1
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TeX.SE meta proposed to predict when their number one user, egreg, will reach 654321 reputation points.

I made a prediction based on a linear interpolation of the 90 past days rep and then an extrapolation.

I think this is an interesting problem so I decided to post it here in case someone wanted to participate and expose his/her methodology. I also asked the question on MMA.SE.

Here is the data of egreg's daily rep for the past 1460 days:

{247105, 247380, 247670, 247915, 248205, 248450, 248710, 
   249035, 249310, 249615, 249860, 250135, 250380, 250655, 250915, 
   251190, 251390, 251650, 251865, 252155, 252400, 252730, 252990, 
   253310, 253540, 253785, 254045, 254275, 254535, 254780, 255085, 
   255330, 255575, 255790, 256005, 256295, 256570, 256800, 257075, 
   257350, 257580, 257900, 258190, 258495, 258785, 259030, 259350, 
   259610, 259900, 260115, 260420, 260665, 260895, 261155, 261400, 
   261675, 261920, 262210, 262485, 262760, 263035, 263265, 263525, 
   263830, 264075, 264320, 264800, 265030, 265245, 265520, 265780, 
   266057, 266272, 266547, 266837, 267142, 267422, 267832, 268077, 
   268322, 268627, 268932, 269177, 269422, 269682, 269897, 270172, 
   270492, 270737, 270967, 271227, 271457, 271717, 271962, 272222, 
   272497, 272787, 273017, 273307, 273582, 273827, 274287, 274517, 
   274747, 275037, 275347, 275637, 275912, 276232, 276447, 276692, 
   276982, 277272, 277577, 277822, 278067, 278342, 278602, 278922, 
   279197, 279472, 279732, 280022, 280297, 280557, 280817, 281092, 
   281367, 281612, 281857, 282102, 282377, 282669, 282944, 283219, 
   283464, 283724, 283954, 284199, 284444, 284779, 285009, 285449, 
   285679, 285954, 286214, 286489, 286749, 287009, 287269, 287514, 
   287744, 287944, 288219, 288509, 288814, 289091, 289351, 289581, 
   289841, 290071, 290451, 290726, 290971, 291246, 291466, 291726, 
   292016, 292291, 292551, 292796, 293026, 293256, 293516, 293791, 
   294126, 294371, 294631, 294876, 295106, 295426, 295701, 295976, 
   296281, 296601, 296861, 297091, 297336, 297581, 297916, 298191, 
   298466, 298756, 299016, 299246, 299476, 299766, 300026, 300271, 
   300501, 300806, 301036, 301341, 301646, 301991, 302221, 302511, 
   302756, 303001, 303216, 303461, 303676, 303966, 304226, 304421, 
   304651, 304896, 305171, 305416, 305646, 305876, 306106, 306351, 
   306626, 306871, 307086, 307361, 307591, 307866, 307991, 308251, 
   308496, 308726, 309081, 309311, 309556, 309896, 310141, 310341, 
   310601, 310906, 311181, 311426, 311701, 312021, 312356, 312601, 
   312891, 313181, 313396, 313686, 313976, 314251, 314576, 314821, 
   315126, 315356, 315661, 315951, 316211, 316471, 316731, 317006, 
   317266, 317556, 317801, 318061, 318336, 318611, 318886, 319191, 
   319481, 319801, 320061, 320321, 320596, 320901, 321116, 321421, 
   321666, 321926, 322201, 322576, 322806, 323006, 323281, 323556, 
   323831, 324136, 324426, 324671, 324931, 325176, 325451, 325681, 
   325956, 326231, 326491, 326721, 327026, 327291, 327536, 327871, 
   328146, 328361, 328606, 328866, 329141, 329401, 329661, 329891, 
   330181, 330441, 330716, 331011, 331376, 331681, 331911, 332216, 
   332461, 332691, 332921, 333196, 333471, 333701, 333961, 334221, 
   334496, 334771, 335081, 335281, 335571, 335876, 336156, 336376, 
   336636, 336851, 337126, 337406, 337606, 337881, 338141, 338371, 
   338616, 338891, 339181, 339426, 339801, 340061, 340321, 340581, 
   340826, 341056, 341331, 341621, 341836, 342126, 342416, 342691, 
   342921, 343181, 343381, 343656, 343916, 344221, 344526, 344726, 
   345001, 345276, 345536, 345796, 346026, 346301, 346531, 346791, 
   347066, 347341, 347601, 347876, 348106, 348426, 348821, 349066, 
   349326, 349601, 349876, 350136, 350531, 350776, 351036, 351281, 
   351541, 351771, 352031, 352336, 352551, 352796, 353071, 353361, 
   353651, 353926, 354156, 354276, 354521, 354796, 355041, 355271, 
   355591, 355881, 356126, 356356, 356676, 356936, 357226, 357546, 
   357791, 358066, 358341, 358601, 358801, 359076, 359336, 359551, 
   359781, 360011, 360301, 360546, 360791, 361096, 361296, 361541, 
   361831, 362076, 362321, 362671, 362946, 363176, 363421, 363666, 
   363881, 364111, 364401, 364691, 364936, 365181, 365456, 365716, 
   366021, 366296, 366571, 366846, 367076, 367291, 367666, 367956, 
   368201, 368461, 368781, 369041, 369301, 369576, 369806, 370096, 
   370356, 370631, 370936, 371166, 371426, 371656, 371931, 372221, 
   372451, 372726, 373046, 373336, 373611, 373946, 374176, 374496, 
   374756, 375001, 375261, 375506, 375751, 376106, 376381, 376656, 
   376871, 377141, 377521, 377751, 377996, 378316, 378636, 378941, 
   379216, 379491, 379781, 380056, 380331, 380576, 380806, 381111, 
   381341, 381726, 381986, 382261, 382506, 382751, 383011, 383241, 
   383516, 383746, 384021, 384296, 384526, 384771, 385031, 385456, 
   385731, 385991, 386281, 386441, 386716, 387041, 387301, 387591, 
   387881, 388156, 388466, 388786, 389031, 389311, 389601, 389906, 
   390166, 390411, 390656, 390886, 391206, 391451, 391666, 391926, 
   392186, 392491, 392751, 392996, 393241, 393501, 393761, 393991, 
   394266, 394526, 394801, 395106, 395396, 395716, 395931, 396131, 
   396346, 396576, 396781, 396996, 397211, 397356, 397561, 397806, 
   398036, 398326, 398571, 398891, 399121, 399351, 399596, 399791, 
   400081, 400371, 400616, 400781, 401026, 401316, 401546, 401821, 
   402066, 402296, 402586, 402891, 403151, 403396, 403596, 403841, 
   404056, 404271, 404506, 404781, 405041, 405286, 405576, 405821, 
   406181, 406396, 406641, 406931, 407176, 407521, 407826, 408071, 
   408286, 408531, 408881, 409126, 409356, 409616, 409721, 409996, 
   410256, 410546, 410776, 411186, 411463, 411663, 411923, 412213, 
   412473, 412703, 412948, 413223, 413398, 413613, 413903, 414193, 
   414453, 414743, 415018, 415263, 415568, 415903, 416133, 416408, 
   416668, 416898, 417203, 417493, 417768, 418073, 418363, 418653, 
   418883, 419128, 419388, 419648, 419938, 420183, 420473, 420733, 
   420993, 421298, 421543, 421863, 422138, 422413, 422703, 422993, 
   423348, 423578, 423898, 424158, 424448, 424693, 424953, 425243, 
   425503, 425868, 426143, 426418, 426648, 426878, 427168, 427443, 
   427703, 427948, 428193, 428483, 428743, 428988, 429278, 429613, 
   429873, 430148, 430408, 430658, 430903, 431148, 431453, 431713, 
   431988, 432218, 432478, 432708, 432998, 433258, 433563, 433793, 
   434068, 434358, 434663, 434923, 435183, 435428, 435703, 435993, 
   436238, 436528, 436743, 437033, 437323, 437568, 437813, 438073, 
   438363, 438653, 438881, 439143, 439388, 439618, 439908, 440138, 
   440383, 440643, 440978, 441298, 441563, 441778, 442023, 442268, 
   442528, 442773, 443033, 443283, 443528, 443773, 444078, 444338, 
   444583, 444878, 445198, 445488, 445733, 446038, 446283, 446573, 
   446833, 447078, 447308, 447613, 447888, 448163, 448438, 448713, 
   448988, 449218, 449493, 449843, 450213, 450533, 450823, 451158, 
   451463, 451753, 452043, 452243, 452533, 452823, 453098, 453388, 
   453633, 453893, 454153, 454413, 454688, 454918, 455163, 455453, 
   455698, 455898, 456173, 456508, 456798, 457073, 457378, 457668, 
   457928, 458203, 458493, 458753, 459013, 459258, 459533, 459778, 
   460038, 460283, 460543, 460833, 461063, 461278, 461523, 461783, 
   462013, 462258, 462533, 462808, 463083, 463358, 463603, 463818, 
   464093, 464338, 464628, 464888, 465183, 465428, 465688, 465918, 
   466163, 466423, 466773, 467033, 467308, 467613, 467933, 468193, 
   468398, 468613, 468918, 469163, 469468, 469778, 470023, 470343, 
   470603, 470848, 471140, 471400, 471645, 471860, 472120, 472380, 
   472715, 472990, 473250, 473495, 473705, 473965, 474210, 474470, 
   474715, 475035, 475280, 475555, 475785, 476045, 476260, 476490, 
   476735, 476995, 477260, 477475, 477675, 477995, 478255, 478515, 
   478760, 479005, 479235, 479540, 479755, 480000, 480230, 480505, 
   480720, 481010, 481170, 481445, 481735, 482045, 482350, 482565, 
   482840, 483145, 483405, 483620, 483865, 484155, 484315, 484560, 
   484820, 485035, 485310, 485555, 485815, 485895, 486155, 486385, 
   486675, 486920, 487135, 487365, 487595, 487870, 488130, 488390, 
   488635, 488865, 489140, 489360, 489575, 489880, 490225, 490470, 
   490745, 491035, 491235, 491590, 491850, 492050, 492280, 492540, 
   492755, 492935, 493060, 493255, 493530, 493805, 494185, 494430, 
   494620, 494885, 495145, 495375, 495635, 495895, 496140, 496420, 
   496640, 496900, 497190, 497435, 497745, 497960, 498050, 498265, 
   498495, 498770, 499000, 499230, 499435, 499625, 499870, 500145, 
   500360, 500620, 500880, 501110, 501220, 501465, 501680, 501970, 
   502245, 502475, 502720, 502830, 502965, 503195, 503415, 503720, 
   504025, 504270, 504515, 504775, 504990, 505235, 505555, 505785, 
   506060, 506275, 506505, 506765, 507025, 507255, 507500, 507775, 
   508035, 508280, 508540, 508815, 509045, 509305, 509520, 509765, 
   510010, 510270, 510515, 510745, 510975, 511190, 511450, 511680, 
   511910, 512125, 512355, 512615, 512830, 513060, 513260, 513425, 
   513685, 513960, 514205, 514495, 514740, 515015, 515260, 515535, 
   515810, 516025, 516240, 516470, 516730, 516990, 517235, 517480, 
   517695, 517970, 518200, 518460, 518720, 518980, 519195, 519440, 
   519687, 519947, 520207, 520482, 520742, 521017, 521234, 521464, 
   521694, 521907, 522167, 522367, 522597, 522812, 523057, 523317, 
   523452, 523712, 523957, 524187, 524432, 524662, 524967, 525117, 
   525422, 525727, 525987, 526232, 526492, 526692, 526952, 527212, 
   527457, 527672, 527932, 528132, 528437, 528727, 528957, 529202, 
   529462, 529677, 530007, 530252, 530497, 530787, 531047, 531247, 
   531492, 531707, 531937, 532152, 532412, 532612, 532887, 533102, 
   533347, 533622, 533867, 534097, 534357, 534587, 534862, 535092, 
   535367, 535642, 535887, 536087, 536317, 536562, 536805, 537097, 
   537327, 537572, 537802, 538017, 538262, 538537, 538857, 539102, 
   539362, 539652, 539791, 540066, 540281, 540511, 540756, 540986, 
   541246, 541491, 541781, 542056, 542316, 542591, 542851, 543126, 
   543341, 543586, 543831, 544076, 544321, 544581, 544841, 545071, 
   545391, 545651, 545926, 546186, 546416, 546736, 546996, 547211, 
   547426, 547746, 547991, 548236, 548511, 548741, 548956, 549166, 
   549396, 549611, 549841, 550116, 550361, 550591, 550821, 551051, 
   551281, 551511, 551786, 552016, 552274, 552564, 552809, 553039, 
   553269, 553514, 553774, 554019, 554264, 554524, 554814, 555074, 
   555289, 555579, 555824, 556024, 556239, 556561, 556791, 557036, 
   557281, 557511, 557756, 558031, 558261, 558536, 558781, 559011, 
   559256, 559516, 559776, 560021, 560341, 560586, 560831, 561091, 
   561351, 561811, 562086, 562346, 562591, 562791, 563036, 563266, 
   563481, 563726, 563971, 564216, 564446, 564646, 564906, 565151, 
   565411, 565686, 565931, 566161, 566421, 566651, 566866, 567186, 
   567416, 567646, 567891, 568121, 568366, 568581, 568826, 569101, 
   569346, 569636, 569851, 570066, 570341, 570556, 570786, 571136, 
   571381, 571656, 571871, 572144, 572334, 572794, 573054, 573284, 
   573544, 573804, 573999, 574244, 574459, 574689, 574919, 575209, 
   575439, 575699, 575899, 576114, 576359, 576604, 576819, 577099, 
   577374, 577604, 577879, 578139, 578384, 578614, 578874, 579119, 
   579349, 579594, 579869, 580114, 580359, 580589, 580834, 581099, 
   581329, 581544, 581819, 582019, 582234, 582494, 582754, 583244, 
   583504, 583749, 583979, 584194, 584314, 584459, 584694, 584909, 
   585109, 585354, 585599, 585754, 585984, 586214, 586474, 586719, 
   586919, 587179, 587414, 587614, 587859, 588074, 588334, 588639, 
   588839, 588979, 589064, 589309, 589509, 589754, 589969, 590199, 
   590414, 590609, 590839, 591084, 591314, 591589, 591819, 592034, 
   592224, 592469, 592669, 592884, 593129, 593329, 593539, 593739, 
   593999, 594214, 594474, 594704, 594934, 595224, 595484, 595759, 
   596019, 596309, 596629, 596889, 597094, 597324, 597584, 597799, 
   598119, 598379, 598609, 598824, 599052, 599269, 599544, 599729, 
   600004, 600234, 600494, 600724, 600954, 601229, 601459, 601689, 
   601979, 602129, 602344, 602579, 602794, 603039, 603299, 603544, 
   603689, 603809, 604039, 604284, 604529, 604744, 604974, 605174, 
   605419, 605749, 605994, 606289, 606519, 606794, 607039, 607269, 
   607544, 607804, 608034, 608294, 608524, 608829, 609119, 609334, 
   609579, 609794, 610084, 610329, 610544, 610789, 611064, 611294, 
   611539, 611799, 612014, 612234, 612509, 612769, 613029, 613289, 
   613504, 613749, 613979, 614239, 614499, 614744, 614974, 615204, 
   615419, 615694, 615939, 616169, 616459, 616704, 616919, 617119, 
   617364, 617609, 617854, 618114, 618344, 618589, 618849, 619094, 
   619249, 619434, 619644, 619889, 620149, 620379, 620574, 620834, 
   621064, 621279, 621584, 621829, 622032}
$\endgroup$
  • $\begingroup$ The problem is unusual insofar as the individual concerned has substantial control over the date. He could decide to stop answering, for instance, to delay the date. $\endgroup$ – whuber Jan 5 '18 at 21:59
  • $\begingroup$ @whuber That's right, but we can assume he is not aware of the post. I'm not looking for the best estimate, but for a good methodology to make the estimation (assuming the reputation is not affected by the meta post). We could assume the rep is a stock value for example. $\endgroup$ – anderstood Jan 5 '18 at 22:03
  • 2
    $\begingroup$ I wrote that comment only after confirming that he is aware of the post, so that assumption is moot. This circumstance throws doubt on any standard choice of methodology. If you don't want to treat this particular problem on its own merits, then I don't think it belongs here: we already have plenty of posts covering methods of predicting time series. $\endgroup$ – whuber Jan 5 '18 at 22:07
  • 1
    $\begingroup$ @whuber OK, I understand. I think there is too much uncertainties to consider the awareness of the individual, so it falls into predicting time series and then I guess it is a duplicate. I'll look for a similar post and flag it as duplicate when I have time. $\endgroup$ – anderstood Jan 5 '18 at 22:11
  • 1
    $\begingroup$ Best to look at the forecasting tag. I personally would try forecasting daily reputation gain (i.e., first differences), using a seasonal model to capture potential weekly seasonality. For instance, forecast::ets() from R fits a model with additive error, no trend and additive weekly seasonality, which you can use to forecast. Forecasting: Principles and Practice by Hyndman & Athanasopoulos is an excellent forecasting textbook. $\endgroup$ – S. Kolassa - Reinstate Monica Jan 6 '18 at 10:47