由于“非遗漏观察次数太少”错误导致R中的ARIMA预测脚本出现问题，并且希望在自己对其进行故障排除失败后寻求一些帮助。
我的确切脚本非常简单，如下所示：
library(forecast)
SalesData <- aggregate(Revenue~SalesCategory+Month, data = dataset, FUN = sum)
SalesForecast <- ts(SalesData$Revenue, start = 0, freq = 12)
fit <- arima(log(SalesForecast), c(1, 1, 0),
seasonal = list(order = c(1, 1, 0),
period = 12))
pred <- predict(fit, n.ahead = 12)
Adjusted.pred <- (2.718^pred$pred)
ts.plot(SalesForecast,Adjusted.pred, log = "y", ylab= "Revenue",
lty = c(1,3),main = "Forecasted Revenue", xlab ="Fiscal Year Months")
值得注意的是，我的销售数据是季节性的，从2013年7月到2016年8月延伸。在此期间，某些产品已被弃用或新增。在重新确定优先级之前，还有一些产品被弃用了几个月，我认为这可能是问题的根本原因。
感谢关于可能是一个非常基本的问题的任何和所有帮助或指导。
最佳， 杰克
Month Revenue SalesCategory
6/1/2014 872.446483 Orange
7/1/2014 27415.60511 Orange
8/1/2014 74292.08374 Orange
9/1/2014 120817.748 Orange
10/1/2014 163667.9254 Orange
11/1/2014 361728.9997 Orange
12/1/2014 287626.8962 Orange
1/1/2015 256132.8191 Orange
2/1/2015 281025.9382 Orange
3/1/2015 622223.3008 Orange
4/1/2015 354815.5095 Orange
5/1/2015 265576.7564 Orange
6/1/2015 360826.4308 Orange
7/1/2013 588025.0006 Blue
8/1/2013 652617.4266 Blue
9/1/2013 650277.7455 Blue
10/1/2013 724311.5886 Blue
11/1/2013 674752.8929 Blue
12/1/2013 871649.6068 Blue
1/1/2014 422410.6554 Blue
2/1/2014 414430.5516 Blue
3/1/2014 399161.6918 Blue
4/1/2014 370860.6502 Blue
5/1/2014 541905.025 Blue
6/1/2014 516731.6737 Blue
7/1/2014 385695.9653 Blue
8/1/2014 449845.4301 Blue
9/1/2014 293212.8969 Blue
10/1/2014 196985.2955 Blue
11/1/2014 230369.0426 Blue
12/1/2014 375275.1204 Blue
1/1/2015 128554.7657 Blue
2/1/2015 136430.5672 Blue
3/1/2015 136033.0716 Blue
4/1/2015 125635.0309 Blue
5/1/2015 152383.778 Blue
6/1/2015 11891.35223 Blue
7/1/2015 10.78232 Blue
8/1/2015 8.600054 Blue
9/1/2015 6.125262 Blue
10/1/2015 3.688184 Blue
11/1/2015 2.378511 Blue
12/1/2015 0.8949777 Blue
1/1/2016 0.1565892 Blue
2/1/2016 0.1817317 Blue
3/1/2016 0.07015 Blue
4/1/2016 0.0327 Blue
5/1/2016 496.01171 Blue
6/1/2016 0 Blue
7/1/2016 0 Blue
8/1/2016 0 Blue
10/1/2014 22559.14026 Black
11/1/2014 113413.3118 Black
12/1/2014 355487.1326 Black
1/1/2015 475413.4705 Black
2/1/2015 541123.0262 Black
3/1/2015 658523.3192 Black
4/1/2015 539569.5451 Black
5/1/2015 537714.0264 Black
6/1/2015 540749.4187 Black
7/1/2015 0 Black
2/1/2014 1045.282484 Gray
3/1/2014 0.01048 Gray
4/1/2014 0 Gray
5/1/2014 0 Gray
12/1/2015 0.4567944 Gray
1/1/2016 67.2964458 Gray
2/1/2016 65.2405035 Gray
3/1/2016 38.7794443 Gray
7/1/2013 103454.2354 White
8/1/2013 171370.7464 White
9/1/2013 283079.2564 White
10/1/2013 424687.7054 White
11/1/2013 612376.0585 White
12/1/2013 945304.5281 White
1/1/2014 341919.2179 White
2/1/2014 478848.2671 White
3/1/2014 774880.0632 White
4/1/2014 686531.079 White
5/1/2014 572505.1634 White
6/1/2014 663797.2645 White
7/1/2014 430098.5142 White
8/1/2014 346898.352 White
9/1/2014 353184.9587 White
10/1/2014 161663.4499 White
11/1/2014 216238.9023 White
12/1/2014 357995.1503 White
1/1/2015 167716.8869 White
2/1/2015 99321.08561 White
3/1/2015 90474.87056 White
4/1/2015 54755.43886 White
5/1/2015 44959.11504 White
6/1/2015 60601.33456 White
7/1/2015 28816.2135 White
8/1/2015 23525.2123 White
9/1/2015 22023.87244 White
10/1/2015 500.628171 White
11/1/2015 11.740983 White
12/1/2015 1.4085756 White
1/1/2016 0.1890511 White
2/1/2016 0.073819 White
3/1/2016 0.1150476 White
4/1/2016 0.0050657 White
5/1/2016 0 White
6/1/2016 0 White
7/1/2016 0 White
8/1/2016 0 White
7/1/2013 485.4243975 Red
8/1/2013 3.39293577 Red
9/1/2013 5.42042393 Red
10/1/2013 8.174868 Red
11/1/2013 8.86948286 Red
12/1/2013 7.27585039 Red
1/1/2014 153.964892 Red
2/1/2014 62.817221 Red
3/1/2014 229.942113 Red
4/1/2014 66.312332 Red
5/1/2014 107.612302 Red
6/1/2014 449.725595 Red
7/1/2014 1652.623186 Red
8/1/2014 2635.510635 Red
9/1/2014 876.361173 Red
10/1/2014 836.938981 Red
11/1/2014 1843.838808 Red
12/1/2014 1918.480787 Red
1/1/2015 0.002048 Red
2/1/2015 0.001432 Red
3/1/2015 0.001059 Red
4/1/2015 0.001613 Red
5/1/2015 0.00135 Red
8/1/2015 0.001 Red
2/1/2016 0.0018374 Red
9/1/2014 0.002087 Yellow
10/1/2014 0 Yellow
11/1/2014 0 Yellow
12/1/2014 0 Yellow
1/1/2015 0 Yellow
2/1/2015 0 Yellow
3/1/2015 242.63139 Yellow
4/1/2015 393.517539 Yellow
5/1/2015 551.942596 Yellow
6/1/2015 544.338007 Yellow
7/1/2015 0 Yellow
8/1/2015 0 Yellow
9/1/2015 0 Yellow
10/1/2015 0 Yellow
11/1/2015 0 Yellow
12/1/2015 232.3945437 Yellow
1/1/2016 187.0862765 Yellow
2/1/2016 0 Yellow
3/1/2016 0 Yellow
4/1/2016 0 Yellow
5/1/2016 0 Yellow
6/1/2016 0 Yellow
7/1/2016 0 Yellow
8/1/2016 0 Yellow
7/1/2013 6.57399404 Teal
8/1/2013 4.94998805 Teal
9/1/2013 9.00774152 Teal
10/1/2013 9.49746566 Teal
11/1/2013 11.31726121 Teal
12/1/2013 9.68909605 Teal
1/1/2014 4.378742 Teal
2/1/2014 4.268959 Teal
3/1/2014 7.889073 Teal
4/1/2014 1.642041 Teal
7/1/2013 0.07857562 Green
8/1/2013 0.02407967 Green
9/1/2013 0.07290788 Green
10/1/2013 0.08540275 Green
11/1/2013 0.05424165 Green
12/1/2013 0.03448481 Green
1/1/2014 0.019639 Green
2/1/2014 0.027405 Green
3/1/2014 0.056806 Green
4/1/2014 0.031718 Green
5/1/2014 0.01583 Green
9/1/2014 6.092477 Maroon
10/1/2014 2.125143 Maroon
11/1/2014 20.971927 Maroon
12/1/2014 5.884376 Maroon
1/1/2015 3.470562 Maroon
2/1/2015 585.412606 Maroon
3/1/2015 22686.97242 Maroon
4/1/2015 97067.40143 Maroon
5/1/2015 121869.2472 Maroon
6/1/2015 135214.5345 Maroon
7/1/2015 89336.47872 Maroon
8/1/2015 92444.65462 Maroon
9/1/2015 132310.2372 Maroon
10/1/2015 115558.5213 Maroon
11/1/2015 162780.6291 Maroon
12/1/2015 163722.6052 Maroon
1/1/2016 104097.89 Maroon
2/1/2016 80201.75931 Maroon
3/1/2016 103797.0382 Maroon
4/1/2016 81507.72535 Maroon
5/1/2016 107493.1832 Maroon
6/1/2016 115225.8871 Maroon
7/1/2016 100779.4421 Maroon
8/1/2016 161750.5709 Maroon
7/1/2013 942744.6418 Burnt Orange
8/1/2013 1008340.789 Burnt Orange
9/1/2013 889803.7261 Burnt Orange
10/1/2013 656217.2015 Burnt Orange
11/1/2013 952755.3652 Burnt Orange
12/1/2013 375981.9599 Burnt Orange
1/1/2014 1209321.384 Burnt Orange
2/1/2014 614167.0686 Burnt Orange
3/1/2014 732154.595 Burnt Orange
4/1/2014 1147855.821 Burnt Orange
5/1/2014 1279385.815 Burnt Orange
6/1/2014 1131145.804 Burnt Orange
7/1/2014 1609763.532 Burnt Orange
8/1/2014 1700764.693 Burnt Orange
9/1/2014 1474718.508 Burnt Orange
10/1/2014 1242259.623 Burnt Orange
11/1/2014 1458237.902 Burnt Orange
12/1/2014 1659004.632 Burnt Orange
1/1/2015 3653607.043 Burnt Orange
2/1/2015 2868265.459 Burnt Orange
3/1/2015 3745311.011 Burnt Orange
4/1/2015 4083569.698 Burnt Orange
5/1/2015 3538107.069 Burnt Orange
6/1/2015 5663504.216 Burnt Orange
7/1/2015 5930931.827 Burnt Orange
8/1/2015 6106445.836 Burnt Orange
9/1/2015 7059156.619 Burnt Orange
10/1/2015 9506117.045 Burnt Orange
11/1/2015 7705094.509 Burnt Orange
12/1/2015 9461014.627 Burnt Orange
1/1/2016 9139009.685 Burnt Orange
2/1/2016 6679580.978 Burnt Orange
3/1/2016 8733237.033 Burnt Orange
4/1/2016 7139955.952 Burnt Orange
5/1/2016 8094093.819 Burnt Orange
6/1/2016 9255422.036 Burnt Orange
7/1/2016 9234943.809 Burnt Orange
8/1/2016 9025449.124 Burnt Orange
7/1/2013 0.00091391 Eggshell
9/1/2013 7.69E-05 Eggshell
10/1/2013 0.0003914 Eggshell
11/1/2013 0.00106852 Eggshell
5/1/2014 0.00027 Eggshell
10/1/2014 9600.611335 Eggshell
11/1/2014 39213.39315 Eggshell
12/1/2014 49611.47325 Eggshell
1/1/2015 39488.54573 Eggshell
2/1/2015 40038.75978 Eggshell
3/1/2015 57500.30278 Eggshell
4/1/2015 58967.08286 Eggshell
5/1/2015 119418.2945 Eggshell
6/1/2015 197875.903 Eggshell
7/1/2015 208291.0205 Eggshell
8/1/2015 199556.3633 Eggshell
9/1/2015 181935.77 Eggshell
10/1/2015 187274.8072 Eggshell
11/1/2015 265091.7069 Eggshell
12/1/2015 235995.82 Eggshell
1/1/2016 162704.3921 Eggshell
2/1/2016 145915.697 Eggshell
3/1/2016 207327.3106 Eggshell
4/1/2016 142476.5606 Eggshell
5/1/2016 185868.0071 Eggshell
6/1/2016 225289.5468 Eggshell
7/1/2016 244246.1984 Eggshell
8/1/2016 244572.2056 Eggshell
7/1/2013 2301622.029 Navy
8/1/2013 2146835.127 Navy
9/1/2013 2038147.979 Navy
10/1/2013 2602763.799 Navy
11/1/2013 2120077.201 Navy
12/1/2013 2100953.325 Navy
1/1/2014 1999920.1 Navy
2/1/2014 1703563.642 Navy
3/1/2014 1669073.378 Navy
4/1/2014 2305637.784 Navy
5/1/2014 2634698.51 Navy
6/1/2014 1687723.38 Navy
7/1/2014 2084579.625 Navy
8/1/2014 2350005.581 Navy
9/1/2014 1573464.772 Navy
10/1/2014 1951579.145 Navy
11/1/2014 3237249.833 Navy
12/1/2014 4171508.264 Navy
1/1/2015 4393928.246 Navy
2/1/2015 5027010.258 Navy
3/1/2015 7353014.705 Navy
4/1/2015 6818122.133 Navy
5/1/2015 7496166.93 Navy
6/1/2015 8110138.619 Navy
7/1/2015 6613409.673 Navy
8/1/2015 7700758.114 Navy
9/1/2015 8873506.303 Navy
10/1/2015 8607743.379 Navy
11/1/2015 8402456.283 Navy
12/1/2015 9140438.689 Navy
1/1/2016 8275840.634 Navy
2/1/2016 7395649.898 Navy
3/1/2016 7866524.705 Navy
4/1/2016 8085877.718 Navy
5/1/2016 9916552.566 Navy
6/1/2016 10679960.28 Navy
7/1/2016 9633510.896 Navy
8/1/2016 9676609.089 Navy
7/1/2013 307.5433145 Purple
8/1/2013 278.1919963 Purple
9/1/2013 287.8129872 Purple
10/1/2013 398.9677103 Purple
11/1/2013 519.0542504 Purple
12/1/2013 635.7302839 Purple
1/1/2014 476.532828 Purple
2/1/2014 235.580273 Purple
3/1/2014 263.450333 Purple
4/1/2014 305.085377 Purple
5/1/2014 524.16711 Purple
6/1/2014 810.060485 Purple
7/1/2014 1010.30702 Purple
8/1/2014 1129.007214 Purple
9/1/2014 1255.477696 Purple
10/1/2014 2.923276 Purple
11/1/2014 0.008834 Purple
12/1/2014 0.004957 Purple
1/1/2015 0.000673 Purple
2/1/2015 0.000973 Purple
3/1/2015 0.001761 Purple
4/1/2015 0 Purple
5/1/2015 0 Purple
6/1/2015 0.000257 Purple
7/1/2015 0.001083 Purple
8/1/2015 0.000198 Purple
9/1/2015 0 Purple
10/1/2015 0.001564 Purple
11/1/2015 0.004523 Purple
12/1/2015 0.0086669 Purple
1/1/2016 0.0025812 Purple
2/1/2016 0.0291021 Purple
3/1/2016 0.0047537 Purple
7/1/2013 0 Violet
11/1/2013 39981.47669 Pink
12/1/2013 292326.5036 Pink
1/1/2014 404725.4259 Pink
2/1/2014 425130.3693 Pink
3/1/2014 614204.0834 Pink
4/1/2014 625968.1274 Pink
5/1/2014 831838.5996 Pink
6/1/2014 1078311.547 Pink
7/1/2014 1180858.811 Pink
8/1/2014 1559672.695 Pink
9/1/2014 1665072.057 Pink
10/1/2014 2221061.833 Pink
11/1/2014 2421959.818 Pink
12/1/2014 2361507.542 Pink
1/1/2015 3438545.036 Pink
2/1/2015 4781433.951 Pink
3/1/2015 5580747.858 Pink
4/1/2015 6009637.904 Pink
5/1/2015 6371627.215 Pink
6/1/2015 8011311.62 Pink
7/1/2015 8377299.761 Pink
8/1/2015 7955153.098 Pink
9/1/2015 8433538.874 Pink
10/1/2015 8949395.599 Pink
11/1/2015 9243816.7 Pink
12/1/2015 10195777.34 Pink
1/1/2016 8187700.993 Pink
2/1/2016 8637261.85 Pink
3/1/2016 9638219.75 Pink
4/1/2016 8915953.669 Pink
5/1/2016 10642506.11 Pink
6/1/2016 10080321.64 Pink
7/1/2016 9666473.977 Pink
8/1/2016 9213704.343 Pink
9/1/2014 0 Brown
10/1/2014 1475.734616 Brown
11/1/2014 10034.69818 Brown
12/1/2014 26777.75776 Brown
1/1/2015 20410.24773 Brown
2/1/2015 9221.681913 Brown
3/1/2015 0 Brown
4/1/2015 0 Brown
5/1/2015 0 Brown
6/1/2015 5423.614942 Brown
7/1/2015 4036.495819 Brown
8/1/2015 393.553677 Brown
9/1/2015 696.459359 Brown
10/1/2015 727.303977 Brown
11/1/2015 695.417502 Brown
12/1/2015 582.9390027 Brown
1/1/2016 312.1278448 Brown
2/1/2016 274.445592 Brown
3/1/2016 63.3483473 Brown
4/1/2016 63.7311201 Brown
5/1/2016 42.7281731 Brown
6/1/2016 82.7233785 Brown
7/1/2016 145.0530579 Brown
8/1/2016 97.7986379 Brown
7/1/2013 235605.6914 Cyan
8/1/2013 174622.2269 Cyan
9/1/2013 120922.6272 Cyan
10/1/2013 196018.4043 Cyan
11/1/2013 288439.6165 Cyan
12/1/2013 510395.0504 Cyan
1/1/2014 433112.6638 Cyan
2/1/2014 749648.1663 Cyan
3/1/2014 737664.4143 Cyan
4/1/2014 715366.6502 Cyan
5/1/2014 686836.1374 Cyan
6/1/2014 817068.5427 Cyan
7/1/2014 719814.6628 Cyan
8/1/2014 689273.6975 Cyan
9/1/2014 770560.6247 Cyan
10/1/2014 839842.8723 Cyan
11/1/2014 851839.7291 Cyan
12/1/2014 863758.5806 Cyan
1/1/2015 590566.349 Cyan
2/1/2015 753776.062 Cyan
3/1/2015 917969.4341 Cyan
4/1/2015 965800.3896 Cyan
5/1/2015 1309092.636 Cyan
6/1/2015 1609904.565 Cyan
7/1/2015 1749263.709 Cyan
8/1/2015 1619434.314 Cyan
9/1/2015 2247759.634 Cyan
10/1/2015 2106483.207 Cyan
11/1/2015 2487187.756 Cyan
12/1/2015 2978032.534 Cyan
1/1/2016 1549134.595 Cyan
2/1/2016 1318296.68 Cyan
3/1/2016 1367194.991 Cyan
4/1/2016 632784.8528 Cyan
5/1/2016 1097796.288 Cyan
6/1/2016 1381051.439 Cyan
7/1/2016 1362576.1 Cyan
8/1/2016 1231926.391 Cyan
11/1/2014 16068.34495 Beige
12/1/2014 31279.44024 Beige
1/1/2015 0 Beige
2/1/2015 9519.657647 Beige
3/1/2015 84356.80876 Beige
4/1/2015 27815.33338 Beige
5/1/2015 8910.925482 Beige
6/1/2015 23344.09193 Beige
7/1/2015 7102.864199 Beige
8/1/2015 10362.03059 Beige
9/1/2015 6908.249406 Beige
10/1/2015 2394.662506 Beige
11/1/2015 6175.75741 Beige
12/1/2015 53700.08375 Beige
1/1/2016 15125.61961 Beige
2/1/2016 27.3084663 Beige
3/1/2016 0 Beige
4/1/2016 0 Beige
7/1/2015 501293.1482 Ivory
8/1/2015 410481.8783 Ivory
9/1/2015 525918.0836 Ivory
10/1/2015 542000.9188 Ivory
11/1/2015 594542.3264 Ivory
12/1/2015 768509.7769 Ivory
1/1/2016 443500.4486 Ivory
2/1/2016 324006.8477 Ivory
3/1/2016 239338.2974 Ivory
4/1/2016 273324.6036 Ivory
5/1/2016 409295.775 Ivory
6/1/2016 700378.9515 Ivory
7/1/2016 401957.6123 Ivory
8/1/2016 447519.7246 Ivory
7/1/2015 1126000.497 Pearl
8/1/2015 951537.4082 Pearl
9/1/2015 786532.6702 Pearl
10/1/2015 841154.3312 Pearl
11/1/2015 905319.6045 Pearl
12/1/2015 956852.9913 Pearl
1/1/2016 789439.4999 Pearl
2/1/2016 674985.6733 Pearl
3/1/2016 574696.5649 Pearl
4/1/2016 518249.4672 Pearl
5/1/2016 510927.4347 Pearl
6/1/2016 595487.3358 Pearl
7/1/2016 466223.3599 Pearl
8/1/2016 579063.8057 Pearl
7/1/2013 12145.51106 Seashell
8/1/2013 13982.8085 Seashell
9/1/2013 12953.67461 Seashell
10/1/2013 10982.11483 Seashell
11/1/2013 6659.117341 Seashell
12/1/2013 8603.827681 Seashell
1/1/2014 5613.780341 Seashell
2/1/2014 5704.915496 Seashell
3/1/2014 5447.09463 Seashell
4/1/2014 4906.073997 Seashell
5/1/2014 5479.032855 Seashell
6/1/2014 5042.746803 Seashell
7/1/2014 3847.818508 Seashell
8/1/2014 5734.458982 Seashell
9/1/2014 6704.587544 Seashell
10/1/2014 7647.074472 Seashell
11/1/2014 6196.864341 Seashell
12/1/2014 7559.830528 Seashell
1/1/2015 4774.247942 Seashell
2/1/2015 5755.55747 Seashell
3/1/2015 9360.679541 Seashell
4/1/2015 8277.280102 Seashell
5/1/2015 9337.191566 Seashell
6/1/2015 9434.954193 Seashell
7/1/2015 7901.575492 Seashell
8/1/2015 7505.799573 Seashell
9/1/2015 8586.209186 Seashell
10/1/2015 9199.235295 Seashell
11/1/2015 10814.8075 Seashell
12/1/2015 10431.21367 Seashell
1/1/2016 4813.805788 Seashell
2/1/2016 4798.322306 Seashell
3/1/2016 6250.045823 Seashell
4/1/2016 4286.18379 Seashell
5/1/2016 4479.507199 Seashell
6/1/2016 24.9639029 Seashell
7/1/2016 0.0166208 Seashell
8/1/2016 0.010681 Seashell
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10/1/2014 9386.679222 Vanilla
11/1/2014 62678.75641 Vanilla
12/1/2014 142998.4728 Vanilla
1/1/2015 88825.31542 Vanilla
2/1/2015 63402.49197 Vanilla
3/1/2015 119038.8152 Vanilla
4/1/2015 79002.37486 Vanilla
5/1/2015 71813.21074 Vanilla
6/1/2015 73068.08446 Vanilla
7/1/2015 58905.05844 Vanilla
8/1/2015 92645.82262 Vanilla
9/1/2015 220728.7663 Vanilla
10/1/2015 180677.913 Vanilla
11/1/2015 255986.6834 Vanilla
12/1/2015 282965.9907 Vanilla
1/1/2016 178225.1344 Vanilla
2/1/2016 176192.8082 Vanilla
3/1/2016 157988.8095 Vanilla
4/1/2016 154261.6344 Vanilla
5/1/2016 382507.0115 Vanilla
6/1/2016 512505.9376 Vanilla
7/1/2016 436928.8583 Vanilla
8/1/2016 478834.7415 Vanilla
9/1/2014 0 Taupe
10/1/2014 0 Taupe
11/1/2014 0 Taupe
12/1/2014 0 Taupe
1/1/2015 0 Taupe
2/1/2015 0 Taupe
3/1/2015 0 Taupe
4/1/2015 0 Taupe
5/1/2015 0 Taupe
6/1/2015 0 Taupe
7/1/2015 0 Taupe
8/1/2015 0 Taupe
9/1/2015 0 Taupe
10/1/2015 0 Taupe
11/1/2015 769.552092 Taupe
12/1/2015 777.2842088 Taupe
1/1/2016 471.9138592 Taupe
2/1/2016 182.6314588 Taupe
3/1/2016 427.5499355 Taupe
4/1/2016 376.1232696 Taupe
5/1/2016 457.9525202 Taupe
6/1/2016 557.8859334 Taupe
7/1/2016 794.7244974 Taupe
8/1/2016 741.0160445 Taupe
7/1/2013 165887.3494 Silver
8/1/2013 182241.6242 Silver
9/1/2013 171394.3484 Silver
10/1/2013 213335.5572 Silver
11/1/2013 227834.7215 Silver
12/1/2013 293496.5852 Silver
1/1/2014 134654.95 Silver
2/1/2014 115044.6029 Silver
3/1/2014 183967.1646 Silver
4/1/2014 184941.7302 Silver
5/1/2014 204545.9821 Silver
6/1/2014 215482.2549 Silver
7/1/2014 173641.8665 Silver
8/1/2014 181926.7956 Silver
9/1/2014 164437.0225 Silver
10/1/2014 215872.1443 Silver
11/1/2014 238221.9449 Silver
12/1/2014 266033.0641 Silver
1/1/2015 144658.1936 Silver
2/1/2015 172184.7977 Silver
3/1/2015 278659.7936 Silver
4/1/2015 225761.0271 Silver
5/1/2015 265556.131 Silver
6/1/2015 269989.4074 Silver
7/1/2015 180198.494 Silver
8/1/2015 219580.0754 Silver
9/1/2015 232183.1621 Silver
10/1/2015 231797.2037 Silver
11/1/2015 239490.8623 Silver
12/1/2015 248202.5771 Silver
1/1/2016 133143.5545 Silver
2/1/2016 127801.4308 Silver
3/1/2016 159318.4877 Silver
4/1/2016 140068.919 Silver
5/1/2016 130573.4838 Silver
6/1/2016 81448.51397 Silver
7/1/2016 134755.0469 Silver
8/1/2016 168724.2546 Silver