Discussion #1

library(forecast)
## Warning: package 'forecast' was built under R version 3.4.3
library(xts)
## Warning: package 'xts' was built under R version 3.4.2
## Loading required package: zoo
## Warning: package 'zoo' was built under R version 3.4.2
## 
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric
library(TTR)
## Warning: package 'TTR' was built under R version 3.4.3
library(tseries)
## Warning: package 'tseries' was built under R version 3.4.3
g<-read.csv("D:/Boston College/MS AE Courses/Spring 2018 - Forecasting Predictive Analytics/Discussions - weekly/GOOG.csv")
# Alerternates of reading this data
# getSymbols("GOOG",from = "2015-03-14",to = "2018-03-14",src = "yahoo")
# g1<-get.hist.quote(instrument = "GOOG", start="2016-03-14", end=Sys.Date(),quote = "AdjClose")
# head(g1)
# g2<-read.csv(file.choose(),header=T)
# head(g2)


names(g)
## [1] "Date"      "Open"      "High"      "Low"       "Close"     "Adj.Close"
## [7] "Volume"
head(g)
##         Date   Open   High     Low  Close Adj.Close  Volume
## 1 2016-03-16 726.37 737.47 724.510 736.09    736.09 1624400
## 2 2016-03-17 736.45 743.07 736.000 737.78    737.78 1860800
## 3 2016-03-18 741.86 742.00 731.830 737.60    737.60 2980700
## 4 2016-03-21 736.50 742.50 733.516 742.09    742.09 1836500
## 5 2016-03-22 737.46 745.00 737.460 740.75    740.75 1269700
## 6 2016-03-23 742.36 745.72 736.150 738.06    738.06 1432100
g<-data.frame(g,o=order(g$Date,decreasing=FALSE))
g=g[,1:7]

# Plot original series
plot(g$Adj.Close,type="l",xlab="time",ylab="closing price",main="historical data")

# additional plots
monthplot(g$Adj.Close)

#seasonplot(g$Adj.Close)
# Data is not seasonal - breaks into an error 

g.ts<-ts(g, start=c(2016, 3), end=c(2018,3), frequency=252)
#plot(g.ts)


g.ts.f<-forecast(g$Adj.Close, 21)
plot(g.ts.f)

g.ts.f
##     Point Forecast    Lo 80    Hi 80    Lo 95    Hi 95
## 505        1149.58 1132.987 1166.173 1124.203 1174.957
## 506        1149.58 1126.114 1173.046 1113.692 1185.468
## 507        1149.58 1120.840 1178.320 1105.626 1193.534
## 508        1149.58 1116.393 1182.767 1098.825 1200.335
## 509        1149.58 1112.475 1186.685 1092.832 1206.328
## 510        1149.58 1108.932 1190.228 1087.414 1211.746
## 511        1149.58 1105.674 1193.486 1082.431 1216.729
## 512        1149.58 1102.641 1196.519 1077.793 1221.367
## 513        1149.58 1099.792 1199.368 1073.436 1225.724
## 514        1149.58 1097.097 1202.063 1069.315 1229.845
## 515        1149.58 1094.534 1204.626 1065.394 1233.766
## 516        1149.58 1092.084 1207.075 1061.648 1237.512
## 517        1149.58 1089.735 1209.425 1058.055 1241.105
## 518        1149.58 1087.474 1211.686 1054.597 1244.563
## 519        1149.58 1085.292 1213.868 1051.260 1247.900
## 520        1149.58 1083.182 1215.978 1048.032 1251.127
## 521        1149.58 1081.136 1218.024 1044.904 1254.256
## 522        1149.58 1079.149 1220.010 1041.866 1257.294
## 523        1149.58 1077.217 1221.943 1038.911 1260.249
## 524        1149.58 1075.335 1223.825 1036.032 1263.128
## 525        1149.58 1073.499 1225.661 1033.224 1265.936

Flat forecasts instead were fixed with the exponential model

# Exponential Time Series
g.ts.ets<-ets(g$Adj.Close)
plot(g.ts.ets)

g.ts.ets
## ETS(M,N,N) 
## 
## Call:
##  ets(y = g$Adj.Close) 
## 
##   Smoothing parameters:
##     alpha = 0.9999 
## 
##   Initial states:
##     l = 736.0291 
## 
##   sigma:  0.0113
## 
##      AIC     AICc      BIC 
## 5434.555 5434.603 5447.223
# Display the forecasts
g.ts.ets$fitted
## Time Series:
## Start = 1 
## End = 504 
## Frequency = 1 
##   [1]  736.0291  736.0900  737.7799  737.6000  742.0896  740.7501  738.0603
##   [8]  735.3003  733.5302  744.7689  750.5294  744.9506  749.9095  745.2904
##  [15]  737.8007  745.6892  740.2806  739.1501  736.1003  743.0893  751.7191
##  [22]  753.1999  758.9994  766.6092  753.9313  752.6701  759.1394  718.7741
##  [29]  723.1496  708.1415  705.8403  691.0215  693.0098  698.2095  692.3606
##  [36]  695.6997  701.4294  711.1190  712.8998  723.1790  715.2908  713.3102
##  [43]  710.8303  716.4894  706.2310  706.6300  700.3206  709.7390  704.2405
##  [50]  720.0884  725.2695  724.1201  732.6591  735.7197  734.1502  730.4004
##  [57]  722.3408  716.5506  716.6500  728.2789  728.5800  719.4109  718.3601
##  [64]  718.2700  718.9199  710.3608  691.7218  693.7098  695.9398  697.4599
##  [71]  701.8696  675.2227  668.2607  680.0388  684.1096  692.0992  699.2093
##  [78]  694.9504  697.7697  695.3602  705.6290  715.0891  720.6395  716.9803
##  [85]  720.9496  719.8501  733.7786  736.9597  741.1896  738.6303  742.7396
##  [92]  739.7703  738.4201  741.7697  745.9096  768.7877  772.8796  771.0702
##  [99]  773.1798  771.6101  782.2189  781.7601  784.2598  784.6800  784.8500
## [106]  783.2201  782.4401  777.1405  779.9097  777.5002  775.4202  772.1504
## [113]  772.0800  769.6403  769.4100  769.5400  772.1498  769.0903  767.0502
## [120]  768.7799  771.4598  780.0792  780.3499  775.3205  759.6615  769.0191
## [127]  759.6909  762.4897  771.7591  768.8803  765.7003  771.4094  776.2195
## [134]  787.2089  786.9001  774.2113  783.0091  781.5601  775.0107  777.2897
## [141]  772.5605  776.4296  776.4700  776.8599  775.0802  785.9389  783.0703
## [148]  786.1397  778.1908  778.5300  779.9599  795.2585  801.4994  796.9704
## [155]  799.3698  813.1086  807.6705  799.0709  795.3504  795.3700  784.5411
## [162]  783.6101  768.7015  762.1307  762.0200  782.5180  790.5092  785.3105
## [169]  762.5623  754.0209  736.0818  758.4877  764.4794  771.2293  760.5411
## [176]  769.1991  768.2701  760.9907  761.6799  768.2393  770.8398  758.0413
## [183]  747.9210  750.4997  762.5188  759.1103  771.1888  776.4195  789.2887
## [190]  789.2700  796.0993  797.0699  797.8499  790.8007  794.1997  796.4198
## [197]  794.5602  791.2603  789.9101  791.5498  785.0506  782.7902  771.8211
## [204]  786.1386  786.8999  794.0193  806.1488  806.6500  804.7902  807.9097
## [211]  806.3601  807.8799  804.6103  806.0699  802.1754  805.0197  819.3086
## [218]  823.8695  835.6688  832.1504  823.3109  802.3221  796.7905  795.6951
## [225]  798.5297  801.4897  801.3400  806.9694  808.3799  809.5599  813.6696
## [232]  819.2394  820.4499  818.9801  824.1595  828.0696  831.6596  830.7601
## [239]  831.3300  828.6403  829.2800  823.2106  835.2388  830.6305  829.0802
## [246]  827.7802  831.9096  835.3696  838.6797  843.2495  845.5397  845.6200
## [253]  847.1999  848.7799  852.1197  848.4004  830.4618  829.5901  817.5812
## [260]  814.4303  819.5095  820.9198  831.4089  831.5000  829.5602  838.5491
## [267]  834.5704  831.4103  827.8804  824.6703  824.7300  823.3501  824.3199
## [274]  823.5601  837.1686  836.8200  838.2099  841.6497  843.1898  862.7580
## [281]  872.2990  871.7300  874.2497  905.9568  912.5693  916.4396  927.0389
## [288]  931.6595  927.1305  934.2993  932.1702  928.7804  930.5998  932.2198
## [295]  937.0795  942.9994  919.6223  930.2389  934.0096  941.8592  948.8193
## [302]  954.9594  969.5385  971.4698  975.8796  964.8611  966.9498  975.5991
## [309]  983.6792  976.5707  980.9396  983.4097  949.8334  942.9007  953.3990
## [316]  950.7603  942.3108  939.7803  957.3682  950.6307  959.4491  957.0903
## [323]  965.5892  952.2714  927.3325  940.4887  917.7923  908.7309  898.7010
## [330]  911.7087  906.6905  918.5888  928.7990  930.0899  943.8286  947.1596
## [337]  955.9891  953.4202  965.3988  970.8895  968.1503  972.9195  980.3393
## [344]  950.7030  947.8003  934.0914  941.5293  930.5011  930.8300  930.3901
## [351]  923.6507  927.9596  929.3598  926.7902  922.9004  907.2416  914.3893
## [358]  922.6692  922.2200  926.9595  910.9816  910.6700  906.6604  924.6882
## [365]  926.9998  921.2806  915.8906  913.8102  921.2892  929.5692  939.3290
## [372]  937.3402  928.4509  927.8101  935.9492  926.5010  929.0798  932.0697
## [379]  935.0897  925.1110  920.2905  915.0005  921.8093  931.5790  932.4499
## [386]  928.5304  920.9707  924.8596  944.4880  949.4995  959.1090  953.2706
## [393]  957.7895  951.6806  969.9582  978.8891  977.0002  972.6004  989.2483
## [400]  987.8302  989.6798  991.9998  992.1800  992.8099  984.4509  988.1996
## [407]  968.4520  970.5398  973.3297  972.5601 1019.2653 1017.1102 1016.6401
## [414] 1025.4991 1025.5799 1032.4793 1025.9007 1033.3292 1039.8493 1031.2609
## [421] 1028.0703 1025.7502 1026.0000 1020.9105 1032.4988 1019.0914 1018.3801
## [428] 1034.4884 1035.9598 1040.6095 1054.2086 1047.4107 1021.6626 1021.4100
## [435] 1010.1711  998.6811 1005.1494 1018.3787 1030.9288 1037.0494 1041.0996
## [442] 1040.4800 1040.6100 1049.1492 1064.1884 1077.1387 1070.6807 1064.9505
## [449] 1063.6301 1060.1203 1056.7403 1049.3707 1048.1401 1046.4002 1064.9981
## [456] 1082.4782 1086.3996 1102.2284 1106.9395 1106.2601 1102.6104 1105.5197
## [463] 1122.2583 1121.7601 1131.9790 1129.7903 1137.5092 1155.8082 1169.9685
## [470] 1164.2406 1170.3694 1175.8394 1175.5800 1163.6911 1169.9393 1167.7002
## [477] 1111.9056 1055.8057 1080.5975 1048.5832 1001.5248 1037.7764 1051.9385
## [484] 1052.1000 1069.6982 1089.5180 1094.7995 1102.4592 1111.3391 1106.6305
## [491] 1126.7880 1143.7483 1118.2926 1104.7313 1069.5236 1078.9191 1090.9288
## [498] 1095.0596 1109.6385 1125.9984 1160.0366 1164.4996 1138.1727 1149.4889