-07-0664 1986-07-0563 1986-07-0449 1986-07-0354 1986-07-0262 1986-07-0156 1986-06-3056 1986-06-2964 1986-06-2867 1986-06-2763 1986-06-2648 1986-06-2545 1986-06-2454 1986-06-2365 1986-06-2259 1986-06-2153 1986-06-2057 1986-06-1953 1986-06-1844 1986-06-1751 1986-06-1662 1986-06-1559 1986-06-1461 1986-06-1359 1986-06-1262 1986-06-1172 1986-06-1050 1986-06-0954 1986-06-0861 1986-06-0767 1986-06-0668 1986-06-0568 1986-06-0449 1986-06-0337 1986-06-0241 1986-06-0156 1986-05-3161 1986-05-3062 1986-05-2954 1986-05-2860 1986-05-2760 1986-05-2652 1986-05-2549 1986-05-2449 1986-05-2347 1986-05-2247 1986-05-2146 1986-05-2047 1986-05-1955 1986-05-1866 1986-05-1757 1986-05-1664 1986-05-1562 1986-05-1457 1986-05-1355 1986-05-1243 1986-05-1143 1986-05-1044 1986-05-0946 1986-05-0846 1986-05-0747 1986-05-0661 1986-05-0551 1986-05-0429 1986-05-0330 1986-05-0238 1986-05-0152 1986-04-3044 1986-04-2948 1986-04-2855 1986-04-2751 1986-04-2651 1986-04-2544 1986-04-2427 1986-04-2322 1986-04-2226 1986-04-2134 1986-04-2053 1986-04-1939 1986-04-1833 1986-04-1738 1986-04-1629 1986-04-1534 1986-04-1431 1986-04-1335 1986-04-1227 1986-04-1132 1986-04-1032 1986-04-0934 1986-04-0840 1986-04-0746 1986-04-0650 1986-04-0550 1986-04-0453 1986-04-0336 1986-04-0236 1986-04-0147 1986-03-3141 1986-03-3055 1986-03-2949 1986-03-2826 1986-03-2729 1986-03-2644 1986-03-2535 1986-03-2428 1986-03-2334 1986-03-2219 1986-03-2110 1986-03-2012 1986-03-1932 1986-03-1830 1986-03-1732 1986-03-1634 1986-03-1538 1986-03-1446 1986-03-1330 1986-03-1231 1986-03-1134 1986-03-1047 1986-03-0927 1986-03-08-1 1986-03-074 1986-03-0622 1986-03-0528 1986-03-0428 1986-03-0330 1986-03-0223 1986-03-0110 1986-02-286 1986-02-279 1986-02-2618 1986-02-2517 1986-02-2417 1986-02-2326 1986-02-2221 1986-02-2122 1986-02-2031 1986-02-1933 1986-02-1842 1986-02-1732 1986-02-1618 1986-02-1516 1986-02-1415 1986-02-134 1986-02-128 1986-02-1114 1986-02-1016 1986-02-0924 1986-02-0823 1986-02-0724 1986-02-0630 1986-02-0534 1986-02-0434 1986-02-0330 1986-02-0231 1986-02-0126 1986-01-3114 1986-01-3016 1986-01-2911 1986-01-281 1986-01-272 1986-01-2621 1986-01-2530 1986-01-2417 1986-01-2320 1986-01-2231 1986-01-2127 1986-01-2029 1986-01-1931 1986-01-1841 1986-01-1741 1986-01-1613 1986-01-15-1 1986-01-1411 1986-01-138 1986-01-1230 1986-01-1121 1986-01-1027 1986-01-0914 1986-01-083 1986-01-077 1986-01-0613 1986-01-0522 1986-01-0428 1986-01-0328 1986-01-0229 1986-01-0116 1985-12-3118 1985-12-3012 1985-12-2916 1985-12-285 1985-12-2717 1985-12-26-2 1985-12-250 1985-12-2411 1985-12-2331 1985-12-226 1985-12-216 1985-12-202 1985-12-19-2 1985-12-181 1985-12-1712 1985-12-1618 1985-12-159 1985-12-148 1985-12-1318 1985-12-1232 1985-12-1138 1985-12-1031 1985-12-0930 1985-12-0827 1985-12-0731 1985-12-0631 1985-12-0530 1985-12-0424 1985-12-0317 1985-12-0217 1985-12-0141 1985-11-3037 1985-11-2936 1985-11-2833 1985-11-2735 1985-11-2633 1985-11-2530 1985-11-2429 1985-11-2331 1985-11-2232 1985-11-2123 1985-11-2029 1985-11-1959 1985-11-1839 1985-11-1740 1985-11-1641 1985-11-1541 1985-11-1443 1985-11-1350 1985-11-1242 1985-11-1142 1985-11-1044 1985-11-0943 1985-11-0832 1985-11-0734 1985-11-0640 1985-11-0545 1985-11-0446 1985-11-0349 1985-11-0251 1985-11-0150 1985-10-3142 1985-10-3042 1985-10-2930 1985-10-2832 1985-10-2735 1985-10-2630 1985-10-2534 1985-10-2455 1985-10-2344 1985-10-2250 1985-10-2146 1985-10-2046 1985-10-1955 1985-10-1846 1985-10-1730 1985-10-1636 1985-10-1549 1985-10-1451 1985-10-1353 1985-10-1245 1985-10-1145 1985-10-1051 1985-10-0953 1985-10-0849 1985-10-0730 1985-10-0637 1985-10-0543 1985-10-0439 1985-10-0336 1985-10-0232 1985-10-0141 1985-09-3044 1985-09-2939 1985-09-2838 1985-09-2744 1985-09-2647 1985-09-2535 1985-09-2442 1985-09-2355 1985-09-2251 1985-09-2150 1985-09-2053 1985-09-1953 1985-09-1849 1985-09-1742 1985-09-1638 1985-09-1538 1985-09-1438 1985-09-1339 1985-09-1244 1985-09-1146 1985-09-1063 1985-09-0967 1985-09-0870 1985-09-0771 1985-09-0670 1985-09-0569 1985-09-0469 1985-09-0361 1985-09-0261 1985-09-0147 1985-08-3153 1985-08-3060 1985-08-2959 1985-08-2855 1985-08-2758 1985-08-2662 1985-08-2564 1985-08-2456 1985-08-2352 1985-08-2248 1985-08-2152 1985-08-2057 1985-08-1957 1985-08-1862 1985-08-1757 1985-08-1664 1985-08-1567 1985-08-1467 1985-08-1366 1985-08-1250 1985-08-1159 1985-08-1058 1985-08-0954 1985-08-0862 1985-08-0768 1985-08-0663 1985-08-0559 1985-08-0455 1985-08-0350 1985-08-0250 1985-08-0158 1985-07-3162 1985-07-3061 1985-07-2956 1985-07-2852 1985-07-2751 1985-07-2657 1985-07-2567 1985-07-2448 1985-07-2349 1985-07-2258 1985-07-2166 1985-07-2069 1985-07-1957 1985-07-1853 1985-07-1750 1985-07-1656 1985-07-1568 1985-07-1469 1985-07-1361 1985-07-1261 1985-07-1157 1985-07-1061 1985-07-0967 1985-07-0867 1985-07-0757 1985-07-0661 1985-07-0562 1985-07-0451 1985-07-0358 1985-07-0262 1985-07-0162 1985-06-3054 1985-06-2950 1985-06-2849 1985-06-2749 1985-06-2649 1985-06-2545 1985-06-2455 1985-06-2355 1985-06-2263 1985-06-2150 1985-06-2052 1985-06-1949 1985-06-1855 1985-06-1752 1985-06-1657 1985-06-1552 1985-06-1446 1985-06-1345 1985-06-1247 1985-06-1149 1985-06-1053 1985-06-0961 1985-06-0857 1985-06-0749 1985-06-0647 1985-06-0548 1985-06-0447 1985-06-0352 1985-06-0257 1985-06-0155 1985-05-3164 1985-05-3049 1985-05-2945 1985-05-2851 1985-05-2761 1985-05-2658 1985-05-2544 1985-05-2445 1985-05-2348 1985-05-2237 1985-05-2143 1985-05-2057 1985-05-1937 1985-05-1836 1985-05-1743 1985-05-1655 1985-05-1562 1985-05-1451 1985-05-1357 1985-05-1264 1985-05-1153 1985-05-1046 1985-05-0933 1985-05-0840 1985-05-0747 1985-05-0654 1985-05-0549 1985-05-0435 1985-05-0341 1985-05-0248 1985-05-0149 1985-04-3037 1985-04-2935 1985-04-2843 1985-04-2744 1985-04-2647 1985-04-2553 1985-04-2455 1985-04-2357 1985-04-2254 1985-04-2151 1985-04-2052 1985-04-1962 1985-04-1838 1985-04-1731 1985-04-1638 1985-04-1550 1985-04-1451 1985-04-1343 1985-04-1235 1985-04-1139 1985-04-1019 1985-04-0916 1985-04-0827 1985-04-0730 1985-04-0637 1985-04-0545 1985-04-0433 1985-04-0332 1985-04-0230 1985-04-0130 1985-03-3138 1985-03-3037 1985-03-2947 1985-03-2855 1985-03-2745 1985-03-2620 1985-03-2526 1985-03-2435 1985-03-2337 1985-03-2231 1985-03-2119 1985-03-2025 1985-03-1921 1985-03-1820 1985-03-1722 1985-03-1622 1985-03-1526 1985-03-1434 1985-03-1328 1985-03-1234 1985-03-1142 1985-03-1031 1985-03-0931 1985-03-0838 1985-03-0725 1985-03-0620 1985-03-0523 1985-03-0435 1985-03-0322 1985-03-0227 1985-03-0133 1985-02-2824 1985-02-2726 1985-02-2629 1985-02-2530 1985-02-2438 1985-02-2342 1985-02-2242 1985-02-2121 1985-02-2013 1985-02-1918 1985-02-1820 1985-02-1724 1985-02-164 1985-02-156 1985-02-1414 1985-02-1315 1985-02-1231 1985-02-1124 1985-02-10-3 1985-02-09-1 1985-02-08-2 1985-02-075 1985-02-0613 1985-02-0513 1985-02-04-13 1985-02-03-5 1985-02-027 1985-02-0110 1985-01-3123 1985-01-307 1985-01-2910 1985-01-2820 1985-01-2711 1985-01-267 1985-01-2514 1985-01-2419 1985-01-2315 1985-01-229 1985-01-21-18 1985-01-20-19 1985-01-19-5 1985-01-1817 1985-01-1717 1985-01-16-1 1985-01-1511 1985-01-1418 1985-01-1312 1985-01-1211 1985-01-1116 1985-01-1016 1985-01-098 1985-01-0815 1985-01-0730 1985-01-0629 1985-01-0524 1985-01-0424 1985-01-0323 1985-01-0226 1985-01-0131 1984-12-3127 1984-12-3029 1984-12-2943 1984-12-2852 1984-12-2728 1984-12-2618 1984-12-2511 1984-12-2421 1984-12-2323 1984-12-2225 1984-12-2130 1984-12-2029 1984-12-1930 1984-12-1828 1984-12-1747 1984-12-1642 1984-12-1544 1984-12-1438 1984-12-1337 1984-12-1236 1984-12-1134 1984-12-1035 1984-12-0912 1984-12-0817 1984-12-076 1984-12-0618 1984-12-0514 1984-12-0418 1984-12-0325 1984-12-0227 1984-12-0131 1984-11-3033 1984-11-2931 1984-11-2833 1984-11-2739 1984-11-2630 1984-11-2525 1984-11-2424 1984-11-2328 1984-11-2227 1984-11-2127 1984-11-2018 1984-11-1926 1984-11-1832 1984-11-1722 1984-11-1627 1984-11-1540 1984-11-1421 1984-11-1325 1984-11-1225 1984-11-1130 1984-11-1048 1984-11-0945 1984-11-0830 1984-11-0725 1984-11-0632 1984-11-0540 1984-11-0442 1984-11-0325 1984-11-0227 1984-11-0146 1984-10-3147 1984-10-3042 1984-10-2944 1984-10-2859 1984-10-2760 1984-10-2660 1984-10-2535 1984-10-2439 1984-10-2345 1984-10-2248 1984-10-2152 1984-10-2038 1984-10-1954 1984-10-1841 1984-10-1748 1984-10-1659 1984-10-1553 1984-10-1449 1984-10-1350 1984-10-1250 1984-10-1150 1984-10-1051 1984-10-0953 1984-10-0856 1984-10-0755 1984-10-0643 1984-10-0541 1984-10-0438 1984-10-0345 1984-10-0237 1984-10-0140 1984-09-3041 1984-09-2933 1984-09-2837 1984-09-2741 1984-09-2642 1984-09-2562 1984-09-2464 1984-09-2365 1984-09-2253 1984-09-2151 1984-09-2058 1984-09-1944 1984-09-1840 1984-09-1736 1984-09-1638 1984-09-1546 1984-09-1457 1984-09-1356 1984-09-1254 1984-09-1159 1984-09-1060 1984-09-0956 1984-09-0857 1984-09-0744 1984-09-0639 1984-09-0545 1984-09-0450 1984-09-0358 1984-09-0258 1984-09-0153 1984-08-3149 1984-08-3063 1984-08-2963 1984-08-2864 1984-08-2753 1984-08-2651 1984-08-2547 1984-08-2454 1984-08-2360 1984-08-2256 1984-08-2145 1984-08-2052 1984-08-1958 1984-08-1859 1984-08-1762 1984-08-1658 1984-08-1557 1984-08-1462 1984-08-1365 1984-08-1265 1984-08-1167 1984-08-1065 1984-08-0968 1984-08-0866 1984-08-0769 1984-08-0668 1984-08-0566 1984-08-0466 1984-08-0367 1984-08-0269 1984-08-0163 1984-07-3156 1984-07-3053 1984-07-2952 1984-07-2854 1984-07-2755 1984-07-2660 1984-07-2557 1984-07-2466 1984-07-2361 1984-07-2259 1984-07-2162 1984-07-2053 1984-07-1950 1984-07-1856 1984-07-1753 1984-07-1661 1984-07-1566 1984-07-1463 1984-07-1364 1984-07-1258 1984-07-1162 1984-07-1065 1984-07-0958 1984-07-0845 1984-07-0749 1984-07-0662 1984-07-0564 1984-07-0465 1984-07-0358 1984-07-0255 1984-07-0159 1984-06-3057 1984-06-2962 1984-06-2853 1984-06-2761 1984-06-2647 1984-06-2553 1984-06-2465 1984-06-2368 1984-06-2254 1984-06-2158 1984-06-2061 1984-06-1966 1984-06-1869 1984-06-1766 1984-06-1654 1984-06-1548 1984-06-1457 1984-06-1367 1984-06-1249 1984-06-1157 1984-06-1067 1984-06-0967 1984-06-0870 1984-06-0770 1984-06-0663 1984-06-0552 1984-06-0450 1984-06-0357 1984-06-0247 1984-06-0146 1984-05-3142 1984-05-3040 1984-05-2944 1984-05-2852 1984-05-2745 1984-05-2652 1984-05-2555 1984-05-2445 1984-05-2355 1984-05-2266 1984-05-2155 1984-05-2056 1984-05-1959 1984-05-1850 1984-05-1732 1984-05-1630 1984-05-1537 1984-05-1441 1984-05-1339 1984-05-1251 1984-05-1154 1984-05-1037 1984-05-0937 1984-05-0839 1984-05-0752 1984-05-0640 1984-05-0542 1984-05-0443 1984-05-0341 1984-05-0234 1984-05-0138 1984-04-3050 1984-04-2944 1984-04-2850 1984-04-2754 1984-04-2643 1984-04-2542 1984-04-2439 1984-04-2338 1984-04-2238 1984-04-2135 1984-04-2032 1984-04-1934 1984-04-1833 1984-04-1733 1984-04-1643 1984-04-1543 1984-04-1443 1984-04-1344 1984-04-1232 1984-04-1127 1984-04-1033 1984-04-0939 1984-04-0824 1984-04-0730 1984-04-0634 1984-04-0536 1984-04-0445 1984-04-0330 1984-04-0228 1984-04-0130 1984-03-3132 1984-03-3028 1984-03-2928 1984-03-2833 1984-03-2729 1984-03-2628 1984-03-2534 1984-03-2423 1984-03-2327 1984-03-2230 1984-03-2132 1984-03-2035 1984-03-1928 1984-03-1828 1984-03-1724 1984-03-1626 1984-03-1525 1984-03-1427 1984-03-1324 1984-03-120 1984-03-117 1984-03-10-4 1984-03-09-6 1984-03-089 1984-03-0714 1984-03-0624 1984-03-0529 1984-03-04-2 1984-03-031 1984-03-028 1984-03-017 1984-02-2914 1984-02-2820 1984-02-2724 1984-02-2611 1984-02-2516 1984-02-2432 1984-02-2328 1984-02-2223 1984-02-2124 1984-02-2031 1984-02-1939 1984-02-1841 1984-02-1742 1984-02-1630 1984-02-1528 1984-02-1437 1984-02-1349 1984-02-1242 1984-02-1142 1984-02-1028 1984-02-0923 1984-02-0812 1984-02-0711 1984-02-0613 1984-02-0524 1984-02-0429 1984-02-0331 1984-02-0220 1984-02-011 1984-01-317 1984-01-3023 1984-01-2927 1984-01-2815 1984-01-2723 1984-01-2627 1984-01-2530 1984-01-2435 1984-01-237 1984-01-22-2 1984-01-21-16 1984-01-20-9 1984-01-19-3 1984-01-182 1984-01-1718 1984-01-160 1984-01-151 1984-01-1416 1984-01-139 1984-01-123 1984-01-114 1984-01-106 1984-01-0922 1984-01-0819 1984-01-0719 1984-01-0626 1984-01-0530 1984-01-0432 1984-01-0326 1984-01-0229 1984-01-0123 1983-12-314 1983-12-30-4 1983-12-29-1 1983-12-2822 1983-12-2711 1983-12-26-8 1983-12-25-12 1983-12-24-13 1983-12-233 1983-12-227 1983-12-2112 1983-12-2010 1983-12-199 1983-12-1815 1983-12-1716 1983-12-1621 1983-12-1531 1983-12-1435 1983-12-1335 1983-12-1236 1983-12-1131 1983-12-1030 1983-12-0926 1983-12-0826 1983-12-0725 1983-12-0627 1983-12-0535 1983-12-0433 1983-12-0329 1983-12-0222 1983-12-0122 1983-11-3026 1983-11-2933 1983-11-2835 1983-11-2738 1983-11-2637 1983-11-2529 1983-11-2432 1983-11-2352 1983-11-2242 1983-11-2141 1983-11-2053 1983-11-1946 1983-11-1827 1983-11-1731 1983-11-1632 1983-11-1534 1983-11-1421 1983-11-1321 1983-11-1223 1983-11-1125 1983-11-1043 1983-11-0932 1983-11-0833 1983-11-0741 1983-11-0635 1983-11-0535 1983-11-0432 1983-11-0337 1983-11-0245 1983-11-0146 1983-10-3129 1983-10-3025 1983-10-2932 1983-10-2845 1983-10-2733 1983-10-2634 1983-10-2542 1983-10-2448 1983-10-2349 1983-10-2244 1983-10-2147 1983-10-2043 1983-10-1934 1983-10-1841 1983-10-1743 1983-10-1640 1983-10-1533 1983-10-1440 1983-10-1345 1983-10-1256 1983-10-1150 1983-10-1048 1983-10-0948 1983-10-0848 1983-10-0736 1983-10-0646 1983-10-0555 1983-10-0462 1983-10-0355 1983-10-0246 1983-10-0154 1983-09-3043 1983-09-2946 1983-09-2845 1983-09-2743 1983-09-2651 1983-09-2534 1983-09-2430 1983-09-2336 1983-09-2237 1983-09-2147 1983-09-2068 1983-09-1967 1983-09-1851 1983-09-1752 1983-09-1656 1983-09-1537 1983-09-1445 1983-09-1353 1983-09-1264 1983-09-1165 1983-09-1062 1983-09-0950 1983-09-0850 1983-09-0757 1983-09-0666 1983-09-0568 1983-09-0461 1983-09-0355 1983-09-0255 1983-09-0156 1983-08-3165 1983-08-3058 1983-08-2960 1983-08-2866 1983-08-2767 1983-08-2666 1983-08-2560 1983-08-2457 1983-08-2364 1983-08-2268 1983-08-2156 1983-08-2067 1983-08-1964 1983-08-1869 1983-08-1762 1983-08-1658 1983-08-1554 1983-08-1450 1983-08-1350 1983-08-1256 1983-08-1163 1983-08-1051 1983-08-0961 1983-08-0862 1983-08-0758 1983-08-0663 1983-08-0567 1983-08-0463 1983-08-0359 1983-08-0259 1983-08-0167 1983-07-3168 1983-07-3070 1983-07-2971 1983-07-2861 1983-07-2756 1983-07-2657 1983-07-2562 1983-07-2466 1983-07-2365 1983-07-2265 1983-07-2167 1983-07-2068 1983-07-1967 1983-07-1867 1983-07-1767 1983-07-1669 1983-07-1566 1983-07-1459 1983-07-1364 1983-07-1268 1983-07-1151 1983-07-1056 1983-07-0957 1983-07-0851 1983-07-0745 1983-07-0648 1983-07-0556 1983-07-0469 1983-07-0366 1983-07-0265 1983-07-0168 1983-06-3063 1983-06-2963 1983-06-2865 1983-06-2764 1983-06-2665 1983-06-2558 1983-06-2466 1983-06-2359 1983-06-2259 1983-06-2156 1983-06-2066 1983-06-1966 1983-06-1861 1983-06-1761 1983-06-1662 1983-06-1561 1983-06-1462 1983-06-1360 1983-06-1257 1983-06-1155 1983-06-1051 1983-06-0942 1983-06-0846 1983-06-0748 1983-06-0651 1983-06-0554 1983-06-0457 1983-06-0348 1983-06-0239 1983-06-0141 1983-05-3146 1983-05-3049 1983-05-2949 1983-05-2843 1983-05-2735 1983-05-2641 1983-05-2549 1983-05-2447 1983-05-2351 1983-05-2259 1983-05-2148 1983-05-2056 1983-05-1953 1983-05-1837 1983-05-1732 1983-05-1639 1983-05-1542 1983-05-1457 1983-05-1346 1983-05-1240 1983-05-1133 1983-05-1028 1983-05-0929 1983-05-0835 1983-05-0759 1983-05-0636 1983-05-0541 1983-05-0440 1983-05-0347 1983-05-0255 1983-05-0153 1983-04-3056 1983-04-2942 1983-04-2849 1983-04-2756 1983-04-2631 1983-04-2534 1983-04-2437 1983-04-2335 1983-04-2236 1983-04-2130 1983-04-2028 1983-04-1923 1983-04-1825 1983-04-1729 1983-04-1631 1983-04-1535 1983-04-1445 1983-04-1342 1983-04-1232 1983-04-1139 1983-04-1041 1983-04-0942 1983-04-0839 1983-04-0747 1983-04-0642 1983-04-0538 1983-04-0439 1983-04-0340 1983-04-0243 1983-04-0132 1983-03-3127 1983-03-3019 1983-03-2921 1983-03-2839 1983-03-2739 1983-03-2619 1983-03-2517 1983-03-2419 1983-03-2317 1983-03-2218 1983-03-2123 1983-03-2032 1983-03-1936 1983-03-1842 1983-03-1731 1983-03-1628 1983-03-1532 1983-03-1440 1983-03-1322 1983-03-1228 1983-03-1128 1983-03-1032 1983-03-0935 1983-03-0845 1983-03-0748 1983-03-0651 1983-03-0550 1983-03-0445 1983-03-0328 1983-03-0223 1983-03-0130 1983-02-2829 1983-02-2719 1983-02-2621 1983-02-2523 1983-02-2426 1983-02-2327 1983-02-2233 1983-02-2137 1983-02-2032 1983-02-1930 1983-02-1830 1983-02-1735 1983-02-1634 1983-02-1535 1983-02-1415 1983-02-137 1983-02-1215 1983-02-1119 1983-02-1015 1983-02-0911 1983-02-0813 1983-02-0722 1983-02-0621 1983-02-0514 1983-02-0420 1983-02-0323 1983-02-0238 1983-02-0119 1983-01-3127 1983-01-3031 1983-01-2927 1983-01-2818 1983-01-2718 1983-01-2625 1983-01-2529 1983-01-2433 1983-01-2333 1983-01-2230 1983-01-2119 1983-01-201 1983-01-196 1983-01-185 1983-01-176 1983-01-1613 1983-01-1520 1983-01-1429 1983-01-1320 1983-01-1221 1983-01-1130 1983-01-1041 1983-01-0921 1983-01-0826 1983-01-0731 1983-01-0632 1983-01-0527 1983-01-0414 1983-01-0319 1983-01-0229 1983-01-0123 h,j,k,l,arrows,drag to pan i,o,+,-,scroll,shift-drag to zoom r,dbl-click to reset c for coordinates ? for help ? -25 0 25 50 75 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 -25.0 -24.5 -24.0 -23.5 -23.0 -22.5 -22.0 -21.5 -21.0 -20.5 -20.0 -19.5 -19.0 -18.5 -18.0 -17.5 -17.0 -16.5 -16.0 -15.5 -15.0 -14.5 -14.0 -13.5 -13.0 -12.5 -12.0 -11.5 -11.0 -10.5 -10.0 -9.5 -9.0 -8.5 -8.0 -7.5 -7.0 -6.5 -6.0 -5.5 -5.0 -4.5 -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5 17.0 17.5 18.0 18.5 19.0 19.5 20.0 20.5 21.0 21.5 22.0 22.5 23.0 23.5 24.0 24.5 25.0 25.5 26.0 26.5 27.0 27.5 28.0 28.5 29.0 29.5 30.0 30.5 31.0 31.5 32.0 32.5 33.0 33.5 34.0 34.5 35.0 35.5 36.0 36.5 37.0 37.5 38.0 38.5 39.0 39.5 40.0 40.5 41.0 41.5 42.0 42.5 43.0 43.5 44.0 44.5 45.0 45.5 46.0 46.5 47.0 47.5 48.0 48.5 49.0 49.5 50.0 50.5 51.0 51.5 52.0 52.5 53.0 53.5 54.0 54.5 55.0 55.5 56.0 56.5 57.0 57.5 58.0 58.5 59.0 59.5 60.0 60.5 61.0 61.5 62.0 62.5 63.0 63.5 64.0 64.5 65.0 65.5 66.0 66.5 67.0 67.5 68.0 68.5 69.0 69.5 70.0 70.5 71.0 71.5 72.0 72.5 73.0 73.5 74.0 74.5 75.0 -25 0 25 50 75 Temperature 
df = copy(data)
df[!,:Temperature] = -data[:,:Temperature]
filter!(row -> month(row.Date) ∈ (1,2,11,12), df)
plot(df, x=:Date, y=:Temperature, Geom.point)
Date Jan 1, 1983 1984 1985 1986 1987 1988 Jan 1, 1983 Apr Jul Oct Jan 1984 Apr Jul Oct Jan 1985 Apr Jul Oct Jan 1986 Apr Jul Oct Jan 1987 Apr Jul Oct Jan 1988 Dec 24, 1983 31 Jan 7, 1984 14 21 28 Feb 4 11 18 25 Mar 3 10 17 24 31 Apr 7 14 21 28 May 5 12 19 26 Jun 2 9 16 23 30 Jul 7 14 21 28 Aug 4 11 18 25 Sep 1 8 15 22 29 Oct 6 13 20 27 Nov 3 10 17 24 Dec 1 8 15 22 29 Jan 5, 1985 12 19 26 Feb 2 9 16 23 Mar 2 9 16 23 30 Apr 6 13 20 27 May 4 11 18 25 Jun 1 8 15 22 29 Jul 6 13 20 27 Aug 3 10 17 24 31 Sep 7 14 21 28 Oct 5 12 19 26 Nov 2 9 16 23 30 Dec 7 14 21 28 Jan 4, 1986 11 18 25 Feb 1 8 15 22 Mar 1 8 15 22 29 Apr 5 12 19 26 May 3 10 17 24 31 Jun 7 14 21 28 Jul 5 12 19 26 Aug 2 9 16 23 30 Sep 6 13 20 27 Oct 4 11 18 25 Nov 1 8 15 22 29 Dec 6 13 20 27 Jan 3, 1987 10 17 24 31 Feb 7 14 21 28 Mar 7 14 21 28 Apr 4 11 18 25 May 2 9 16 23 30 Jun 6 13 20 27 Jul 4 11 18 25 Aug 1 8 15 22 29 Sep 5 12 19 26 Oct 3 10 17 24 31 Nov 7 14 21 28 Dec 5 12 19 26 Jan 2, 1988 Jan 1, 1983 1986 1989 1987-12-31-26 1987-12-30-12 1987-12-29-18 1987-12-28-31 1987-12-27-25 1987-12-26-26 1987-12-25-35 1987-12-24-29 1987-12-23-32 1987-12-22-21 1987-12-21-28 1987-12-20-36 1987-12-19-30 1987-12-18-26 1987-12-17-26 1987-12-16-27 1987-12-15-30 1987-12-14-28 1987-12-13-31 1987-12-12-32 1987-12-11-29 1987-12-10-32 1987-12-09-43 1987-12-08-34 1987-12-07-26 1987-12-06-21 1987-12-05-27 1987-12-04-27 1987-12-03-29 1987-12-02-28 1987-12-01-30 1987-11-30-36 1987-11-29-39 1987-11-28-41 1987-11-27-35 1987-11-26-38 1987-11-25-42 1987-11-24-39 1987-11-23-24 1987-11-22-13 1987-11-21-16 1987-11-20-22 1987-11-19-30 1987-11-18-38 1987-11-17-53 1987-11-16-39 1987-11-15-29 1987-11-14-37 1987-11-13-34 1987-11-12-25 1987-11-11-25 1987-11-10-28 1987-11-09-36 1987-11-08-45 1987-11-07-39 1987-11-06-29 1987-11-05-31 1987-11-04-56 1987-11-03-55 1987-11-02-49 1987-11-01-45 1987-02-28-35 1987-02-27-32 1987-02-26-25 1987-02-25-20 1987-02-24-26 1987-02-23-31 1987-02-22-32 1987-02-21-20 1987-02-20-14 1987-02-19-12 1987-02-18-21 1987-02-17-8 1987-02-16-7 1987-02-15-8 1987-02-14-20 1987-02-13-21 1987-02-12-31 1987-02-11-18 1987-02-10-16 1987-02-09-15 1987-02-08-16 1987-02-07-29 1987-02-06-20 1987-02-05-16 1987-02-04-24 1987-02-03-32 1987-02-02-35 1987-02-01-25 1987-01-31-25 1987-01-30-26 1987-01-29-24 1987-01-28-13 1987-01-270 1987-01-26-7 1987-01-25-1 1987-01-243 1987-01-231 1987-01-22-23 1987-01-21-15 1987-01-20-23 1987-01-19-24 1987-01-18-28 1987-01-17-19 1987-01-16-22 1987-01-15-31 1987-01-14-35 1987-01-13-25 1987-01-12-27 1987-01-11-28 1987-01-10-28 1987-01-09-25 1987-01-08-27 1987-01-07-32 1987-01-06-13 1987-01-05-13 1987-01-04-17 1987-01-03-23 1987-01-02-30 1987-01-01-26 1986-12-31-30 1986-12-30-26 1986-12-29-21 1986-12-28-25 1986-12-27-28 1986-12-26-29 1986-12-25-31 1986-12-24-26 1986-12-23-19 1986-12-22-17 1986-12-21-23 1986-12-20-27 1986-12-19-28 1986-12-18-30 1986-12-17-32 1986-12-16-25 1986-12-15-27 1986-12-14-15 1986-12-13-15 1986-12-12-19 1986-12-11-17 1986-12-10-17 1986-12-09-39 1986-12-08-37 1986-12-07-31 1986-12-06-22 1986-12-05-23 1986-12-04-24 1986-12-03-33 1986-12-02-32 1986-12-01-30 1986-11-30-33 1986-11-29-36 1986-11-28-31 1986-11-27-31 1986-11-26-28 1986-11-25-22 1986-11-24-27 1986-11-23-30 1986-11-22-31 1986-11-21-33 1986-11-20-30 1986-11-19-27 1986-11-18-32 1986-11-17-34 1986-11-16-34 1986-11-15-15 1986-11-14-11 1986-11-13-16 1986-11-12-28 1986-11-11-33 1986-11-10-26 1986-11-09-43 1986-11-08-49 1986-11-07-40 1986-11-06-42 1986-11-05-37 1986-11-04-39 1986-11-03-24 1986-11-02-44 1986-11-01-49 1986-02-28-6 1986-02-27-9 1986-02-26-18 1986-02-25-17 1986-02-24-17 1986-02-23-26 1986-02-22-21 1986-02-21-22 1986-02-20-31 1986-02-19-33 1986-02-18-42 1986-02-17-32 1986-02-16-18 1986-02-15-16 1986-02-14-15 1986-02-13-4 1986-02-12-8 1986-02-11-14 1986-02-10-16 1986-02-09-24 1986-02-08-23 1986-02-07-24 1986-02-06-30 1986-02-05-34 1986-02-04-34 1986-02-03-30 1986-02-02-31 1986-02-01-26 1986-01-31-14 1986-01-30-16 1986-01-29-11 1986-01-28-1 1986-01-27-2 1986-01-26-21 1986-01-25-30 1986-01-24-17 1986-01-23-20 1986-01-22-31 1986-01-21-27 1986-01-20-29 1986-01-19-31 1986-01-18-41 1986-01-17-41 1986-01-16-13 1986-01-151 1986-01-14-11 1986-01-13-8 1986-01-12-30 1986-01-11-21 1986-01-10-27 1986-01-09-14 1986-01-08-3 1986-01-07-7 1986-01-06-13 1986-01-05-22 1986-01-04-28 1986-01-03-28 1986-01-02-29 1986-01-01-16 1985-12-31-18 1985-12-30-12 1985-12-29-16 1985-12-28-5 1985-12-27-17 1985-12-262 1985-12-250 1985-12-24-11 1985-12-23-31 1985-12-22-6 1985-12-21-6 1985-12-20-2 1985-12-192 1985-12-18-1 1985-12-17-12 1985-12-16-18 1985-12-15-9 1985-12-14-8 1985-12-13-18 1985-12-12-32 1985-12-11-38 1985-12-10-31 1985-12-09-30 1985-12-08-27 1985-12-07-31 1985-12-06-31 1985-12-05-30 1985-12-04-24 1985-12-03-17 1985-12-02-17 1985-12-01-41 1985-11-30-37 1985-11-29-36 1985-11-28-33 1985-11-27-35 1985-11-26-33 1985-11-25-30 1985-11-24-29 1985-11-23-31 1985-11-22-32 1985-11-21-23 1985-11-20-29 1985-11-19-59 1985-11-18-39 1985-11-17-40 1985-11-16-41 1985-11-15-41 1985-11-14-43 1985-11-13-50 1985-11-12-42 1985-11-11-42 1985-11-10-44 1985-11-09-43 1985-11-08-32 1985-11-07-34 1985-11-06-40 1985-11-05-45 1985-11-04-46 1985-11-03-49 1985-11-02-51 1985-11-01-50 1985-02-28-24 1985-02-27-26 1985-02-26-29 1985-02-25-30 1985-02-24-38 1985-02-23-42 1985-02-22-42 1985-02-21-21 1985-02-20-13 1985-02-19-18 1985-02-18-20 1985-02-17-24 1985-02-16-4 1985-02-15-6 1985-02-14-14 1985-02-13-15 1985-02-12-31 1985-02-11-24 1985-02-103 1985-02-091 1985-02-082 1985-02-07-5 1985-02-06-13 1985-02-05-13 1985-02-0413 1985-02-035 1985-02-02-7 1985-02-01-10 1985-01-31-23 1985-01-30-7 1985-01-29-10 1985-01-28-20 1985-01-27-11 1985-01-26-7 1985-01-25-14 1985-01-24-19 1985-01-23-15 1985-01-22-9 1985-01-2118 1985-01-2019 1985-01-195 1985-01-18-17 1985-01-17-17 1985-01-161 1985-01-15-11 1985-01-14-18 1985-01-13-12 1985-01-12-11 1985-01-11-16 1985-01-10-16 1985-01-09-8 1985-01-08-15 1985-01-07-30 1985-01-06-29 1985-01-05-24 1985-01-04-24 1985-01-03-23 1985-01-02-26 1985-01-01-31 1984-12-31-27 1984-12-30-29 1984-12-29-43 1984-12-28-52 1984-12-27-28 1984-12-26-18 1984-12-25-11 1984-12-24-21 1984-12-23-23 1984-12-22-25 1984-12-21-30 1984-12-20-29 1984-12-19-30 1984-12-18-28 1984-12-17-47 1984-12-16-42 1984-12-15-44 1984-12-14-38 1984-12-13-37 1984-12-12-36 1984-12-11-34 1984-12-10-35 1984-12-09-12 1984-12-08-17 1984-12-07-6 1984-12-06-18 1984-12-05-14 1984-12-04-18 1984-12-03-25 1984-12-02-27 1984-12-01-31 1984-11-30-33 1984-11-29-31 1984-11-28-33 1984-11-27-39 1984-11-26-30 1984-11-25-25 1984-11-24-24 1984-11-23-28 1984-11-22-27 1984-11-21-27 1984-11-20-18 1984-11-19-26 1984-11-18-32 1984-11-17-22 1984-11-16-27 1984-11-15-40 1984-11-14-21 1984-11-13-25 1984-11-12-25 1984-11-11-30 1984-11-10-48 1984-11-09-45 1984-11-08-30 1984-11-07-25 1984-11-06-32 1984-11-05-40 1984-11-04-42 1984-11-03-25 1984-11-02-27 1984-11-01-46 1984-02-29-14 1984-02-28-20 1984-02-27-24 1984-02-26-11 1984-02-25-16 1984-02-24-32 1984-02-23-28 1984-02-22-23 1984-02-21-24 1984-02-20-31 1984-02-19-39 1984-02-18-41 1984-02-17-42 1984-02-16-30 1984-02-15-28 1984-02-14-37 1984-02-13-49 1984-02-12-42 1984-02-11-42 1984-02-10-28 1984-02-09-23 1984-02-08-12 1984-02-07-11 1984-02-06-13 1984-02-05-24 1984-02-04-29 1984-02-03-31 1984-02-02-20 1984-02-01-1 1984-01-31-7 1984-01-30-23 1984-01-29-27 1984-01-28-15 1984-01-27-23 1984-01-26-27 1984-01-25-30 1984-01-24-35 1984-01-23-7 1984-01-222 1984-01-2116 1984-01-209 1984-01-193 1984-01-18-2 1984-01-17-18 1984-01-160 1984-01-15-1 1984-01-14-16 1984-01-13-9 1984-01-12-3 1984-01-11-4 1984-01-10-6 1984-01-09-22 1984-01-08-19 1984-01-07-19 1984-01-06-26 1984-01-05-30 1984-01-04-32 1984-01-03-26 1984-01-02-29 1984-01-01-23 1983-12-31-4 1983-12-304 1983-12-291 1983-12-28-22 1983-12-27-11 1983-12-268 1983-12-2512 1983-12-2413 1983-12-23-3 1983-12-22-7 1983-12-21-12 1983-12-20-10 1983-12-19-9 1983-12-18-15 1983-12-17-16 1983-12-16-21 1983-12-15-31 1983-12-14-35 1983-12-13-35 1983-12-12-36 1983-12-11-31 1983-12-10-30 1983-12-09-26 1983-12-08-26 1983-12-07-25 1983-12-06-27 1983-12-05-35 1983-12-04-33 1983-12-03-29 1983-12-02-22 1983-12-01-22 1983-11-30-26 1983-11-29-33 1983-11-28-35 1983-11-27-38 1983-11-26-37 1983-11-25-29 1983-11-24-32 1983-11-23-52 1983-11-22-42 1983-11-21-41 1983-11-20-53 1983-11-19-46 1983-11-18-27 1983-11-17-31 1983-11-16-32 1983-11-15-34 1983-11-14-21 1983-11-13-21 1983-11-12-23 1983-11-11-25 1983-11-10-43 1983-11-09-32 1983-11-08-33 1983-11-07-41 1983-11-06-35 1983-11-05-35 1983-11-04-32 1983-11-03-37 1983-11-02-45 1983-11-01-46 1983-02-28-29 1983-02-27-19 1983-02-26-21 1983-02-25-23 1983-02-24-26 1983-02-23-27 1983-02-22-33 1983-02-21-37 1983-02-20-32 1983-02-19-30 1983-02-18-30 1983-02-17-35 1983-02-16-34 1983-02-15-35 1983-02-14-15 1983-02-13-7 1983-02-12-15 1983-02-11-19 1983-02-10-15 1983-02-09-11 1983-02-08-13 1983-02-07-22 1983-02-06-21 1983-02-05-14 1983-02-04-20 1983-02-03-23 1983-02-02-38 1983-02-01-19 1983-01-31-27 1983-01-30-31 1983-01-29-27 1983-01-28-18 1983-01-27-18 1983-01-26-25 1983-01-25-29 1983-01-24-33 1983-01-23-33 1983-01-22-30 1983-01-21-19 1983-01-20-1 1983-01-19-6 1983-01-18-5 1983-01-17-6 1983-01-16-13 1983-01-15-20 1983-01-14-29 1983-01-13-20 1983-01-12-21 1983-01-11-30 1983-01-10-41 1983-01-09-21 1983-01-08-26 1983-01-07-31 1983-01-06-32 1983-01-05-27 1983-01-04-14 1983-01-03-19 1983-01-02-29 1983-01-01-23 h,j,k,l,arrows,drag to pan i,o,+,-,scroll,shift-drag to zoom r,dbl-click to reset c for coordinates ? for help ? -60 -40 -20 0 20 -60 -55 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 -60.0 -59.5 -59.0 -58.5 -58.0 -57.5 -57.0 -56.5 -56.0 -55.5 -55.0 -54.5 -54.0 -53.5 -53.0 -52.5 -52.0 -51.5 -51.0 -50.5 -50.0 -49.5 -49.0 -48.5 -48.0 -47.5 -47.0 -46.5 -46.0 -45.5 -45.0 -44.5 -44.0 -43.5 -43.0 -42.5 -42.0 -41.5 -41.0 -40.5 -40.0 -39.5 -39.0 -38.5 -38.0 -37.5 -37.0 -36.5 -36.0 -35.5 -35.0 -34.5 -34.0 -33.5 -33.0 -32.5 -32.0 -31.5 -31.0 -30.5 -30.0 -29.5 -29.0 -28.5 -28.0 -27.5 -27.0 -26.5 -26.0 -25.5 -25.0 -24.5 -24.0 -23.5 -23.0 -22.5 -22.0 -21.5 -21.0 -20.5 -20.0 -19.5 -19.0 -18.5 -18.0 -17.5 -17.0 -16.5 -16.0 -15.5 -15.0 -14.5 -14.0 -13.5 -13.0 -12.5 -12.0 -11.5 -11.0 -10.5 -10.0 -9.5 -9.0 -8.5 -8.0 -7.5 -7.0 -6.5 -6.0 -5.5 -5.0 -4.5 -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5 17.0 17.5 18.0 18.5 19.0 19.5 20.0 -60 -40 -20 0 20 Temperature

The runs method

Two cluster definitions are used in Extremes.jl. The first one is based on the runs method: exceedances separated by fewer than $r$ non-exceedances are assumed to belong to the same cluster (see Chapter 10 of Beirlant et al., 2004). The parameter $r$ is generally referred to as the runlength parameter. When $r = 0$, each exceedance forms a separate cluster.

When using the threshold of -10°F and the runlength of 4, 17 clusters are idenfied:

threshold =  -10.0
cluster = getcluster(df[:,:Temperature], threshold, runlength=4)

The first cluster can be retrieved as follows:

first(cluster)
Cluster
u₁: -10.0
u₂: -10.0
position: [17, 18, 19, 20]
value: [-6, -5, -6, -1]

The GP distribution can be fitted on the cluster maximal exceedances (the cluster maximum can be computed with the maximum method applied to the Cluster type):

julia> z = maximum.(cluster)17-element Vector{Int64}:
 -1
 -7
 13
 16
 -1
 -6
 -8
 19
 -4
  2
 -3
  1
 -1
 -4
 -6
  3
 -7

The two thresholds method

With the two thresholds method, a cluster of threshold exceedances is defined as a streak of data higher than a second threshold $u₂$ whose at least one data is higher than a first threshold $u₁$, where $u₁ ≥ u₂$.

When using the $u₁ = 0°F$ as the first threshold and $u₂ = -10°F$ as the second threshold, 11 clusters are idenfied:

u₁ = -10
u₂ = -15
cluster = getcluster(df[:,:Temperature], u₁, u₂)

The first cluster can be retrieved as follows:

first(cluster)
Cluster
u₁: -10
u₂: -15
position: [16, 17, 18, 19, 20]
value: [-13, -6, -5, -6, -1]

The GP distribution can be fitted on the cluster maximal exceedances:

julia> z = maximum.(cluster)27-element Vector{Int64}:
 -1
 -7
 13
  4
 -3
  0
 16
 -1
 -6
 -8
  ⋮
  2
 -5
 -3
  1
 -1
 -4
 -6
  3
 -7