背景
因此，首先需要一些背景来衡量我可能拥有的理解水平。目前正在完成硕士论文，尽管我确实有基本的了解，但统计数据一直是其中可以忽略不计的一部分。我目前的问题让我怀疑我在实践中可以/应该做什么，越来越多的在线阅读和文学似乎适得其反。
我想达到什么目的？
因此，对于我的论文，我加入了一家公司，我试图回答的一般问题基本上是预测过程如何受到某些系统的实施的影响（这会影响用于预测过程的数据）。
期望的结果是理解：
- 有明显的变化吗？（例如统计证明）
- 变化有多大？（均值和方差）
- 在这个预测过程中哪些因素很重要（以及因素的影响如何从休息前 > 休息后变化）
为了回答 1 和 2，我获得了时间序列对象形式的历史数据（在这个阶段更多但无关紧要）。我使用的软件是R。
数据
数据包含每天（2.5 年）的加权分数，表明预测过程执行得有多糟糕（与实际事件的偏差）。这个时间序列对象包含这 2.5 年中从一小时前到事件实际发生（1 小时间隔）发生的预测的加权分数（因此，该间隔的每一天都有一个加权分数）。同样，为其他时间间隔（例如 1-2、2-3 小时等）构建了多个时间序列。
myts1 <- structure(c(412.028462047, 468.938224875, 372.353242472, 662.26844965,
526.872020535, 396.434818388, 515.597528222, 536.940884418, 642.878650146,
458.935314286, 544.096691918, 544.378838523, 486.854043968, 478.952935122,
533.171083451, 507.543369365, 475.992539251, 411.626822157, 574.256785085,
489.424743512, 558.03917366, 488.892234577, 1081.570101272, 488.410996801,
420.058151274, 548.43547725, 759.563191992, 699.857042552, 505.546581256,
2399.735167563, 959.058553387, 565.776425823, 794.327364085,
1060.096712241, 636.011672603, 592.842508666, 643.576323635,
639.649884944, 420.788373053, 506.948276856, 503.484363746, 466.642585817,
554.521681602, 578.44355769, 589.29487224, 636.837396631, 647.548662447,
740.222655163, 391.545826142, 537.551842222, 908.940523615, 590.446686171,
543.002925217, 1406.486794264, 1007.596435757, 617.098818856,
633.848676718, 576.040175894, 881.49475483, 687.276105325, 628.977801859,
1398.136047241, 749.644445942, 639.958039461, 649.265606673,
645.57852203, 577.862446744, 663.218073256, 593.034544803, 672.096591437,
544.776355324, 720.242877214, 824.963939263, 596.581822515, 885.215989867,
693.456405627, 552.170633931, 618.855329732, 1030.291011295,
615.889921256, 799.498196448, 570.398558528, 680.670975027, 563.404802085,
494.790365745, 756.684436338, 523.051238729, 535.502475619, 520.8344231,
623.971011973, 928.274580287, 639.702434094, 583.234364572, 623.144865566,
673.342687695, 567.501447619, 602.473664361, 655.181508321, 593.662768316,
617.830786992, 652.461315007, 496.505155747, 550.24687917, 588.952116381,
456.603281447, 425.963966309, 454.729462342, 487.22846023, 613.269432488,
474.916140657, 505.93051487, 536.401546008, 555.824475073, 509.429036303,
632.232746263, 677.102831732, 506.605957979, 701.99882145, 499.770942819,
555.599224002, 557.634152694, 448.693828549, 661.921921922, 447.00540349,
561.194112634, 590.797954608, 590.739061378, 445.949400588, 725.589882976,
480.650749378, 587.03144903, 483.054524693, 428.813155209, 540.609606719,
495.756149832, 409.713220791, 492.43287131, 618.492643291, 723.203623076,
461.433833742, 420.414959481, 480.501175081, 564.955582744, 453.0704893,
506.711353939, 521.12661934, 487.509966405, 483.442305774, 506.932771141,
442.871555249, 873.285819221, 1201.628963682, 1392.479592817,
693.292446258, 629.477998542, 660.777526646, 414.376675251, 475.517946081,
501.626384564, 470.216781646, 444.195433559, 697.258566625, 546.966755779,
428.945521943, 388.203080434, 579.759476551, 548.433130604, 453.950530959,
460.613845164, 534.329569431, 560.663080722, 660.799405665, 432.3134958,
569.59842379, 518.195281689, 650.007266105, 521.642137647, 442.763872575,
687.470213886, 951.651918891, 589.611971045, 493.203713291, 431.966577408,
616.912296912, 685.80916291, 502.518373775, 595.630289879, 563.104035749,
523.383707347, 532.042896625, 470.949823756, 603.408124923, 615.301428799,
708.26541245, 725.853182875, 705.777543119, 530.351781147, 698.828825921,
462.173187592, 366.411986505, 848.613888761, 502.940599188, 456.044881766,
605.321231272, 629.861109863, 431.130428123, 509.672767868, 457.598828697,
553.932034119, 610.181457495, 581.59017099, 540.788638119, 705.226962669,
610.670142045, 566.392016015, 611.086310256, 603.256299175, 766.372982953,
801.921868916, 761.708239486, 580.712445849, 575.53616943, 540.066255921,
608.133122153, 735.063468208, 637.091441112, 778.874033589, 689.350099602,
1003.219851026, 624.107808848, 635.887051641, 420.915060155,
511.460563095, 817.08209288, 603.089908306, 772.6493477, 797.148459813,
588.255963229, 499.050860875, 502.059987, 565.524637543, 1663.182976069,
2281.49950544, 1442.687607103, 1024.355834401, 899.519857882,
988.585993922, 612.834835776, 641.686600038, 717.951451466, 746.441686309,
1147.770724052, 596.279691286, 932.861076555, 497.228997645,
764.895725484, 659.054003787, 1148.227820587, 1403.462969143,
624.733620842, 803.199038618, 839.637983048, 1278.286165347,
774.363457936, 662.767213211, 627.251799204, 650.180035442, 1296.405174964,
662.928010153, 523.095967567, 620.727894789, 650.876097695, 509.534317267,
479.922326477, 613.743251306, 430.117763379, 1825.108688714,
744.708270099, 455.818978039, 370.908485795, 771.317824437, 688.219350724,
468.16351523, 791.649828808, 666.360829114, 1427.809117119, 2861.163543428,
1090.887950582, 621.942045727, 397.381382335, 397.697308586,
494.441558442, 474.314526966, 888.812606506, 476.031636688, 651.907747324,
389.95997873, 680.776897408, 1499.093314237, 1077.571595752,
765.690897368, 571.545469449, 590.64855754, 492.371592484, 580.811781306,
873.628734717, 602.958435426, 549.877214337, 546.66120979, 394.75285753,
520.238244635, 517.217468365, 903.057976974, 528.477241796, 378.958677302,
491.589659729, 548.665964908, 453.512746452, 481.081050678, 491.499714029,
628.539705456, 672.540312912, 1686.825394554, 1367.577856001,
600.373039737, 417.511405109, 511.75535978, 440.677427555, 493.430816323,
533.025975459, 547.429120615, 432.168874608, 555.098163047, 521.644301834,
667.159371501, 421.591007887, 757.218378664, 615.572602597, 433.961482908,
528.813953729, 633.228715271, 519.648748842, 437.342815473, 551.877832301,
703.377801948, 536.673383258, 658.597165739, 1449.850501569,
615.204142853, 499.197033946, 853.692014263, 490.213941347, 812.68824521,
521.364349414, 818.757704456, 848.59674442, 646.819554339, 471.051626838,
598.326620222, 782.58569568, 754.880939869, 636.572395084, 686.076138643,
530.158582782, 524.696479569, 525.441231521, 593.834663615, 415.830854949,
590.135594493, 591.019407595, 503.321975981, 515.371205208, 494.805384342,
567.397190671, 482.180658052, 724.099533838, 791.107121538, 564.673191002,
572.551388184, 729.46937136, 943.538757014, 519.051645932, 994.190842696,
866.69659257, 610.021553913, 547.791568399, 578.854543644, 684.826681706,
815.179238308, 617.050464226, 623.818649573, 537.163825262, 529.850027242,
926.531531345, 588.578930644, 457.329084489, 380.160216157, 494.287689357,
463.885244047, 451.611520014, 762.508948042, 773.74942889, 1642.691010358,
555.226392541, 659.433830806, 454.348720108, 388.274823265, 650.63824747,
632.327400443, 584.93699748, 484.815917524, 733.153950316, 471.349864174,
418.755413722, 547.060192029, 742.028289483, 521.119798289, 1176.207996336,
524.730544122, 430.009783422, 558.479383664, 574.162550914, 526.08247269,
611.207728202, 551.202548069, 472.046973518, 517.490179087, 556.135143079,
628.084374004, 413.677676623, 439.814082201, 1011.775306843,
684.443831473, 546.421742134, 578.853727684, 517.693483714, 638.112468944,
631.531739664, 501.897019514, 661.11860926, 521.695715961, 474.403897254,
463.294645328, 559.583511974, 531.953658919, 740.412596176, 534.815607516,
462.329096628, 637.941748843, 702.69170843, 471.390065606, 590.458408612,
617.006573387, 565.411288964, 472.986933034, 567.745850996, 596.925622448,
474.068038429, 653.56453828, 612.893376781, 711.545758298, 527.783301631,
478.530081662, 519.751192408, 536.550807025, 443.437342694, 587.403769673,
601.15805729, 556.497167238, 374.228230116, 477.027420471, 494.984999444,
879.314339401, 704.997313272, 626.546803934, 653.296523326, 435.581408863,
633.048339362, 403.889616794, 488.214190958, 575.631003993, 430.984422675,
437.83561603, 522.277281965, 475.602597701, 527.12160277, 944.139469794,
474.50403295, 579.478722386, 459.088134733, 503.246692031, 610.022771263,
446.143895372, 625.022916127, 517.435543013, 891.375454252, 555.864115385,
474.764739145, 921.714956231, 645.896256587, 1536.221634415,
816.575921465, 596.491670621, 503.56011064, 720.743463226, 905.835642175,
1360.481537034, 653.224092421, 633.505228314, 546.064475635,
482.454025258, 962.715357696, 618.202090733, 803.895156435, 668.047995992,
594.566585046, 839.597813143, 457.375793588, 631.863607862, 475.266615122,
664.569635822, 481.886574644, 1614.962054217, 869.212340286,
501.400781534, 478.670649186, 521.824073342, 684.720851031, 597.124676952,
605.903108456, 491.358096619, 430.812042311, 388.350092055, 488.132638097,
413.131448595, 391.891460495, 430.760685279, 731.99097305, 382.200799877,
511.48361093, 560.620999712, 528.369543055, 536.348770159, 721.297750609,
491.321646454, 509.521489714, 561.318889907, 553.24041301, 459.235996646,
354.741174128, 339.775552834, 432.548724483, 438.672630955, 508.177204773,
496.199702536, 643.867549669, 611.460979278, 861.190516859, 662.56052508,
524.398593443, 529.585928069, 607.575374022, 495.001029442, 700.371352785,
794.753142167, 466.792229932, 435.426320832, 450.903747896, 622.562955777,
1562.215153595, 725.069249874, 612.357398912, 418.579228487,
381.667629501, 528.173266471, 687.876352966, 655.845568131, 423.589678964,
612.545707971, 951.362478322, 1800.162370822, 600.672989388,
531.048286916, 527.565406977, 402.380659606, 607.699770367, 1486.296473731,
686.560841226, 4176.136413427, 3086.067140966, 1872.815975088,
771.413460362, 843.791946967, 652.825527602, 642.443948966, 726.208291336,
641.092848676, 488.237988698, 606.154989706, 1426.027951807,
959.347533388, 649.856202928, 527.580884911, 400.545393834, 568.268813107,
631.257023117, 515.755741256, 682.375587555, 583.855170876, 506.146152757,
517.095094378, 563.415777949, 801.015579658, 649.56360904, 732.097267107,
456.626323752, 499.170138889, 549.393587002, 556.589070013, 590.180621262,
667.709332802, 421.738377899, 661.178862228, 570.833727593, 631.139001868,
545.835879493, 559.918523671, 1364.379214546, 985.777069008,
644.949427255, 493.066294248, 476.852498787, 379.716401582, 715.333935018,
459.326945313, 621.665546323, 476.317803131, 519.803138696, 409.241665463,
465.206511176, 594.689036224, 443.841857849, 399.830019307, 570.65982956,
516.562325113, 381.909941529, 532.130831616, 650.329631588, 661.055942562,
1136.942413908, 508.543555485, 976.852889691, 1461.16921717,
646.062436059, 593.093537367, 624.839875084, 453.453385269, 584.633165187,
507.616009915, 516.857276979, 434.651983821, 572.755844368, 454.901132196,
707.698546138, 760.341584614, 449.252091224, 623.217222998, 625.061550699,
2030.045687713, 1582.036383383, 677.325281969, 571.588930686,
493.235172445, 556.291968991, 424.360693057, 436.333980583, 484.105667103,
505.231040152, 378.767240615, 495.943549377, 321.856525703, 363.651848067,
557.201599565, 603.658298878, 558.958198405, 789.717963533, 480.370977054,
509.366153138, 467.526623793, 576.508422894, 661.322171003, 520.804998847,
342.109381368, 473.512224982, 984.139466992, 487.586712759, 605.914245454,
459.190981983, 678.728907858, 342.511103348, 436.746013478, 520.896987467,
818.078350515, 527.494249096, 713.52499017, 610.365469264, 462.965548015,
362.931986459, 810.610193032, 393.455578799, 536.720944152, 551.490260933,
464.369987186, 275.832746918, 513.723009815, 491.945195301, 438.865839297,
257.252871794, 615.513481211, 420.507536576, 392.035094971, 392.963333027,
435.276624468, 253.431425091, 592.873595776, 500.615067792, 503.491101855,
475.352827724, 1135.11762886, 723.666909467, 712.259187274, 559.738346197,
490.958692763, 435.998397207, 729.341315271, 406.369683231, 632.626098862,
565.318329487, 394.031553179, 356.627786519, 374.075606064, 336.505546227,
393.168901965, 480.183256037, 573.840777708, 187.680483645, 170.978544639,
209.134883957, 193.039610198, 224.362544607, 210.946012575, 166.006351727,
201.500604051, 160.008039339, 229.847327915, 193.655724693, 255.575881835,
207.0547762, 186.835573846, 247.776981217, 574.489201771, 602.683083111,
202.592131296, 205.827635803, 279.139480224, 367.898232724, 245.75114848,
304.004111775, 231.706217872, 159.750034155, 207.584399879, 239.854118732,
212.711257914, 181.755353255, 225.98761652, 206.570825973, 193.940523176,
203.851963746, 170.700301226, 226.41517367, 183.87542452, 206.640800387,
218.953856594, 176.127748987, 168.205878516, 201.718224491, 171.421791143,
193.065350731, 235.118975292, 217.002358158, 197.563916607, 219.266588546,
168.044251777, 182.1752633, 172.514392523, 192.250197416, 171.023249603,
151.848998035, 151.678097242, 173.28609604, 194.852548067, 178.742929426,
180.591580951, 189.241987711, 206.960325123, 207.639468123, 307.389246296,
197.203559504, 201.143394951, 313.861245405, 215.87226561, 218.500147257,
201.993836847, 204.461813487, 180.04803872, 305.301279156, 214.880173012,
250.930811019, 284.90370816, 212.518096229, 195.034955147, 190.236951118,
257.088555132, 189.502428671, 239.652450054, 243.53269907, 289.820554649,
249.011846483, 279.393483142, 194.006529415, 214.59905786, 247.746491522,
224.723467084, 191.086994265, 271.654470268, 183.455652269, 327.307813653,
149.721791725, 170.538132352, 192.954323882, 172.459631548, 199.829129152,
163.257916856, 179.33550074, 207.618752518, 191.969484656, 191.506188821,
176.446694609, 194.818608621, 167.891653012, 167.000377869, 201.869893803,
183.895614224, 148.510174938, 157.27033831, 166.573696008, 309.557485177,
595.559287832, 232.318746483, 188.295593138, 157.721093739, 177.753625321,
214.844940799, 226.812056373, 213.910815993, 188.973729833, 243.306529363,
202.733401293, 197.296870477, 182.523989567, 170.428625204, 172.593507241,
151.926342178, 283.415923815, 163.456408737, 172.273699114, 159.382452668,
182.158974043, 156.532047405, 182.768725504, 239.318216814, 151.579013694,
148.216885776, 241.346766195, 257.110058666, 147.931152011, 186.2508302,
197.379372605, 155.69798218, 147.370235658, 180.961415272, 168.372900875,
297.9454882, 177.640856836, 170.535749604, 166.211309731, 178.463064513,
175.035906056, 179.971897406, 162.858094293, 164.056675362, 250.151933362,
195.49943188, 175.281720263, 182.392087534, 144.341091392, 241.466298465,
184.806150673, 167.932448156, 150.621075732, 178.510315062, 209.913152992,
222.798716921, 153.536476868, 190.326281004, 173.708412622, 148.075945402,
149.147879365, 181.5851776, 141.012604897, 157.982751461, 159.364653673,
151.777006477, 191.065323099, 139.076429662, 172.452344359, 182.482693518,
287.424045314, 169.327943406, 298.970852166, 145.238645275, 175.211717467,
165.116950464, 187.006564993, 160.959119092, 198.552333833, 170.406040157,
162.10770001, 146.356131036, 170.336552623, 163.095730104, 155.192077125,
217.182324478, 231.270198833, 256.905250226, 184.59676245, 175.557146633,
164.246298131, 221.695058452, 197.911691457, 188.427830442, 259.361745153,
164.243672823, 190.67188784, 182.331604811, 190.352555581, 248.738493256,
196.854564795, 164.974185334, 332.650385373, 169.081552611, 193.578840033,
192.166911863, 214.174943222, 271.287900593, 224.675083031, 171.950208574,
173.867031268, 139.260432794, 177.012491325, 171.268066406, 132.714578168,
197.224558817, 152.561299656, 143.415562042), .Tsp = c(2016.3306010929,
2018.99909424358, 365), class = "ts")
处理到现在
现在我已经明白，对于问题 1，我可以对结构性中断进行测试，以确定中断是否以及何时发生（具有已知的中断日期）。为此，我在 R 中使用 strucchange 包并利用断点函数。
但是，我的主管也推荐了CUSUM （用于未知休息日期）测试。不确定这里最好的是什么？
编辑：
我看到 Andrew 的 supF 测试针对所有可能的中断进行 Chow 测试。如果 F（或 Chow）统计量的最大值变得太大，则拒绝。（发现 -对时间序列进行 chow 测试）
使用 struccchange 获取休息日期的代码
library(strucchange)
test2 <- Fstats(myts1~1) #Gets a sequence of fstatistics for all possible
# break points within the middle 70% of myts1
myts1.fs <- test2$Fstats #These are the fstats
bp.myts1 <- breakpoints(myts1~1) #Gets the breakpoint based on the F-stats
plot(myts1) #plots the series myts1
lines(bp.myts1) #plots the break date implied by the sup F test
bd.myts1 <- breakdates(bp.myts1) #Obtains the implied break data (2018.35,
# referring to day 128 (0.35*365 = day number))
sctest(test2) #Obtains a p-value for the implied breakpoint
ci.myts1 <- confint(bp.myts1) #95% CI for the location break date
plot(myts1)
lines(ci.myts1) #This shows the interval around the estimated break date
使用它我可以获得中断日期和95% CI，这告诉我发生了中断。但是，由于公式为 myts1~1，因此此中断是均值，反映了对常数的回归。如果我理解正确，残差是myts1的贬值值，因此我正在研究平均值的变化。该图使用中断日期和置信区间可视化数据。
问题
Q0：在开始这个分析之前，我想知道我是否应该关注这些预测误差是如何分布的以及如何针对某些特征进行校正？除了发生的中断和一些异常值之外，这似乎是一个相当稳定的过程。
Q1：如何计算方差的变化？我可以想象方差的变化也可能发生在与平均值不同的时间点？说方差的中断也是均值的中断是否正确，但是平方贬值序列的均值中断？没有太多可以找到的。
Q2：鉴于我现在已经获得了均值和方差中断的充分证据，我该如何量化这种变化？例如，在休息日之后，方差已从 X 转移到 Y？是否像沿休息日期拆分时间序列并汇总有关这两个部分的统计数据一样简单？
Q3：如果我对其他时间间隔重新运行中断分析，我如何比较不同预测范围内均值和方差的变化如何演变。这又是对统计数据的简单总结，还是有一个测试来评估错误的不同程度？
补充 Q3:##
在创建这些时间序列时，会考虑到预测事件发生前 10 小时的预测误差。
以一天为例：将预测分成 1 小时的 bin（创建 10 个 bin），然后在每个 bin 内，将所有预测汇总为加权平均值（根据不同的变量加权）。这意味着对于每一天，每个 bin 有一个加权分数（总共 10 个）。
将其转换为我在这篇文章中提供的时间序列对象（myts1，涵盖最后一小时）会产生以下结果：一个时间序列，其中每个点对应于给定时间间隔内当天的加权平均值。基本上每个 bin 包含 975 个不同的天数，每个天数的平均加权值（纯历史数据）。
我对这部分的想法：我添加了一张图片，其中包含 10 个垃圾箱中的 9 个垃圾箱，这清楚地表明，随着时间的推移，中断变得不那么明显了。鉴于这 10 个时间序列，我为每个时间序列重新运行“Score-CUSUM”（均值/方差）检验。从那里可以确定该系统的效果在哪个时间变得“明显”（如均值/方差的绝对变化）并且从操作的角度来看是可用的。
Q3.1这样分析时间序列有意义吗？我认为我重新运行 SCORE-CUSUM 测试 10 次并不重要？
Q3.1分割休息时如何处理跨越 6 个月的 95% CI？（在 4 小时后的垃圾箱中找到）
Q3.2在比较这 10 个时间间隔的不同模型（错误）时，我是否应该关注？
我希望我的解释足够，如有必要可以提供更多信息。
编辑：我添加了一个列格式的 csv 文件（由 ; 分隔），这还包括每天发生的事件数，但是，绘制时似乎没有相关性。链接：https ://www.dropbox.com/s/5pilmn43bps9ss4/Data.csv?dl=0
EDIT2：应该补充一点，实际实施发生在时间序列中的时间点 2018 年第 136 天左右。
EDIT3：将第 1 小时到第 2 小时的第二个预测间隔添加为 R 中 pastebin 中的 TS 对象： https ://pastebin.com/50sb4RtP （主帖字符限制）
