hw 10

Repeat time series for Nile dataset

nile.ts <- ts(Nile, start=1, frequency=10) 
summary(nile.ts)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   456.0   798.5   893.5   919.4  1032.5  1370.0

nile.hw1 <-HoltWinters(nile.ts,gamma=FALSE)
nile.hw1

## 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

plot(nile.ts)

plot(nile.hw1)

nile.p <- predict(nile.hw1,n.ahead=10)
ts.plot(nile.ts,nile.p)

Perform time series for AirPassengers dataset alpha=0.5,beta=1,gamma=1

airp.ts<-ts(AirPassengers,start=1, frequency=12)
summary(airp.ts)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   104.0   180.0   265.5   280.3   360.5   622.0

airp.hw<-HoltWinters(airp.ts,alpha=0.5,beta=1, gamma=1)
airp.hw

## Holt-Winters exponential smoothing with trend and additive seasonal component.
## 
## Call:
## HoltWinters(x = airp.ts, alpha = 0.5, beta = 1, gamma = 1)
## 
## Smoothing parameters:
##  alpha: 0.5
##  beta : 1
##  gamma: 1
## 
## Coefficients:
##            [,1]
## a    552.062072
## b   -106.594593
## s1    64.476621
## s2   145.091539
## s3   231.496968
## s4   222.433688
## s5   115.175935
## s6    40.827961
## s7     6.953914
## s8   -80.399339
## s9  -209.706145
## s10 -255.372687
## s11 -268.656665
## s12 -120.062072

plot(airp.ts)

plot(airp.hw)

airp.p<- predict(airp.hw,n.ahead=12)
ts.plot(airp.ts,airp.p)

Time series for AirPassengers alpha=Null, beta=1, gamma=Null

airp.ts1<-ts(AirPassengers,start=1, frequency=10)
summary(airp.ts1)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   104.0   180.0   265.5   280.3   360.5   622.0

airp.hw1<-HoltWinters(airp.ts1,alpha=NULL,beta=1, gamma=NULL)
airp.hw1

## Holt-Winters exponential smoothing with trend and additive seasonal component.
## 
## Call:
## HoltWinters(x = airp.ts1, alpha = NULL, beta = 1, gamma = NULL)
## 
## Smoothing parameters:
##  alpha: 0.9493386
##  beta : 1
##  gamma: 1
## 
## Coefficients:
##            [,1]
## a   431.7884126
## b    27.0306710
## s1    8.1637757
## s2   13.1442083
## s3   10.6643227
## s4   23.1524072
## s5   15.9061745
## s6   -5.1141818
## s7  -26.5039556
## s8  -23.4314649
## s9  -14.7577416
## s10   0.2115874

plot(airp.ts1)

plot(airp.hw1)

airp.p1<- predict(airp.hw1,n.ahead=10)
ts.plot(airp.ts1,airp.p1)