Dis3

passengermiles <- read.csv("~/Downloads/passenger-miles-mil-flown-domest.csv")

library(fpp)

## Loading required package: forecast

## Loading required package: fma

## Loading required package: expsmooth

## Loading required package: lmtest

## Loading required package: zoo

## 
## Attaching package: 'zoo'

## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric

## Loading required package: tseries

library(forecast)
library(fma)
library(expsmooth)
library(lmtest)
library(zoo)

passenger.ts = ts(passengermiles[,2],frequency=12,start=c(1962,7))
plot(passenger.ts,xlab="Month",ylab="miles flown(millions)",main= "Passenger miles flown domestic U.K.1962-1972")

head(passenger.ts)

##        Jul   Aug   Sep   Oct   Nov   Dec
## 1962 101.6 101.5  84.3  51.0  38.5  33.7

tail(passenger.ts)

##        Jan   Feb   Mar   Apr   May   Jun
## 1972  76.8  68.8  90.5 102.6 128.3    NA

## Arima Model
fit1=auto.arima(passenger.ts)
fit1

## Series: passenger.ts 
## ARIMA(1,1,1)(0,1,1)[12] 
## 
## Coefficients:
##          ar1      ma1     sma1
##       0.5015  -0.8534  -0.5221
## s.e.  0.1313   0.0735   0.1460
## 
## sigma^2 estimated as 22.87:  log likelihood=-317.5
## AIC=642.99   AICc=643.38   BIC=653.68

summary(fit1)

## Series: passenger.ts 
## ARIMA(1,1,1)(0,1,1)[12] 
## 
## Coefficients:
##          ar1      ma1     sma1
##       0.5015  -0.8534  -0.5221
## s.e.  0.1313   0.0735   0.1460
## 
## sigma^2 estimated as 22.87:  log likelihood=-317.5
## AIC=642.99   AICc=643.38   BIC=653.68
## 
## Training set error measures:
##                      ME    RMSE      MAE        MPE     MAPE      MASE
## Training set -0.3410848 4.47029 3.420549 -0.7388153 3.959829 0.5041305
##                     ACF1
## Training set -0.02806555

fit2=Arima(passenger.ts,order=c(1,1,1), seasonal=c(0,1,0))
fit2

## Series: passenger.ts 
## ARIMA(1,1,1)(0,1,0)[12] 
## 
## Coefficients:
##          ar1      ma1
##       0.3777  -0.8657
## s.e.  0.1474   0.0934
## 
## sigma^2 estimated as 26.92:  log likelihood=-324.8
## AIC=655.6   AICc=655.83   BIC=663.62

##ETS
fit3=ets(passenger.ts, model="ZZZ")

## Warning in ets(passenger.ts, model = "ZZZ"): Missing values encountered.
## Using longest contiguous portion of time series

fit3

## ETS(A,Ad,A) 
## 
## Call:
##  ets(y = passenger.ts, model = "ZZZ") 
## 
##   Smoothing parameters:
##     alpha = 0.7281 
##     beta  = 1e-04 
##     gamma = 1e-04 
##     phi   = 0.9788 
## 
##   Initial states:
##     l = 55.651 
##     b = 1.1837 
##     s=26.4599 10 -5.4469 -18.8031 -34.9832 -33.0782
##            -30.3075 -31.1193 -7.665 27.3536 47.4661 50.1235
## 
##   sigma:  4.2322
## 
##      AIC     AICc      BIC 
## 948.0833 954.9233 998.1075

plot(fit3)

summary(fit3)

## ETS(A,Ad,A) 
## 
## Call:
##  ets(y = passenger.ts, model = "ZZZ") 
## 
##   Smoothing parameters:
##     alpha = 0.7281 
##     beta  = 1e-04 
##     gamma = 1e-04 
##     phi   = 0.9788 
## 
##   Initial states:
##     l = 55.651 
##     b = 1.1837 
##     s=26.4599 10 -5.4469 -18.8031 -34.9832 -33.0782
##            -30.3075 -31.1193 -7.665 27.3536 47.4661 50.1235
## 
##   sigma:  4.2322
## 
##      AIC     AICc      BIC 
## 948.0833 954.9233 998.1075 
## 
## Training set error measures:
##                     ME     RMSE      MAE        MPE     MAPE      MASE
## Training set 0.1104657 4.232196 3.313952 0.09477059 4.026201 0.4884199
##                    ACF1
## Training set 0.01556275