library(Rcmdr)
## Loading required package: splines
## Loading required package: RcmdrMisc
## Loading required package: car
## Loading required package: sandwich
## The Commander GUI is launched only in interactive sessions
#install.packages(RcmdrPlugin.epack)
library(forecast)
## Loading required package: zoo
##
## Attaching package: 'zoo'
##
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
##
## Loading required package: timeDate
## This is forecast 6.2
data("AirPassengers")
a=ets(AirPassengers)
a
## ETS(M,A,M)
##
## Call:
## ets(y = AirPassengers)
##
## Smoothing parameters:
## alpha = 0.5901
## beta = 0.0058
## gamma = 1e-04
##
## Initial states:
## l = 126.9791
## b = 1.6483
## s=0.8865 0.7928 0.9226 1.0582 1.2186 1.2371
## 1.1069 0.9818 0.985 1.0149 0.8946 0.901
##
## sigma: 0.0367
##
## AIC AICc BIC
## 1391.174 1395.457 1438.691
predict(a,10)
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Jan 1961 444.9979 424.0692 465.9267 412.9901 477.0057
## Feb 1961 444.1187 419.8324 468.4049 406.9760 481.2613
## Mar 1961 506.4125 475.2920 537.5330 458.8178 554.0072
## Apr 1961 493.9890 460.5937 527.3844 442.9153 545.0628
## May 1961 494.8520 458.5835 531.1205 439.3841 550.3198
## Jun 1961 560.6983 516.6174 604.7792 493.2823 628.1143
## Jul 1961 629.8161 577.1310 682.5012 549.2412 710.3910
## Aug 1961 623.4715 568.3301 678.6129 539.1400 707.8031
## Sep 1961 544.0719 493.4577 594.6861 466.6642 621.4796
## Oct 1961 476.6947 430.2464 523.1430 405.6581 547.7313
str(predict(a,20))
## List of 9
## $ model :List of 18
## ..$ loglik : num -680
## ..$ aic : num 1391
## ..$ bic : num 1439
## ..$ aicc : num 1395
## ..$ mse : num 121
## ..$ amse : num 194
## ..$ fit :List of 4
## .. ..$ value : num 1359
## .. ..$ par : num [1:16] 5.90e-01 5.82e-03 1.21e-04 1.27e+02 1.65 ...
## .. ..$ fail : int 1
## .. ..$ fncount: int 2001
## ..$ residuals : Time-Series [1:144] from 1949 to 1961: -0.0336 0.0329 -0.0134 -0.011 -0.0747 ...
## ..$ fitted : Time-Series [1:144] from 1949 to 1961: 116 114 134 130 131 ...
## ..$ states : mts [1:145, 1:14] 127 126 130 131 132 ...
## .. ..- attr(*, "dimnames")=List of 2
## .. .. ..$ : NULL
## .. .. ..$ : chr [1:14] "l" "b" "s1" "s2" ...
## .. ..- attr(*, "tsp")= num [1:3] 1949 1961 12
## .. ..- attr(*, "class")= chr [1:3] "mts" "ts" "matrix"
## ..$ par : Named num [1:16] 5.90e-01 5.82e-03 1.21e-04 1.27e+02 1.65 ...
## .. ..- attr(*, "names")= chr [1:16] "alpha" "beta" "gamma" "l" ...
## ..$ m : num 12
## ..$ method : chr "ETS(M,A,M)"
## ..$ components: chr [1:4] "M" "A" "M" "FALSE"
## ..$ call : language ets(y = AirPassengers)
## ..$ initstate : Named num [1:14] 126.979 1.648 0.887 0.793 0.923 ...
## .. ..- attr(*, "names")= chr [1:14] "l" "b" "s1" "s2" ...
## ..$ sigma2 : num 0.00135
## ..$ x : Time-Series [1:144] from 1949 to 1961: 112 118 132 129 121 135 148 148 136 119 ...
## ..- attr(*, "class")= chr "ets"
## $ mean : Time-Series [1:20] from 1961 to 1963: 445 444 506 494 495 ...
## $ level : num [1:2] 80 95
## $ x : Time-Series [1:144] from 1949 to 1961: 112 118 132 129 121 135 148 148 136 119 ...
## $ upper : mts [1:20, 1:2] 466 468 538 527 531 ...
## ..- attr(*, "dimnames")=List of 2
## .. ..$ : NULL
## .. ..$ : chr [1:2] "Series 1" "Series 2"
## ..- attr(*, "tsp")= num [1:3] 1961 1963 12
## ..- attr(*, "class")= chr [1:3] "mts" "ts" "matrix"
## $ lower : mts [1:20, 1:2] 424 420 475 461 459 ...
## ..- attr(*, "dimnames")=List of 2
## .. ..$ : NULL
## .. ..$ : chr [1:2] "Series 1" "Series 2"
## ..- attr(*, "tsp")= num [1:3] 1961 1963 12
## ..- attr(*, "class")= chr [1:3] "mts" "ts" "matrix"
## $ fitted : Time-Series [1:144] from 1949 to 1961: 116 114 134 130 131 ...
## $ method : chr "ETS(M,A,M)"
## $ residuals: Time-Series [1:144] from 1949 to 1961: -0.0336 0.0329 -0.0134 -0.011 -0.0747 ...
## - attr(*, "class")= chr "forecast"
b=auto.arima(AirPassengers)
b
## Series: AirPassengers
## ARIMA(0,1,1)(0,1,0)[12]
##
## Coefficients:
## ma1
## -0.3184
## s.e. 0.0877
##
## sigma^2 estimated as 137.3: log likelihood=-508.32
## AIC=1020.64 AICc=1020.73 BIC=1026.39
predict(b,10)
## $pred
## Jan Feb Mar Apr May Jun Jul
## 1961 446.7582 420.7582 448.7582 490.7582 501.7582 564.7582 651.7582
## Aug Sep Oct
## 1961 635.7582 537.7582 490.7582
##
## $se
## Jan Feb Mar Apr May Jun Jul
## 1961 11.71600 14.17842 16.27239 18.12605 19.80699 21.35602 22.80006
## Aug Sep Oct
## 1961 24.15793 25.44344 26.66705
ts.plot(AirPassengers)
#MAPE should be minimum, and AIC should be minimum