Question

Nile
## Time Series:
## Start = 1871 
## End = 1970 
## Frequency = 1 
##   [1] 1120 1160  963 1210 1160 1160  813 1230 1370 1140  995  935 1110  994
##  [15] 1020  960 1180  799  958 1140 1100 1210 1150 1250 1260 1220 1030 1100
##  [29]  774  840  874  694  940  833  701  916  692 1020 1050  969  831  726
##  [43]  456  824  702 1120 1100  832  764  821  768  845  864  862  698  845
##  [57]  744  796 1040  759  781  865  845  944  984  897  822 1010  771  676
##  [71]  649  846  812  742  801 1040  860  874  848  890  744  749  838 1050
##  [85]  918  986  797  923  975  815 1020  906  901 1170  912  746  919  718
##  [99]  714  740

load nile dataset

nile <- data.frame(Nile)
nile
##     Nile
## 1   1120
## 2   1160
## 3    963
## 4   1210
## 5   1160
## 6   1160
## 7    813
## 8   1230
## 9   1370
## 10  1140
## 11   995
## 12   935
## 13  1110
## 14   994
## 15  1020
## 16   960
## 17  1180
## 18   799
## 19   958
## 20  1140
## 21  1100
## 22  1210
## 23  1150
## 24  1250
## 25  1260
## 26  1220
## 27  1030
## 28  1100
## 29   774
## 30   840
## 31   874
## 32   694
## 33   940
## 34   833
## 35   701
## 36   916
## 37   692
## 38  1020
## 39  1050
## 40   969
## 41   831
## 42   726
## 43   456
## 44   824
## 45   702
## 46  1120
## 47  1100
## 48   832
## 49   764
## 50   821
## 51   768
## 52   845
## 53   864
## 54   862
## 55   698
## 56   845
## 57   744
## 58   796
## 59  1040
## 60   759
## 61   781
## 62   865
## 63   845
## 64   944
## 65   984
## 66   897
## 67   822
## 68  1010
## 69   771
## 70   676
## 71   649
## 72   846
## 73   812
## 74   742
## 75   801
## 76  1040
## 77   860
## 78   874
## 79   848
## 80   890
## 81   744
## 82   749
## 83   838
## 84  1050
## 85   918
## 86   986
## 87   797
## 88   923
## 89   975
## 90   815
## 91  1020
## 92   906
## 93   901
## 94  1170
## 95   912
## 96   746
## 97   919
## 98   718
## 99   714
## 100  740

-Repeat the ts(),

nile.ts <- ts(nile, start=1, frequency=10)
summary(nile.ts)
##       Nile       
##  Min.   : 456.0  
##  1st Qu.: 798.5  
##  Median : 893.5  
##  Mean   : 919.4  
##  3rd Qu.:1032.5  
##  Max.   :1370.0

-Repeat HoltWinters()

nile.hltWtrs <- HoltWinters(nile.ts, gamma=FALSE)
nile.hltWtrs
## Holt-Winters exponential smoothing with trend and without seasonal component.
## 
## Call:
## HoltWinters(x = nile.ts, gamma = FALSE)
## 
## Smoothing parameters:
##  alpha: 0.4190643
##  beta : 0.05987705
##  gamma: FALSE
## 
## Coefficients:
##         [,1]
## a 756.913740
## b  -7.424597

-Repeat the predict()

nile.prdct <- predict(nile.hltWtrs, n.ahead = 10)
nile.prdct
## Time Series:
## Start = c(11, 1) 
## End = c(11, 10) 
## Frequency = 10 
##            fit
##  [1,] 749.4891
##  [2,] 742.0645
##  [3,] 734.6400
##  [4,] 727.2154
##  [5,] 719.7908
##  [6,] 712.3662
##  [7,] 704.9416
##  [8,] 697.5170
##  [9,] 690.0924
## [10,] 682.6678

-Repeat the plot()

ts.plot(nile.ts,nile.prdct)

plot(nile.ts)

plot(nile.hltWtrs)

-Repeat the same functions with different values of alpha, beta, and gamma of your choosing on. AirPassengers Repeat the ts()

ap.ts <- ts(AirPassengers, start=1, frequency=10)
ap.ts
## Time Series:
## Start = c(1, 1) 
## End = c(15, 4) 
## Frequency = 10 
##   [1] 112 118 132 129 121 135 148 148 136 119 104 118 115 126 141 135 125
##  [18] 149 170 170 158 133 114 140 145 150 178 163 172 178 199 199 184 162
##  [35] 146 166 171 180 193 181 183 218 230 242 209 191 172 194 196 196 236
##  [52] 235 229 243 264 272 237 211 180 201 204 188 235 227 234 264 302 293
##  [69] 259 229 203 229 242 233 267 269 270 315 364 347 312 274 237 278 284
##  [86] 277 317 313 318 374 413 405 355 306 271 306 315 301 356 348 355 422
## [103] 465 467 404 347 305 336 340 318 362 348 363 435 491 505 404 359 310
## [120] 337 360 342 406 396 420 472 548 559 463 407 362 405 417 391 419 461
## [137] 472 535 622 606 508 461 390 432

-Repeat HoltWinters()

ap.hltWtrs <- HoltWinters(ap.ts, alpha = 0.5,beta = 0.5, gamma = 0.5)
ap.hltWtrs
## Holt-Winters exponential smoothing with trend and additive seasonal component.
## 
## Call:
## HoltWinters(x = ap.ts, alpha = 0.5, beta = 0.5, gamma = 0.5)
## 
## Smoothing parameters:
##  alpha: 0.5
##  beta : 0.5
##  gamma: 0.5
## 
## Coefficients:
##            [,1]
## a   338.9700725
## b   -63.7244028
## s1   19.7077757
## s2   -0.5764355
## s3  -36.7311454
## s4  -42.0547400
## s5  -45.5343836
## s6  -45.7962881
## s7  -35.8723082
## s8   13.2699144
## s9   42.7911919
## s10  66.9341373

-Repeat the predict()

ap.prdct <- predict(ap.hltWtrs, n.head=10)
ap.prdct
## Time Series:
## Start = c(15, 5) 
## End = c(15, 5) 
## Frequency = 10 
##           fit
## [1,] 294.9534

-Repeat the plot()

ts.plot(ap.ts,ap.prdct)

plot(ap.ts)

plot(ap.hltWtrs)

plot(ap.prdct)

-Repeat the same functions with different values of alpha, beta, and gamma of your choosing on. EuStockMarkets When using the EuStockMarkets, choose one column

es <- EuStockMarkets[,2]

-Repeat the ts()

es.ts <- ts(es, start=1, frequency=10)

-Repeat HoltWinters()

es.hltWtrs <- HoltWinters(es.ts, alpha = 0.3,beta = 0.2, gamma = 0.01)
es.hltWtrs
## Holt-Winters exponential smoothing with trend and additive seasonal component.
## 
## Call:
## HoltWinters(x = es.ts, alpha = 0.3, beta = 0.2, gamma = 0.01)
## 
## Smoothing parameters:
##  alpha: 0.3
##  beta : 0.2
##  gamma: 0.01
## 
## Coefficients:
##             [,1]
## a   7545.3729323
## b    -58.7161493
## s1     0.8350917
## s2     4.8421540
## s3     0.5373249
## s4    -1.4020256
## s5     1.3752334
## s6    -5.0260308
## s7    -5.8744244
## s8     3.3358325
## s9    -6.9745805
## s10    0.9914411

-Repeat the predict()

es.prdct <- predict(es.hltWtrs, n.ahead = 10)
es.prdct
## Time Series:
## Start = c(187, 1) 
## End = c(187, 10) 
## Frequency = 10 
##            fit
##  [1,] 7487.492
##  [2,] 7432.783
##  [3,] 7369.762
##  [4,] 7309.106
##  [5,] 7253.167
##  [6,] 7188.050
##  [7,] 7128.485
##  [8,] 7078.980
##  [9,] 7009.953
## [10,] 6959.203

-Repeat the plot()

ts.plot(es.ts,es.prdct)

plot(es.ts)

plot(es.hltWtrs)

plot(es.prdct)