Assignment

Repeat the same functions with different values of alpha, beta, and gamma of your choosing on…

*AirPassengers

*EuStockMarkets

When using the EuStockMarkets, choose one column

Nile Data

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
plot(Nile)

frequency(Nile)
## [1] 1
Nile_ts <- ts(Nile, start=1, frequency=2) 
summary(Nile_ts)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   456.0   798.5   893.5   919.4  1032.5  1370.0
plot(decompose(Nile_ts))

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

plot(Nile_hw)

Nile_pt <- predict(Nile_hw, n.ahead=10)
ts.plot(Nile_ts, Nile_pt)

Air Passenger Data

AirPassengers
##      Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
## 1949 112 118 132 129 121 135 148 148 136 119 104 118
## 1950 115 126 141 135 125 149 170 170 158 133 114 140
## 1951 145 150 178 163 172 178 199 199 184 162 146 166
## 1952 171 180 193 181 183 218 230 242 209 191 172 194
## 1953 196 196 236 235 229 243 264 272 237 211 180 201
## 1954 204 188 235 227 234 264 302 293 259 229 203 229
## 1955 242 233 267 269 270 315 364 347 312 274 237 278
## 1956 284 277 317 313 318 374 413 405 355 306 271 306
## 1957 315 301 356 348 355 422 465 467 404 347 305 336
## 1958 340 318 362 348 363 435 491 505 404 359 310 337
## 1959 360 342 406 396 420 472 548 559 463 407 362 405
## 1960 417 391 419 461 472 535 622 606 508 461 390 432
plot(AirPassengers)

frequency(AirPassengers)
## [1] 12
AirPassengers_ts <- ts(AirPassengers, start=1, frequency=2) 
summary(AirPassengers_ts)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   104.0   180.0   265.5   280.3   360.5   622.0
plot(decompose(AirPassengers_ts))

AirPassengers_hw <- HoltWinters(AirPassengers_ts, gamma=F, seasonal = "additive") 
AirPassengers_hw
## Holt-Winters exponential smoothing with trend and without seasonal component.
## 
## Call:
## HoltWinters(x = AirPassengers_ts, gamma = F, seasonal = "additive")
## 
## Smoothing parameters:
##  alpha: 1
##  beta : 0.003218516
##  gamma: FALSE
## 
## Coefficients:
##         [,1]
## a 432.000000
## b   4.597605
plot(AirPassengers_ts)

plot(AirPassengers_hw)

AirPassengers_pt <- predict(AirPassengers_hw, n.ahead=10)
ts.plot(AirPassengers_ts, AirPassengers_pt)