#Load library
library(quantmod)
## Loading required package: xts
## Loading required package: zoo
##
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
## Loading required package: TTR
## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo
library(rugarch)
## Loading required package: parallel
##
## Attaching package: 'rugarch'
## The following object is masked from 'package:stats':
##
## sigma
library(forecast)
library(tseries)
library(PerformanceAnalytics)
##
## Attaching package: 'PerformanceAnalytics'
## The following object is masked from 'package:graphics':
##
## legend
getSymbols("AMZN")
## 'getSymbols' currently uses auto.assign=TRUE by default, but will
## use auto.assign=FALSE in 0.5-0. You will still be able to use
## 'loadSymbols' to automatically load data. getOption("getSymbols.env")
## and getOption("getSymbols.auto.assign") will still be checked for
## alternate defaults.
##
## This message is shown once per session and may be disabled by setting
## options("getSymbols.warning4.0"=FALSE). See ?getSymbols for details.
## [1] "AMZN"
View(AMZN) #will display the data
summary(AMZN)
## Index AMZN.Open AMZN.High AMZN.Low
## Min. :2007-01-03 Min. : 35.29 Min. : 37.07 Min. : 34.68
## 1st Qu.:2010-07-30 1st Qu.: 137.12 1st Qu.: 139.12 1st Qu.: 135.30
## Median :2014-02-27 Median : 315.17 Median : 318.18 Median : 311.35
## Mean :2014-02-26 Mean : 744.95 Mean : 752.99 Mean : 735.96
## 3rd Qu.:2017-09-24 3rd Qu.:1002.50 3rd Qu.:1008.27 3rd Qu.: 995.63
## Max. :2021-04-23 Max. :3547.00 Max. :3552.25 Max. :3486.69
## AMZN.Close AMZN.Volume AMZN.Adjusted
## Min. : 35.03 Min. : 881300 Min. : 35.03
## 1st Qu.: 137.29 1st Qu.: 3086975 1st Qu.: 137.29
## Median : 315.35 Median : 4439700 Median : 315.35
## Mean : 744.78 Mean : 5559670 Mean : 744.78
## 3rd Qu.:1000.86 3rd Qu.: 6656425 3rd Qu.:1000.86
## Max. :3531.45 Max. :104329200 Max. :3531.45
chartSeries(AMZN["2019-12"]) #candlestick format
chartSeries(AMZN)
addBBands()
#Daily returns
returns <- CalculateReturns(AMZN$AMZN.Close)
returns <- returns[-1]
View(returns)
hist(returns)
chart.Histogram(returns,
methods = c('add.density','add.normal'),
colorset = c('yellow','red','blue'))
chartSeries(returns,theme = 'white')
modelfit <- auto.arima(AMZN$AMZN.Close,lambda = "auto")
modelfit
## Series: AMZN$AMZN.Close
## ARIMA(0,1,2) with drift
## Box Cox transformation: lambda= 0.1594431
##
## Coefficients:
## ma1 ma2 drift
## -0.0355 -0.0335 0.0032
## s.e. 0.0167 0.0168 0.0009
##
## sigma^2 estimated as 0.003425: log likelihood=5112.81
## AIC=-10217.62 AICc=-10217.6 BIC=-10192.86
boxplot(modelfit$residuals)
adf.test(AMZN$AMZN.Close)
## Warning in adf.test(AMZN$AMZN.Close): p-value greater than printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: AMZN$AMZN.Close
## Dickey-Fuller = 0.37453, Lag order = 15, p-value = 0.99
## alternative hypothesis: stationary
Acf(AMZN$AMZN.Close)
Pacf(AMZN$AMZN.Close)
ret_AMZN <- 100*diff(log(AMZN$AMZN.Close[2274:2638]))
ret_AMZN
## AMZN.Close
## 2016-01-13 NA
## 2016-01-14 1.905046848
## 2016-01-15 -3.924231082
## 2016-01-19 0.751316081
## 2016-01-20 -0.472840139
## 2016-01-21 0.566800999
## 2016-01-22 3.647319859
## 2016-01-25 0.025152609
## 2016-01-26 0.788123915
## 2016-01-27 -3.022351329
## 2016-01-28 8.538868225
## 2016-01-29 -7.915117055
## 2016-02-01 -2.098527190
## 2016-02-02 -4.031040211
## 2016-02-03 -3.883529334
## 2016-02-04 0.972528426
## 2016-02-05 -6.576007647
## 2016-02-08 -2.833874508
## 2016-02-09 -1.243096894
## 2016-02-10 1.729517964
## 2016-02-11 2.683454944
## 2016-02-12 0.644968112
## 2016-02-16 2.727315943
## 2016-02-17 2.464112655
## 2016-02-18 -1.718477982
## 2016-02-19 1.868159581
## 2016-02-22 4.496366935
## 2016-02-23 -1.179402759
## 2016-02-24 0.198734644
## 2016-02-25 0.200154413
## 2016-02-26 0.014401556
## 2016-02-29 -0.489273826
## 2016-03-01 4.688185379
## 2016-03-02 0.201862307
## 2016-03-03 -0.469903598
## 2016-03-04 -0.407759341
## 2016-03-07 -2.168921158
## 2016-03-08 -0.452332437
## 2016-03-09 -0.141112437
## 2016-03-10 -0.096562600
## 2016-03-11 1.892766061
## 2016-03-14 0.657933407
## 2016-03-15 0.634573875
## 2016-03-16 -0.477725879
## 2016-03-17 -2.616341686
## 2016-03-18 -1.324329287
## 2016-03-21 0.343555481
## 2016-03-22 1.166497486
## 2016-03-23 1.619351226
## 2016-03-24 2.311440394
## 2016-03-28 -0.529750810
## 2016-03-29 2.383964423
## 2016-03-30 0.810036219
## 2016-03-31 -0.847083798
## 2016-04-01 0.815342470
## 2016-04-04 -0.891176923
## 2016-04-05 -1.195606129
## 2016-04-06 2.683166060
## 2016-04-07 -1.784703370
## 2016-04-08 0.534554882
## 2016-04-11 0.223432856
## 2016-04-12 1.207585377
## 2016-04-13 1.913050090
## 2016-04-14 0.959887096
## 2016-04-15 0.824623639
## 2016-04-18 1.500132960
## 2016-04-19 -1.179503403
## 2016-04-20 0.807365209
## 2016-04-21 -0.314874589
## 2016-04-22 -1.678025790
## 2016-04-25 0.914422341
## 2016-04-26 -1.499530443
## 2016-04-27 -1.685437404
## 2016-04-28 -0.756270428
## 2016-04-29 9.136102549
## 2016-05-02 3.612008943
## 2016-05-03 -1.849262636
## 2016-05-04 -0.062580353
## 2016-05-05 -1.775999364
## 2016-05-06 2.229580529
## 2016-05-09 0.856914152
## 2016-05-10 3.373138655
## 2016-05-11 1.434745093
## 2016-05-12 0.656814051
## 2016-05-13 -1.121979782
## 2016-05-16 0.104181403
## 2016-05-17 -2.189378962
## 2016-05-18 0.313055565
## 2016-05-19 0.153299596
## 2016-05-20 0.610849953
## 2016-05-23 -0.864567288
## 2016-05-24 1.063575740
## 2016-05-25 0.587586418
## 2016-05-26 0.921833493
## 2016-05-27 -0.374170365
## 2016-05-31 1.470377387
## 2016-06-01 -0.464555871
## 2016-06-02 1.215751608
## 2016-06-03 -0.371447559
## 2016-06-06 0.163881689
## 2016-06-07 -0.412279371
## 2016-06-08 0.399899179
## 2016-06-09 0.138900651
## 2016-06-10 -1.347602095
## 2016-06-13 -0.372603867
## 2016-06-14 0.566036346
## 2016-06-15 -0.703144448
## 2016-06-16 0.453984304
## 2016-06-17 -1.561938462
## 2016-06-20 1.072946771
## 2016-06-21 0.253176664
## 2016-06-22 -0.731909867
## 2016-06-23 1.602630981
## 2016-06-24 -3.254241216
## 2016-06-27 -1.093289698
## 2016-06-28 2.371283619
## 2016-06-29 1.074783141
## 2016-06-30 0.002797474
## 2016-07-01 1.395984383
## 2016-07-05 0.332923178
## 2016-07-06 1.297684086
## 2016-07-07 -0.141092428
## 2016-07-08 1.246658838
## 2016-07-11 1.062971332
## 2016-07-12 -0.741687008
## 2016-07-13 -0.748577038
## 2016-07-14 -0.192743566
## 2016-07-15 -0.780154833
## 2016-07-18 0.085627014
## 2016-07-19 0.525740015
## 2016-07-20 0.776752317
## 2016-07-21 -0.173134027
## 2016-07-22 0.057744565
## 2016-07-25 -0.707326116
## 2016-07-26 -0.545006496
## 2016-07-27 0.146707265
## 2016-07-28 2.140713777
## 2016-07-29 0.820426863
## 2016-08-01 1.169970710
## 2016-08-02 -0.936979867
## 2016-08-03 -0.784048825
## 2016-08-04 0.809027035
## 2016-08-05 0.682492906
## 2016-08-08 0.075693690
## 2016-08-09 0.228032441
## 2016-08-10 0.032533656
## 2016-08-11 0.348096471
## 2016-08-12 0.171007686
## 2016-08-15 -0.528213555
## 2016-08-16 -0.580742250
## 2016-08-17 0.077194821
## 2016-08-18 -0.022233223
## 2016-08-19 -0.939705280
## 2016-08-22 0.286128404
## 2016-08-23 0.390298606
## 2016-08-24 -0.684349839
## 2016-08-25 0.259810236
## 2016-08-26 1.279941723
## 2016-08-29 0.297343970
## 2016-08-30 -0.482167850
## 2016-08-31 0.205624447
## 2016-09-01 0.189640399
## 2016-09-02 0.235895927
## 2016-09-06 2.104719696
## 2016-09-07 -0.558048300
## 2016-09-08 -0.053550692
## 2016-09-09 -3.098289891
## 2016-09-12 1.482105042
## 2016-09-13 -1.367718547
## 2016-09-14 0.010514026
## 2016-09-15 1.123618719
## 2016-09-16 1.140686808
## 2016-09-19 -0.440268474
## 2016-09-20 0.658387170
## 2016-09-21 1.212787068
## 2016-09-22 1.876578736
## 2016-09-23 0.130396863
## 2016-09-26 -0.821237845
## 2016-09-27 2.098798917
## 2016-09-28 1.533317534
## 2016-09-29 0.039814572
## 2016-09-30 0.991391743
## 2016-10-03 -0.068099283
## 2016-10-04 -0.324396936
## 2016-10-05 1.230951847
## 2016-10-06 -0.320282603
## 2016-10-07 -0.265301840
## 2016-10-10 0.271248127
## 2016-10-11 -1.280576815
## 2016-10-12 0.371154772
## 2016-10-13 -0.578345316
## 2016-10-14 -0.765026586
## 2016-10-17 -1.223800175
## 2016-10-18 0.576477973
## 2016-10-19 0.004889258
## 2016-10-20 -0.905405410
## 2016-10-21 1.064262154
## 2016-10-24 2.305366394
## 2016-10-25 -0.347826340
## 2016-10-26 -1.518933013
## 2016-10-27 -0.515561271
## 2016-10-28 -5.273750393
## 2016-10-31 1.724026493
## 2016-11-01 -0.559924021
## 2016-11-02 -2.559825049
## 2016-11-03 0.191836228
## 2016-11-04 -1.574199551
## 2016-11-07 3.881057659
## 2016-11-08 0.358624772
## 2016-11-09 -2.035167663
## 2016-11-10 -3.896785582
## 2016-11-11 -0.454978200
## 2016-11-14 -2.735274603
## 2016-11-15 3.306027375
## 2016-11-16 0.436321374
## 2016-11-17 1.318816087
## 2016-11-18 0.495853341
## 2016-11-21 2.576501776
## 2016-11-22 0.681011358
## 2016-11-23 -0.665628566
## 2016-11-25 0.032041218
## 2016-11-28 -1.758124692
## 2016-11-29 -0.555814898
## 2016-11-30 -1.579583667
## 2016-12-01 -0.926240089
## 2016-12-02 -0.446094970
## 2016-12-05 2.536637689
## 2016-12-06 0.703376234
## 2016-12-07 0.742608279
## 2016-12-08 -0.401881991
## 2016-12-09 0.173172526
## 2016-12-12 -1.117239500
## 2016-12-13 1.853477952
## 2016-12-14 -0.715420750
## 2016-12-15 -1.022352313
## 2016-12-16 -0.425342195
## 2016-12-19 1.080223383
## 2016-12-20 0.679146923
## 2016-12-21 -0.080423792
## 2016-12-22 -0.554343032
## 2016-12-23 -0.753148733
## 2016-12-27 1.411259350
## 2016-12-28 0.094585922
## 2016-12-29 -0.908101170
## 2016-12-30 -2.017207290
## 2017-01-03 0.505473236
## 2017-01-04 0.464641278
## 2017-01-05 3.026969514
## 2017-01-06 1.971591861
## 2017-01-09 0.116766562
## 2017-01-10 -0.128069604
## 2017-01-11 0.391242181
## 2017-01-12 1.813202440
## 2017-01-13 0.429243100
## 2017-01-17 -0.912198409
## 2017-01-18 -0.277021086
## 2017-01-19 0.193007018
## 2017-01-20 -0.087792039
## 2017-01-23 1.174522067
## 2017-01-24 0.555990139
## 2017-01-25 1.697491911
## 2017-01-26 0.313905016
## 2017-01-27 -0.403602381
## 2017-01-30 -0.647004618
## 2017-01-31 -0.834419491
## 2017-02-01 1.071375815
## 2017-02-02 0.908938394
## 2017-02-03 -3.606123496
## 2017-02-06 -0.316471232
## 2017-02-07 0.599948095
## 2017-02-08 0.883473180
## 2017-02-09 0.201083872
## 2017-02-10 0.739930957
## 2017-02-13 1.090162387
## 2017-02-14 -0.016738875
## 2017-02-15 0.751600760
## 2017-02-16 0.170733837
## 2017-02-17 0.110109706
## 2017-02-21 1.336479266
## 2017-02-22 -0.096961779
## 2017-02-23 -0.400513830
## 2017-02-24 -0.818891014
## 2017-02-27 0.401448692
## 2017-02-28 -0.425114831
## 2017-03-01 0.946941218
## 2017-03-02 -0.490020784
## 2017-03-03 0.114202711
## 2017-03-06 -0.385504668
## 2017-03-07 -0.069709862
## 2017-03-08 0.528138821
## 2017-03-09 0.293513566
## 2017-03-10 -0.063323445
## 2017-03-13 0.249554031
## 2017-03-14 -0.241342018
## 2017-03-15 0.051590972
## 2017-03-16 0.052744334
## 2017-03-17 -0.130147816
## 2017-03-20 0.545257024
## 2017-03-21 -1.619868629
## 2017-03-22 0.574719363
## 2017-03-23 -0.080214344
## 2017-03-24 -0.209099954
## 2017-03-27 0.142992291
## 2017-03-28 1.078221057
## 2017-03-29 2.117607323
## 2017-03-30 0.230772492
## 2017-03-31 1.157204665
## 2017-04-03 0.559044456
## 2017-04-04 1.703835470
## 2017-04-05 0.269808924
## 2017-04-06 -1.217125345
## 2017-04-07 -0.379221933
## 2017-04-10 1.349688966
## 2017-04-11 -0.517298942
## 2017-04-12 -0.681648275
## 2017-04-13 -1.298237925
## 2017-04-17 1.938874754
## 2017-04-18 0.198257759
## 2017-04-19 -0.508050755
## 2017-04-20 0.317554200
## 2017-04-21 -0.392090756
## 2017-04-24 0.983423099
## 2017-04-25 0.023142538
## 2017-04-26 0.183826771
## 2017-04-27 0.994720276
## 2017-04-28 0.717166206
## 2017-05-01 2.481415194
## 2017-05-02 -0.136133245
## 2017-05-03 -0.626068445
## 2017-05-04 -0.372626261
## 2017-05-05 -0.361173767
## 2017-05-08 1.581387357
## 2017-05-09 0.397509176
## 2017-05-10 -0.406989310
## 2017-05-11 -0.140255009
## 2017-05-12 1.438494892
## 2017-05-15 -0.352208969
## 2017-05-16 0.841987063
## 2017-05-17 -2.230536503
## 2017-05-18 1.442818146
## 2017-05-19 0.140751300
## 2017-05-22 1.121990516
## 2017-05-23 0.089588157
## 2017-05-24 0.902720751
## 2017-05-25 1.320364835
## 2017-05-26 0.241310415
## 2017-05-30 0.092345524
## 2017-05-31 -0.208908438
## 2017-06-01 0.133631793
## 2017-06-02 1.076564619
## 2017-06-05 0.456877611
## 2017-06-06 -0.828070191
## 2017-06-07 0.702413333
## 2017-06-08 0.019799934
## 2017-06-09 -3.214632946
## 2017-06-12 -1.379178642
## 2017-06-13 1.632354218
## 2017-06-14 -0.441434876
## 2017-06-15 -1.267638820
## 2017-06-16 2.412154469
## 2017-06-19 0.752440509
## 2017-06-20 -0.259584400
## 2017-06-21 0.966506051
## 2017-06-22 -0.092835354
## 2017-06-23 0.243386988
train <- ret_AMZN[1:(0.9*length(ret_AMZN))] #Here we train our data
train
## AMZN.Close
## 2016-01-13 NA
## 2016-01-14 1.905046848
## 2016-01-15 -3.924231082
## 2016-01-19 0.751316081
## 2016-01-20 -0.472840139
## 2016-01-21 0.566800999
## 2016-01-22 3.647319859
## 2016-01-25 0.025152609
## 2016-01-26 0.788123915
## 2016-01-27 -3.022351329
## 2016-01-28 8.538868225
## 2016-01-29 -7.915117055
## 2016-02-01 -2.098527190
## 2016-02-02 -4.031040211
## 2016-02-03 -3.883529334
## 2016-02-04 0.972528426
## 2016-02-05 -6.576007647
## 2016-02-08 -2.833874508
## 2016-02-09 -1.243096894
## 2016-02-10 1.729517964
## 2016-02-11 2.683454944
## 2016-02-12 0.644968112
## 2016-02-16 2.727315943
## 2016-02-17 2.464112655
## 2016-02-18 -1.718477982
## 2016-02-19 1.868159581
## 2016-02-22 4.496366935
## 2016-02-23 -1.179402759
## 2016-02-24 0.198734644
## 2016-02-25 0.200154413
## 2016-02-26 0.014401556
## 2016-02-29 -0.489273826
## 2016-03-01 4.688185379
## 2016-03-02 0.201862307
## 2016-03-03 -0.469903598
## 2016-03-04 -0.407759341
## 2016-03-07 -2.168921158
## 2016-03-08 -0.452332437
## 2016-03-09 -0.141112437
## 2016-03-10 -0.096562600
## 2016-03-11 1.892766061
## 2016-03-14 0.657933407
## 2016-03-15 0.634573875
## 2016-03-16 -0.477725879
## 2016-03-17 -2.616341686
## 2016-03-18 -1.324329287
## 2016-03-21 0.343555481
## 2016-03-22 1.166497486
## 2016-03-23 1.619351226
## 2016-03-24 2.311440394
## 2016-03-28 -0.529750810
## 2016-03-29 2.383964423
## 2016-03-30 0.810036219
## 2016-03-31 -0.847083798
## 2016-04-01 0.815342470
## 2016-04-04 -0.891176923
## 2016-04-05 -1.195606129
## 2016-04-06 2.683166060
## 2016-04-07 -1.784703370
## 2016-04-08 0.534554882
## 2016-04-11 0.223432856
## 2016-04-12 1.207585377
## 2016-04-13 1.913050090
## 2016-04-14 0.959887096
## 2016-04-15 0.824623639
## 2016-04-18 1.500132960
## 2016-04-19 -1.179503403
## 2016-04-20 0.807365209
## 2016-04-21 -0.314874589
## 2016-04-22 -1.678025790
## 2016-04-25 0.914422341
## 2016-04-26 -1.499530443
## 2016-04-27 -1.685437404
## 2016-04-28 -0.756270428
## 2016-04-29 9.136102549
## 2016-05-02 3.612008943
## 2016-05-03 -1.849262636
## 2016-05-04 -0.062580353
## 2016-05-05 -1.775999364
## 2016-05-06 2.229580529
## 2016-05-09 0.856914152
## 2016-05-10 3.373138655
## 2016-05-11 1.434745093
## 2016-05-12 0.656814051
## 2016-05-13 -1.121979782
## 2016-05-16 0.104181403
## 2016-05-17 -2.189378962
## 2016-05-18 0.313055565
## 2016-05-19 0.153299596
## 2016-05-20 0.610849953
## 2016-05-23 -0.864567288
## 2016-05-24 1.063575740
## 2016-05-25 0.587586418
## 2016-05-26 0.921833493
## 2016-05-27 -0.374170365
## 2016-05-31 1.470377387
## 2016-06-01 -0.464555871
## 2016-06-02 1.215751608
## 2016-06-03 -0.371447559
## 2016-06-06 0.163881689
## 2016-06-07 -0.412279371
## 2016-06-08 0.399899179
## 2016-06-09 0.138900651
## 2016-06-10 -1.347602095
## 2016-06-13 -0.372603867
## 2016-06-14 0.566036346
## 2016-06-15 -0.703144448
## 2016-06-16 0.453984304
## 2016-06-17 -1.561938462
## 2016-06-20 1.072946771
## 2016-06-21 0.253176664
## 2016-06-22 -0.731909867
## 2016-06-23 1.602630981
## 2016-06-24 -3.254241216
## 2016-06-27 -1.093289698
## 2016-06-28 2.371283619
## 2016-06-29 1.074783141
## 2016-06-30 0.002797474
## 2016-07-01 1.395984383
## 2016-07-05 0.332923178
## 2016-07-06 1.297684086
## 2016-07-07 -0.141092428
## 2016-07-08 1.246658838
## 2016-07-11 1.062971332
## 2016-07-12 -0.741687008
## 2016-07-13 -0.748577038
## 2016-07-14 -0.192743566
## 2016-07-15 -0.780154833
## 2016-07-18 0.085627014
## 2016-07-19 0.525740015
## 2016-07-20 0.776752317
## 2016-07-21 -0.173134027
## 2016-07-22 0.057744565
## 2016-07-25 -0.707326116
## 2016-07-26 -0.545006496
## 2016-07-27 0.146707265
## 2016-07-28 2.140713777
## 2016-07-29 0.820426863
## 2016-08-01 1.169970710
## 2016-08-02 -0.936979867
## 2016-08-03 -0.784048825
## 2016-08-04 0.809027035
## 2016-08-05 0.682492906
## 2016-08-08 0.075693690
## 2016-08-09 0.228032441
## 2016-08-10 0.032533656
## 2016-08-11 0.348096471
## 2016-08-12 0.171007686
## 2016-08-15 -0.528213555
## 2016-08-16 -0.580742250
## 2016-08-17 0.077194821
## 2016-08-18 -0.022233223
## 2016-08-19 -0.939705280
## 2016-08-22 0.286128404
## 2016-08-23 0.390298606
## 2016-08-24 -0.684349839
## 2016-08-25 0.259810236
## 2016-08-26 1.279941723
## 2016-08-29 0.297343970
## 2016-08-30 -0.482167850
## 2016-08-31 0.205624447
## 2016-09-01 0.189640399
## 2016-09-02 0.235895927
## 2016-09-06 2.104719696
## 2016-09-07 -0.558048300
## 2016-09-08 -0.053550692
## 2016-09-09 -3.098289891
## 2016-09-12 1.482105042
## 2016-09-13 -1.367718547
## 2016-09-14 0.010514026
## 2016-09-15 1.123618719
## 2016-09-16 1.140686808
## 2016-09-19 -0.440268474
## 2016-09-20 0.658387170
## 2016-09-21 1.212787068
## 2016-09-22 1.876578736
## 2016-09-23 0.130396863
## 2016-09-26 -0.821237845
## 2016-09-27 2.098798917
## 2016-09-28 1.533317534
## 2016-09-29 0.039814572
## 2016-09-30 0.991391743
## 2016-10-03 -0.068099283
## 2016-10-04 -0.324396936
## 2016-10-05 1.230951847
## 2016-10-06 -0.320282603
## 2016-10-07 -0.265301840
## 2016-10-10 0.271248127
## 2016-10-11 -1.280576815
## 2016-10-12 0.371154772
## 2016-10-13 -0.578345316
## 2016-10-14 -0.765026586
## 2016-10-17 -1.223800175
## 2016-10-18 0.576477973
## 2016-10-19 0.004889258
## 2016-10-20 -0.905405410
## 2016-10-21 1.064262154
## 2016-10-24 2.305366394
## 2016-10-25 -0.347826340
## 2016-10-26 -1.518933013
## 2016-10-27 -0.515561271
## 2016-10-28 -5.273750393
## 2016-10-31 1.724026493
## 2016-11-01 -0.559924021
## 2016-11-02 -2.559825049
## 2016-11-03 0.191836228
## 2016-11-04 -1.574199551
## 2016-11-07 3.881057659
## 2016-11-08 0.358624772
## 2016-11-09 -2.035167663
## 2016-11-10 -3.896785582
## 2016-11-11 -0.454978200
## 2016-11-14 -2.735274603
## 2016-11-15 3.306027375
## 2016-11-16 0.436321374
## 2016-11-17 1.318816087
## 2016-11-18 0.495853341
## 2016-11-21 2.576501776
## 2016-11-22 0.681011358
## 2016-11-23 -0.665628566
## 2016-11-25 0.032041218
## 2016-11-28 -1.758124692
## 2016-11-29 -0.555814898
## 2016-11-30 -1.579583667
## 2016-12-01 -0.926240089
## 2016-12-02 -0.446094970
## 2016-12-05 2.536637689
## 2016-12-06 0.703376234
## 2016-12-07 0.742608279
## 2016-12-08 -0.401881991
## 2016-12-09 0.173172526
## 2016-12-12 -1.117239500
## 2016-12-13 1.853477952
## 2016-12-14 -0.715420750
## 2016-12-15 -1.022352313
## 2016-12-16 -0.425342195
## 2016-12-19 1.080223383
## 2016-12-20 0.679146923
## 2016-12-21 -0.080423792
## 2016-12-22 -0.554343032
## 2016-12-23 -0.753148733
## 2016-12-27 1.411259350
## 2016-12-28 0.094585922
## 2016-12-29 -0.908101170
## 2016-12-30 -2.017207290
## 2017-01-03 0.505473236
## 2017-01-04 0.464641278
## 2017-01-05 3.026969514
## 2017-01-06 1.971591861
## 2017-01-09 0.116766562
## 2017-01-10 -0.128069604
## 2017-01-11 0.391242181
## 2017-01-12 1.813202440
## 2017-01-13 0.429243100
## 2017-01-17 -0.912198409
## 2017-01-18 -0.277021086
## 2017-01-19 0.193007018
## 2017-01-20 -0.087792039
## 2017-01-23 1.174522067
## 2017-01-24 0.555990139
## 2017-01-25 1.697491911
## 2017-01-26 0.313905016
## 2017-01-27 -0.403602381
## 2017-01-30 -0.647004618
## 2017-01-31 -0.834419491
## 2017-02-01 1.071375815
## 2017-02-02 0.908938394
## 2017-02-03 -3.606123496
## 2017-02-06 -0.316471232
## 2017-02-07 0.599948095
## 2017-02-08 0.883473180
## 2017-02-09 0.201083872
## 2017-02-10 0.739930957
## 2017-02-13 1.090162387
## 2017-02-14 -0.016738875
## 2017-02-15 0.751600760
## 2017-02-16 0.170733837
## 2017-02-17 0.110109706
## 2017-02-21 1.336479266
## 2017-02-22 -0.096961779
## 2017-02-23 -0.400513830
## 2017-02-24 -0.818891014
## 2017-02-27 0.401448692
## 2017-02-28 -0.425114831
## 2017-03-01 0.946941218
## 2017-03-02 -0.490020784
## 2017-03-03 0.114202711
## 2017-03-06 -0.385504668
## 2017-03-07 -0.069709862
## 2017-03-08 0.528138821
## 2017-03-09 0.293513566
## 2017-03-10 -0.063323445
## 2017-03-13 0.249554031
## 2017-03-14 -0.241342018
## 2017-03-15 0.051590972
## 2017-03-16 0.052744334
## 2017-03-17 -0.130147816
## 2017-03-20 0.545257024
## 2017-03-21 -1.619868629
## 2017-03-22 0.574719363
## 2017-03-23 -0.080214344
## 2017-03-24 -0.209099954
## 2017-03-27 0.142992291
## 2017-03-28 1.078221057
## 2017-03-29 2.117607323
## 2017-03-30 0.230772492
## 2017-03-31 1.157204665
## 2017-04-03 0.559044456
## 2017-04-04 1.703835470
## 2017-04-05 0.269808924
## 2017-04-06 -1.217125345
## 2017-04-07 -0.379221933
## 2017-04-10 1.349688966
## 2017-04-11 -0.517298942
## 2017-04-12 -0.681648275
## 2017-04-13 -1.298237925
## 2017-04-17 1.938874754
## 2017-04-18 0.198257759
## 2017-04-19 -0.508050755
## 2017-04-20 0.317554200
## 2017-04-21 -0.392090756
## 2017-04-24 0.983423099
## 2017-04-25 0.023142538
## 2017-04-26 0.183826771
## 2017-04-27 0.994720276
## 2017-04-28 0.717166206
## 2017-05-01 2.481415194
## 2017-05-02 -0.136133245
test <- ret_AMZN[(0.9*length(ret_AMZN)+1):length(ret_AMZN)] #We test data if there is any bug or not
test
## AMZN.Close
## 2017-05-03 -0.62606844
## 2017-05-04 -0.37262626
## 2017-05-05 -0.36117377
## 2017-05-08 1.58138736
## 2017-05-09 0.39750918
## 2017-05-10 -0.40698931
## 2017-05-11 -0.14025501
## 2017-05-12 1.43849489
## 2017-05-15 -0.35220897
## 2017-05-16 0.84198706
## 2017-05-17 -2.23053650
## 2017-05-18 1.44281815
## 2017-05-19 0.14075130
## 2017-05-22 1.12199052
## 2017-05-23 0.08958816
## 2017-05-24 0.90272075
## 2017-05-25 1.32036483
## 2017-05-26 0.24131041
## 2017-05-30 0.09234552
## 2017-05-31 -0.20890844
## 2017-06-01 0.13363179
## 2017-06-02 1.07656462
## 2017-06-05 0.45687761
## 2017-06-06 -0.82807019
## 2017-06-07 0.70241333
## 2017-06-08 0.01979993
## 2017-06-09 -3.21463295
## 2017-06-12 -1.37917864
## 2017-06-13 1.63235422
## 2017-06-14 -0.44143488
## 2017-06-15 -1.26763882
## 2017-06-16 2.41215447
## 2017-06-19 0.75244051
## 2017-06-20 -0.25958440
## 2017-06-21 0.96650605
## 2017-06-22 -0.09283535
#We will fit arima now
fit <- Arima(train, order = c(2,0,2))
fit
## Series: train
## ARIMA(2,0,2) with non-zero mean
##
## Coefficients:
## ar1 ar2 ma1 ma2 mean
## -0.1091 -0.9140 0.1179 1.0000 0.1492
## s.e. 0.0333 0.0249 0.0125 0.0132 0.0917
##
## sigma^2 estimated as 2.551: log likelihood=-616.69
## AIC=1245.38 AICc=1245.64 BIC=1268.12
#Will perform predictions based on data
preds <- predict(fit,n.head =length(ret_AMZN)-(0.9*length(ret_AMZN)))$pred
preds
## Time Series:
## Start = 329
## End = 329
## Frequency = 1
## [1] 0.06257735
#Test forecast
test_forecast <- forecast(fit,h=25)
test_forecast
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 329 0.06257735 -1.989674 2.114829 -3.076070 3.201225
## 330 0.43242074 -1.619884 2.484726 -2.706309 3.571150
## 331 0.19752216 -1.861275 2.256319 -2.951136 3.346180
## 332 -0.11490717 -2.173967 1.944152 -3.263967 3.034153
## 333 0.13387784 -1.930323 2.198079 -3.023045 3.290801
## 334 0.39231382 -1.672408 2.457035 -2.765405 3.550033
## 335 0.13672546 -1.931956 2.205407 -3.027050 3.300501
## 336 -0.07161642 -2.141070 1.997837 -3.236572 3.093340
## 337 0.18472639 -1.887686 2.257139 -2.984755 3.354208
## 338 0.34719803 -1.726198 2.420594 -2.823787 3.518184
## 339 0.09516898 -1.980365 2.170703 -3.079086 3.269424
## 340 -0.02584601 -2.102516 2.050824 -3.201839 3.150147
## 341 0.21771816 -1.860437 2.295873 -2.960546 3.395982
## 342 0.30176349 -1.777618 2.381145 -2.878377 3.481903
## 343 0.06996906 -2.010396 2.150334 -3.111674 3.251612
## 344 0.01843163 -2.063189 2.100052 -3.165133 3.201996
## 345 0.23592223 -1.846311 2.318156 -2.948579 3.420423
## 346 0.25930638 -1.824159 2.342772 -2.927079 3.445691
## 347 0.05796089 -2.025856 2.141778 -3.128962 3.244884
## 348 0.05854888 -2.026433 2.143531 -3.130156 3.247254
## 349 0.24252232 -1.842639 2.327683 -2.946456 3.431501
## 350 0.22191775 -1.864310 2.308146 -2.968693 3.412528
## 351 0.05600637 -2.030296 2.142308 -3.134717 3.246730
## 352 0.09293673 -1.994315 2.180188 -3.099239 3.285112
## 353 0.24055793 -1.846712 2.327828 -2.951646 3.432762
#Plot the forecast
plot(test_forecast, main = "ARIMA forecast for Microsoft Stock" )
accuracy(test_forecast)
## ME RMSE MAE MPE MAPE MASE
## Training set 2.998316e-05 1.584823 1.06437 91.73259 171.9876 0.6839252
## ACF1
## Training set -0.02093559
#Box test for lag=2
Box.test(modelfit$residuals,lag = 2 ,type="Ljung-Box")
##
## Box-Ljung test
##
## data: modelfit$residuals
## X-squared = 0.0038526, df = 2, p-value = 0.9981
Box.test(modelfit$residuals,type="Ljung-Box")
##
## Box-Ljung test
##
## data: modelfit$residuals
## X-squared = 0.0009836, df = 1, p-value = 0.975
plot(as.ts(AMZN$AMZN.Close),col = "red")
price_forecast <- forecast(modelfit,h=20)
plot(price_forecast,col="darkgreen")
head(price_forecast$mean)
## Time Series:
## Start = 3603
## End = 3608
## Frequency = 1
## [1] 3344.752 3346.787 3349.753 3352.721 3355.691 3358.664
head(price_forecast$lower)
## Time Series:
## Start = 3603
## End = 3608
## Frequency = 1
## 80% 95%
## 3603 3276.561 3240.938
## 3604 3252.314 3203.217
## 3605 3236.221 3177.443
## 3606 3222.957 3155.990
## 3607 3211.550 3137.377
## 3608 3201.483 3120.812
head(price_forecast$upper)
## Time Series:
## Start = 3603
## End = 3608
## Frequency = 1
## 80% 95%
## 3603 3414.133 3451.348
## 3604 3443.556 3495.727
## 3605 3466.614 3529.851
## 3606 3486.849 3559.659
## 3607 3505.232 3586.635
## 3608 3522.281 3611.572
#Dividing data into train and test
N <- length(AMZN$AMZN.Close)
n <- 0.7*N
n
## [1] 2521.4
train <- AMZN$AMZN.Close[1:n,]
test <- AMZN$AMZN.Close[(n+1):N,]
trainarimafit <- auto.arima(train, lambda = "auto")
predlen=length(test)
head(predlen)
## [1] 1080
trainarimafit <- forecast(trainarimafit, h=predlen)
head(trainarimafit)
## $method
## [1] "ARIMA(0,1,0) with drift"
##
## $model
## Series: train
## ARIMA(0,1,0) with drift
## Box Cox transformation: lambda= 0.3532548
##
## Coefficients:
## drift
## 0.0077
## s.e. 0.0031
##
## sigma^2 estimated as 0.02371: log likelihood=1139.64
## AIC=-2275.27 AICc=-2275.27 BIC=-2263.61
##
## $level
## [1] 80 95
##
## $mean
## Time Series:
## Start = 2522
## End = 3601
## Frequency = 1
## [1] 781.0235 781.5972 782.1712 782.7455 783.3201 783.8949 784.4700
## [8] 785.0454 785.6210 786.1969 786.7731 787.3496 787.9263 788.5034
## [15] 789.0806 789.6582 790.2360 790.8141 791.3925 791.9712 792.5501
## [22] 793.1293 793.7088 794.2885 794.8685 795.4488 796.0294 796.6102
## [29] 797.1914 797.7728 798.3544 798.9364 799.5186 800.1011 800.6838
## [36] 801.2669 801.8502 802.4338 803.0176 803.6018 804.1862 804.7709
## [43] 805.3558 805.9411 806.5266 807.1123 807.6984 808.2847 808.8714
## [50] 809.4582 810.0454 810.6328 811.2205 811.8085 812.3968 812.9853
## [57] 813.5741 814.1632 814.7526 815.3422 815.9322 816.5224 817.1128
## [64] 817.7036 818.2946 818.8859 819.4775 820.0693 820.6614 821.2538
## [71] 821.8465 822.4395 823.0327 823.6262 824.2200 824.8141 825.4084
## [78] 826.0030 826.5979 827.1931 827.7885 828.3843 828.9803 829.5765
## [85] 830.1731 830.7699 831.3671 831.9644 832.5621 833.1601 833.7583
## [92] 834.3568 834.9556 835.5546 836.1539 836.7536 837.3534 837.9536
## [99] 838.5541 839.1548 839.7558 840.3571 840.9586 841.5605 842.1626
## [106] 842.7650 843.3676 843.9706 844.5738 845.1773 845.7811 846.3852
## [113] 846.9895 847.5942 848.1991 848.8042 849.4097 850.0154 850.6215
## [120] 851.2278 851.8343 852.4412 853.0483 853.6558 854.2635 854.8714
## [127] 855.4797 856.0882 856.6970 857.3061 857.9155 858.5252 859.1351
## [134] 859.7453 860.3558 860.9666 861.5777 862.1890 862.8006 863.4125
## [141] 864.0247 864.6372 865.2499 865.8629 866.4762 867.0898 867.7037
## [148] 868.3178 868.9322 869.5470 870.1619 870.7772 871.3928 872.0086
## [155] 872.6247 873.2411 873.8578 874.4747 875.0920 875.7095 876.3273
## [162] 876.9454 877.5638 878.1824 878.8013 879.4206 880.0401 880.6598
## [169] 881.2799 881.9002 882.5209 883.1418 883.7630 884.3844 885.0062
## [176] 885.6282 886.2505 886.8731 887.4960 888.1192 888.7427 889.3664
## [183] 889.9904 890.6147 891.2393 891.8642 892.4893 893.1147 893.7405
## [190] 894.3665 894.9927 895.6193 896.2462 896.8733 897.5007 898.1284
## [197] 898.7564 899.3847 900.0132 900.6421 901.2712 901.9006 902.5303
## [204] 903.1603 903.7905 904.4211 905.0519 905.6830 906.3144 906.9461
## [211] 907.5780 908.2103 908.8428 909.4757 910.1088 910.7421 911.3758
## [218] 912.0098 912.6440 913.2786 913.9134 914.5485 915.1839 915.8195
## [225] 916.4555 917.0917 917.7283 918.3651 919.0022 919.6396 920.2772
## [232] 920.9152 921.5534 922.1920 922.8308 923.4699 924.1093 924.7490
## [239] 925.3889 926.0292 926.6697 927.3105 927.9516 928.5930 929.2347
## [246] 929.8767 930.5189 931.1615 931.8043 932.4474 933.0908 933.7345
## [253] 934.3785 935.0227 935.6673 936.3121 936.9572 937.6026 938.2483
## [260] 938.8943 939.5406 940.1872 940.8340 941.4812 942.1286 942.7763
## [267] 943.4243 944.0726 944.7212 945.3700 946.0192 946.6686 947.3183
## [274] 947.9684 948.6187 949.2693 949.9201 950.5713 951.2228 951.8745
## [281] 952.5266 953.1789 953.8315 954.4844 955.1376 955.7911 956.4449
## [288] 957.0989 957.7533 958.4079 959.0628 959.7181 960.3736 961.0294
## [295] 961.6854 962.3418 962.9985 963.6554 964.3127 964.9702 965.6280
## [302] 966.2862 966.9446 967.6033 968.2622 968.9215 969.5811 970.2409
## [309] 970.9011 971.5615 972.2223 972.8833 973.5446 974.2062 974.8681
## [316] 975.5302 976.1927 976.8555 977.5185 978.1819 978.8455 979.5094
## [323] 980.1737 980.8382 981.5030 982.1681 982.8334 983.4991 984.1651
## [330] 984.8313 985.4979 986.1647 986.8319 987.4993 988.1670 988.8350
## [337] 989.5033 990.1719 990.8408 991.5100 992.1794 992.8492 993.5192
## [344] 994.1896 994.8602 995.5311 996.2024 996.8739 997.5457 998.2178
## [351] 998.8902 999.5629 1000.2359 1000.9091 1001.5827 1002.2566 1002.9307
## [358] 1003.6051 1004.2799 1004.9549 1005.6302 1006.3059 1006.9818 1007.6580
## [365] 1008.3345 1009.0113 1009.6884 1010.3657 1011.0434 1011.7214 1012.3996
## [372] 1013.0782 1013.7570 1014.4362 1015.1156 1015.7954 1016.4754 1017.1557
## [379] 1017.8363 1018.5172 1019.1984 1019.8799 1020.5617 1021.2438 1021.9262
## [386] 1022.6089 1023.2919 1023.9751 1024.6587 1025.3425 1026.0267 1026.7111
## [393] 1027.3959 1028.0809 1028.7663 1029.4519 1030.1378 1030.8240 1031.5106
## [400] 1032.1974 1032.8845 1033.5719 1034.2596 1034.9476 1035.6359 1036.3244
## [407] 1037.0133 1037.7025 1038.3920 1039.0818 1039.7718 1040.4622 1041.1528
## [414] 1041.8438 1042.5351 1043.2266 1043.9184 1044.6106 1045.3030 1045.9958
## [421] 1046.6888 1047.3821 1048.0758 1048.7697 1049.4639 1050.1584 1050.8532
## [428] 1051.5483 1052.2438 1052.9395 1053.6355 1054.3318 1055.0284 1055.7253
## [435] 1056.4225 1057.1200 1057.8177 1058.5158 1059.2142 1059.9129 1060.6119
## [442] 1061.3112 1062.0107 1062.7106 1063.4108 1064.1113 1064.8120 1065.5131
## [449] 1066.2145 1066.9161 1067.6181 1068.3204 1069.0229 1069.7258 1070.4290
## [456] 1071.1324 1071.8362 1072.5402 1073.2446 1073.9492 1074.6542 1075.3594
## [463] 1076.0650 1076.7709 1077.4770 1078.1835 1078.8902 1079.5973 1080.3046
## [470] 1081.0123 1081.7202 1082.4285 1083.1370 1083.8458 1084.5550 1085.2644
## [477] 1085.9742 1086.6842 1087.3946 1088.1052 1088.8162 1089.5274 1090.2390
## [484] 1090.9508 1091.6630 1092.3754 1093.0882 1093.8012 1094.5146 1095.2283
## [491] 1095.9422 1096.6565 1097.3710 1098.0859 1098.8010 1099.5165 1100.2323
## [498] 1100.9483 1101.6647 1102.3814 1103.0983 1103.8156 1104.5332 1105.2510
## [505] 1105.9692 1106.6877 1107.4065 1108.1255 1108.8449 1109.5646 1110.2846
## [512] 1111.0049 1111.7255 1112.4464 1113.1675 1113.8890 1114.6108 1115.3329
## [519] 1116.0553 1116.7781 1117.5011 1118.2244 1118.9480 1119.6719 1120.3961
## [526] 1121.1206 1121.8455 1122.5706 1123.2960 1124.0218 1124.7478 1125.4741
## [533] 1126.2008 1126.9277 1127.6550 1128.3825 1129.1104 1129.8386 1130.5670
## [540] 1131.2958 1132.0249 1132.7542 1133.4839 1134.2139 1134.9442 1135.6748
## [547] 1136.4057 1137.1369 1137.8684 1138.6002 1139.3323 1140.0647 1140.7974
## [554] 1141.5305 1142.2638 1142.9974 1143.7314 1144.4656 1145.2002 1145.9350
## [561] 1146.6702 1147.4057 1148.1414 1148.8775 1149.6139 1150.3506 1151.0876
## [568] 1151.8248 1152.5624 1153.3004 1154.0386 1154.7771 1155.5159 1156.2550
## [575] 1156.9945 1157.7342 1158.4743 1159.2146 1159.9553 1160.6962 1161.4375
## [582] 1162.1791 1162.9210 1163.6631 1164.4056 1165.1484 1165.8915 1166.6350
## [589] 1167.3787 1168.1227 1168.8670 1169.6117 1170.3566 1171.1019 1171.8474
## [596] 1172.5933 1173.3395 1174.0860 1174.8328 1175.5798 1176.3272 1177.0750
## [603] 1177.8230 1178.5713 1179.3199 1180.0689 1180.8181 1181.5677 1182.3175
## [610] 1183.0677 1183.8182 1184.5690 1185.3201 1186.0715 1186.8232 1187.5752
## [617] 1188.3275 1189.0801 1189.8331 1190.5863 1191.3399 1192.0938 1192.8479
## [624] 1193.6024 1194.3572 1195.1123 1195.8677 1196.6234 1197.3795 1198.1358
## [631] 1198.8925 1199.6494 1200.4067 1201.1642 1201.9221 1202.6803 1203.4388
## [638] 1204.1976 1204.9567 1205.7162 1206.4759 1207.2360 1207.9963 1208.7570
## [645] 1209.5180 1210.2792 1211.0408 1211.8027 1212.5650 1213.3275 1214.0903
## [652] 1214.8535 1215.6169 1216.3807 1217.1448 1217.9091 1218.6738 1219.4388
## [659] 1220.2042 1220.9698 1221.7357 1222.5020 1223.2685 1224.0354 1224.8026
## [666] 1225.5701 1226.3379 1227.1060 1227.8744 1228.6432 1229.4122 1230.1816
## [673] 1230.9512 1231.7212 1232.4915 1233.2621 1234.0330 1234.8043 1235.5758
## [680] 1236.3477 1237.1198 1237.8923 1238.6651 1239.4382 1240.2116 1240.9853
## [687] 1241.7594 1242.5337 1243.3084 1244.0833 1244.8586 1245.6342 1246.4101
## [694] 1247.1864 1247.9629 1248.7397 1249.5169 1250.2944 1251.0722 1251.8503
## [701] 1252.6287 1253.4074 1254.1864 1254.9658 1255.7454 1256.5254 1257.3057
## [708] 1258.0863 1258.8672 1259.6485 1260.4300 1261.2119 1261.9940 1262.7765
## [715] 1263.5593 1264.3424 1265.1258 1265.9096 1266.6936 1267.4780 1268.2627
## [722] 1269.0477 1269.8330 1270.6186 1271.4045 1272.1908 1272.9774 1273.7642
## [729] 1274.5514 1275.3390 1276.1268 1276.9149 1277.7034 1278.4921 1279.2812
## [736] 1280.0706 1280.8603 1281.6504 1282.4407 1283.2314 1284.0223 1284.8136
## [743] 1285.6052 1286.3972 1287.1894 1287.9819 1288.7748 1289.5680 1290.3615
## [750] 1291.1553 1291.9494 1292.7439 1293.5386 1294.3337 1295.1291 1295.9248
## [757] 1296.7208 1297.5172 1298.3138 1299.1108 1299.9081 1300.7057 1301.5036
## [764] 1302.3019 1303.1004 1303.8993 1304.6985 1305.4980 1306.2978 1307.0980
## [771] 1307.8984 1308.6992 1309.5003 1310.3017 1311.1034 1311.9055 1312.7078
## [778] 1313.5105 1314.3135 1315.1168 1315.9204 1316.7244 1317.5286 1318.3332
## [785] 1319.1381 1319.9433 1320.7489 1321.5547 1322.3609 1323.1674 1323.9742
## [792] 1324.7813 1325.5888 1326.3965 1327.2046 1328.0130 1328.8217 1329.6307
## [799] 1330.4401 1331.2498 1332.0598 1332.8701 1333.6807 1334.4916 1335.3029
## [806] 1336.1145 1336.9264 1337.7386 1338.5512 1339.3640 1340.1772 1340.9907
## [813] 1341.8045 1342.6187 1343.4331 1344.2479 1345.0630 1345.8784 1346.6941
## [820] 1347.5102 1348.3266 1349.1433 1349.9603 1350.7776 1351.5953 1352.4132
## [827] 1353.2315 1354.0501 1354.8691 1355.6883 1356.5079 1357.3278 1358.1480
## [834] 1358.9686 1359.7894 1360.6106 1361.4321 1362.2539 1363.0760 1363.8985
## [841] 1364.7213 1365.5444 1366.3678 1367.1916 1368.0156 1368.8400 1369.6647
## [848] 1370.4897 1371.3151 1372.1408 1372.9668 1373.7931 1374.6197 1375.4467
## [855] 1376.2739 1377.1016 1377.9295 1378.7577 1379.5863 1380.4152 1381.2444
## [862] 1382.0739 1382.9038 1383.7340 1384.5645 1385.3953 1386.2264 1387.0579
## [869] 1387.8897 1388.7218 1389.5542 1390.3870 1391.2201 1392.0535 1392.8872
## [876] 1393.7212 1394.5556 1395.3903 1396.2253 1397.0607 1397.8963 1398.7323
## [883] 1399.5686 1400.4052 1401.2422 1402.0795 1402.9171 1403.7550 1404.5933
## [890] 1405.4318 1406.2707 1407.1100 1407.9495 1408.7894 1409.6296 1410.4701
## [897] 1411.3109 1412.1521 1412.9936 1413.8354 1414.6775 1415.5200 1416.3628
## [904] 1417.2059 1418.0493 1418.8931 1419.7372 1420.5816 1421.4263 1422.2714
## [911] 1423.1168 1423.9625 1424.8085 1425.6549 1426.5016 1427.3486 1428.1959
## [918] 1429.0436 1429.8915 1430.7399 1431.5885 1432.4375 1433.2867 1434.1364
## [925] 1434.9863 1435.8366 1436.6871 1437.5381 1438.3893 1439.2409 1440.0928
## [932] 1440.9450 1441.7975 1442.6504 1443.5036 1444.3571 1445.2110 1446.0651
## [939] 1446.9197 1447.7745 1448.6296 1449.4851 1450.3409 1451.1971 1452.0535
## [946] 1452.9103 1453.7674 1454.6249 1455.4827 1456.3407 1457.1992 1458.0579
## [953] 1458.9170 1459.7764 1460.6361 1461.4962 1462.3566 1463.2173 1464.0784
## [960] 1464.9397 1465.8014 1466.6635 1467.5258 1468.3885 1469.2515 1470.1148
## [967] 1470.9785 1471.8425 1472.7068 1473.5715 1474.4365 1475.3018 1476.1674
## [974] 1477.0334 1477.8997 1478.7663 1479.6332 1480.5005 1481.3681 1482.2361
## [981] 1483.1043 1483.9729 1484.8418 1485.7111 1486.5807 1487.4506 1488.3208
## [988] 1489.1914 1490.0623 1490.9335 1491.8051 1492.6770 1493.5492 1494.4217
## [995] 1495.2946 1496.1678 1497.0413 1497.9152 1498.7894 1499.6639 1500.5388
## [1002] 1501.4139 1502.2895 1503.1653 1504.0415 1504.9180 1505.7948 1506.6720
## [1009] 1507.5495 1508.4273 1509.3055 1510.1839 1511.0628 1511.9419 1512.8214
## [1016] 1513.7012 1514.5813 1515.4618 1516.3426 1517.2237 1518.1052 1518.9870
## [1023] 1519.8691 1520.7516 1521.6344 1522.5175 1523.4009 1524.2847 1525.1688
## [1030] 1526.0533 1526.9381 1527.8232 1528.7086 1529.5944 1530.4805 1531.3669
## [1037] 1532.2537 1533.1408 1534.0282 1534.9160 1535.8041 1536.6925 1537.5813
## [1044] 1538.4704 1539.3598 1540.2496 1541.1397 1542.0301 1542.9208 1543.8119
## [1051] 1544.7034 1545.5951 1546.4872 1547.3796 1548.2724 1549.1655 1550.0589
## [1058] 1550.9526 1551.8467 1552.7411 1553.6359 1554.5310 1555.4264 1556.3222
## [1065] 1557.2182 1558.1147 1559.0114 1559.9085 1560.8059 1561.7037 1562.6018
## [1072] 1563.5002 1564.3990 1565.2981 1566.1975 1567.0972 1567.9973 1568.8978
## [1079] 1569.7985 1570.6996
##
## $lower
## Time Series:
## Start = 2522
## End = 3601
## Frequency = 1
## 80% 95%
## 2522 766.4568 758.8174
## 2523 761.0389 750.2991
## 2524 757.0292 743.9342
## 2525 753.7475 738.6824
## 2526 750.9305 734.1410
## 2527 748.4431 730.1035
## 2528 746.2051 726.4473
## 2529 744.1645 723.0927
## 2530 742.2849 719.9842
## 2531 740.5400 717.0814
## 2532 738.9099 714.3540
## 2533 737.3791 711.7783
## 2534 735.9353 709.3356
## 2535 734.5687 707.0106
## 2536 733.2709 704.7908
## 2537 732.0352 702.6656
## 2538 730.8557 700.6264
## 2539 729.7276 698.6654
## 2540 728.6465 696.7762
## 2541 727.6087 694.9531
## 2542 726.6110 693.1911
## 2543 725.6505 691.4859
## 2544 724.7247 689.8336
## 2545 723.8313 688.2306
## 2546 722.9683 686.6739
## 2547 722.1338 685.1607
## 2548 721.3262 683.6884
## 2549 720.5439 682.2548
## 2550 719.7857 680.8578
## 2551 719.0503 679.4954
## 2552 718.3364 678.1660
## 2553 717.6432 676.8678
## 2554 716.9695 675.5994
## 2555 716.3145 674.3594
## 2556 715.6774 673.1466
## 2557 715.0573 671.9598
## 2558 714.4536 670.7978
## 2559 713.8656 669.6597
## 2560 713.2927 668.5444
## 2561 712.7342 667.4512
## 2562 712.1897 666.3791
## 2563 711.6586 665.3273
## 2564 711.1404 664.2952
## 2565 710.6347 663.2820
## 2566 710.1411 662.2871
## 2567 709.6590 661.3098
## 2568 709.1882 660.3495
## 2569 708.7283 659.4057
## 2570 708.2789 658.4779
## 2571 707.8398 657.5656
## 2572 707.4105 656.6682
## 2573 706.9908 655.7854
## 2574 706.5805 654.9167
## 2575 706.1792 654.0616
## 2576 705.7867 653.2199
## 2577 705.4027 652.3911
## 2578 705.0271 651.5749
## 2579 704.6596 650.7709
## 2580 704.2999 649.9788
## 2581 703.9480 649.1984
## 2582 703.6035 648.4292
## 2583 703.2663 647.6710
## 2584 702.9362 646.9236
## 2585 702.6131 646.1866
## 2586 702.2967 645.4599
## 2587 701.9870 644.7431
## 2588 701.6837 644.0361
## 2589 701.3867 643.3385
## 2590 701.0960 642.6503
## 2591 700.8112 641.9712
## 2592 700.5324 641.3009
## 2593 700.2593 640.6394
## 2594 699.9919 639.9864
## 2595 699.7301 639.3416
## 2596 699.4736 638.7051
## 2597 699.2225 638.0765
## 2598 698.9766 637.4557
## 2599 698.7357 636.8426
## 2600 698.4999 636.2370
## 2601 698.2690 635.6387
## 2602 698.0429 635.0477
## 2603 697.8215 634.4637
## 2604 697.6048 633.8867
## 2605 697.3926 633.3165
## 2606 697.1848 632.7530
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## 2608 696.7824 631.6455
## 2609 696.5876 631.1013
## 2610 696.3969 630.5633
## 2611 696.2103 630.0314
## 2612 696.0278 629.5055
## 2613 695.8492 628.9855
## 2614 695.6744 628.4714
## 2615 695.5035 627.9629
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## 2617 695.1729 626.9626
## 2618 695.0131 626.4706
## 2619 694.8568 625.9840
## 2620 694.7041 625.5026
## 2621 694.5548 625.0264
## 2622 694.4090 624.5553
## 2623 694.2665 624.0892
## 2624 694.1274 623.6280
## 2625 693.9915 623.1717
## 2626 693.8588 622.7201
## 2627 693.7293 622.2732
## 2628 693.6029 621.8310
## 2629 693.4796 621.3934
## 2630 693.3594 620.9602
## 2631 693.2421 620.5315
## 2632 693.1278 620.1072
## 2633 693.0164 619.6872
## 2634 692.9078 619.2714
## 2635 692.8021 618.8598
## 2636 692.6992 618.4524
## 2637 692.5991 618.0491
## 2638 692.5017 617.6497
## 2639 692.4069 617.2544
## 2640 692.3149 616.8629
## 2641 692.2254 616.4753
## 2642 692.1385 616.0916
## 2643 692.0542 615.7116
## 2644 691.9724 615.3353
## 2645 691.8931 614.9627
## 2646 691.8162 614.5937
## 2647 691.7418 614.2283
## 2648 691.6698 613.8664
## 2649 691.6001 613.5080
## 2650 691.5328 613.1530
## 2651 691.4678 612.8014
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## 2653 691.3447 612.1084
## 2654 691.2864 611.7668
## 2655 691.2304 611.4284
## 2656 691.1766 611.0933
## 2657 691.1250 610.7613
## 2658 691.0755 610.4324
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## 2660 690.9827 609.7840
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## 2664 690.8219 608.5231
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## 2675 690.5393 605.2881
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## 2812 700.2329 583.8149
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## $upper
## Time Series:
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## 3414 2147.6550 2624.1681
## 3415 2149.2304 2626.2457
## 3416 2150.8062 2628.3238
## 3417 2152.3824 2630.4026
## 3418 2153.9592 2632.4820
## 3419 2155.5365 2634.5620
## 3420 2157.1142 2636.6426
## 3421 2158.6924 2638.7238
## 3422 2160.2711 2640.8056
## 3423 2161.8503 2642.8880
## 3424 2163.4300 2644.9710
## 3425 2165.0101 2647.0547
## 3426 2166.5908 2649.1389
## 3427 2168.1719 2651.2237
## 3428 2169.7535 2653.3092
## 3429 2171.3356 2655.3952
## 3430 2172.9182 2657.4819
## 3431 2174.5013 2659.5692
## 3432 2176.0849 2661.6571
## 3433 2177.6689 2663.7456
## 3434 2179.2534 2665.8347
## 3435 2180.8385 2667.9244
## 3436 2182.4240 2670.0147
## 3437 2184.0100 2672.1056
## 3438 2185.5965 2674.1972
## 3439 2187.1834 2676.2893
## 3440 2188.7709 2678.3821
## 3441 2190.3589 2680.4755
## 3442 2191.9473 2682.5695
## 3443 2193.5362 2684.6641
## 3444 2195.1256 2686.7593
## 3445 2196.7156 2688.8551
## 3446 2198.3060 2690.9515
## 3447 2199.8968 2693.0486
## 3448 2201.4882 2695.1463
## 3449 2203.0801 2697.2445
## 3450 2204.6725 2699.3434
## 3451 2206.2653 2701.4429
## 3452 2207.8587 2703.5431
## 3453 2209.4525 2705.6438
## 3454 2211.0468 2707.7451
## 3455 2212.6416 2709.8471
## 3456 2214.2369 2711.9497
## 3457 2215.8327 2714.0529
## 3458 2217.4290 2716.1567
## 3459 2219.0258 2718.2612
## 3460 2220.6231 2720.3662
## 3461 2222.2209 2722.4719
## 3462 2223.8191 2724.5782
## 3463 2225.4179 2726.6851
## 3464 2227.0172 2728.7926
## 3465 2228.6169 2730.9007
## 3466 2230.2171 2733.0095
## 3467 2231.8179 2735.1189
## 3468 2233.4191 2737.2289
## 3469 2235.0208 2739.3395
## 3470 2236.6230 2741.4507
## 3471 2238.2258 2743.5626
## 3472 2239.8290 2745.6750
## 3473 2241.4327 2747.7881
## 3474 2243.0369 2749.9019
## 3475 2244.6416 2752.0162
## 3476 2246.2468 2754.1312
## 3477 2247.8525 2756.2468
## 3478 2249.4586 2758.3630
## 3479 2251.0653 2760.4798
## 3480 2252.6725 2762.5972
## 3481 2254.2802 2764.7153
## 3482 2255.8883 2766.8340
## 3483 2257.4970 2768.9533
## 3484 2259.1062 2771.0733
## 3485 2260.7159 2773.1938
## 3486 2262.3260 2775.3150
## 3487 2263.9367 2777.4368
## 3488 2265.5478 2779.5593
## 3489 2267.1595 2781.6823
## 3490 2268.7717 2783.8060
## 3491 2270.3843 2785.9304
## 3492 2271.9975 2788.0553
## 3493 2273.6111 2790.1809
## 3494 2275.2253 2792.3071
## 3495 2276.8399 2794.4339
## 3496 2278.4551 2796.5613
## 3497 2280.0707 2798.6894
## 3498 2281.6869 2800.8181
## 3499 2283.3036 2802.9474
## 3500 2284.9207 2805.0774
## 3501 2286.5384 2807.2080
## 3502 2288.1565 2809.3392
## 3503 2289.7752 2811.4710
## 3504 2291.3944 2813.6035
## 3505 2293.0140 2815.7366
## 3506 2294.6342 2817.8703
## 3507 2296.2548 2820.0047
## 3508 2297.8760 2822.1397
## 3509 2299.4977 2824.2753
## 3510 2301.1199 2826.4115
## 3511 2302.7425 2828.5484
## 3512 2304.3657 2830.6859
## 3513 2305.9894 2832.8241
## 3514 2307.6136 2834.9629
## 3515 2309.2383 2837.1023
## 3516 2310.8635 2839.2423
## 3517 2312.4892 2841.3830
## 3518 2314.1154 2843.5243
## 3519 2315.7421 2845.6662
## 3520 2317.3693 2847.8088
## 3521 2318.9970 2849.9520
## 3522 2320.6252 2852.0958
## 3523 2322.2540 2854.2403
## 3524 2323.8832 2856.3854
## 3525 2325.5129 2858.5311
## 3526 2327.1432 2860.6775
## 3527 2328.7739 2862.8245
## 3528 2330.4052 2864.9721
## 3529 2332.0370 2867.1204
## 3530 2333.6692 2869.2693
## 3531 2335.3020 2871.4189
## 3532 2336.9353 2873.5690
## 3533 2338.5691 2875.7198
## 3534 2340.2034 2877.8713
## 3535 2341.8382 2880.0234
## 3536 2343.4735 2882.1761
## 3537 2345.1093 2884.3295
## 3538 2346.7456 2886.4835
## 3539 2348.3825 2888.6381
## 3540 2350.0198 2890.7934
## 3541 2351.6576 2892.9493
## 3542 2353.2960 2895.1059
## 3543 2354.9349 2897.2631
## 3544 2356.5743 2899.4209
## 3545 2358.2141 2901.5794
## 3546 2359.8545 2903.7385
## 3547 2361.4954 2905.8982
## 3548 2363.1369 2908.0586
## 3549 2364.7788 2910.2196
## 3550 2366.4212 2912.3813
## 3551 2368.0642 2914.5436
## 3552 2369.7076 2916.7065
## 3553 2371.3516 2918.8701
## 3554 2372.9960 2921.0344
## 3555 2374.6410 2923.1992
## 3556 2376.2865 2925.3647
## 3557 2377.9325 2927.5309
## 3558 2379.5791 2929.6977
## 3559 2381.2261 2931.8651
## 3560 2382.8736 2934.0332
## 3561 2384.5217 2936.2019
## 3562 2386.1703 2938.3713
## 3563 2387.8193 2940.5413
## 3564 2389.4689 2942.7120
## 3565 2391.1190 2944.8833
## 3566 2392.7696 2947.0552
## 3567 2394.4208 2949.2278
## 3568 2396.0724 2951.4010
## 3569 2397.7246 2953.5749
## 3570 2399.3772 2955.7494
## 3571 2401.0304 2957.9246
## 3572 2402.6841 2960.1004
## 3573 2404.3383 2962.2768
## 3574 2405.9931 2964.4539
## 3575 2407.6483 2966.6317
## 3576 2409.3041 2968.8101
## 3577 2410.9603 2970.9891
## 3578 2412.6171 2973.1688
## 3579 2414.2744 2975.3491
## 3580 2415.9322 2977.5301
## 3581 2417.5905 2979.7117
## 3582 2419.2494 2981.8940
## 3583 2420.9087 2984.0769
## 3584 2422.5686 2986.2605
## 3585 2424.2290 2988.4447
## 3586 2425.8899 2990.6295
## 3587 2427.5513 2992.8151
## 3588 2429.2133 2995.0012
## 3589 2430.8757 2997.1880
## 3590 2432.5387 2999.3755
## 3591 2434.2022 3001.5636
## 3592 2435.8662 3003.7523
## 3593 2437.5307 3005.9418
## 3594 2439.1958 3008.1318
## 3595 2440.8613 3010.3225
## 3596 2442.5274 3012.5139
## 3597 2444.1940 3014.7059
## 3598 2445.8611 3016.8985
## 3599 2447.5288 3019.0918
## 3600 2449.1969 3021.2858
## 3601 2450.8656 3023.4804
#Plotting mean predicted values vs real data
meanvalues <- as.vector(trainarimafit$mean)
precios <- as.vector(test$AMZN.Close)
par(plot(meanvalues, type= "l", col= "red"))
## named list()
lines(precios, type = "l")
#We convert dataset as prophet input requires
df <- data.frame(ds = index(AMZN),
y = as.numeric(AMZN[,'AMZN.Close']))
#Annualized volatility
sd(returns)
## [1] 0.02419624
sqrt(252) * sd(returns)
## [1] 0.3841035
charts.RollingPerformance(R = returns["2008::2020"],
width = 23,
fun = "sd.annualized",
scale = 252,
main = "Amazon's monthly rolling volatility")
library(prophet)
## Loading required package: Rcpp
## Loading required package: rlang
#prophet model application
prophetpred <- prophet(df,daily.seasonality = TRUE)
future <- make_future_dataframe(prophetpred, periods = 30)
forecastprophet <- predict(prophetpred, future)
par(plot(future,type="l",col="red"))
## named list()