Discussion 2

Monthly reported number of chickenpox, New York city, 1931-1972

library(forecast)

## Warning: package 'forecast' was built under R version 3.3.2

library(fpp)

## Loading required package: fma

## Warning: package 'fma' was built under R version 3.3.2

## Loading required package: expsmooth

## Loading required package: lmtest

## Warning: package 'lmtest' was built under R version 3.3.2

## Loading required package: zoo

## Warning: package 'zoo' was built under R version 3.3.2

## 
## Attaching package: 'zoo'

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

## Loading required package: tseries

## Warning: package 'tseries' was built under R version 3.3.2

library(xts)

## Warning: package 'xts' was built under R version 3.3.2

library(tseries)


chickenpox= read.csv("Desktop/Forcasting/monthly-reported-number-of-chick.csv")


str(chickenpox)

## 'data.frame':    498 obs. of  2 variables:
##  $ Month                                                          : Factor w/ 498 levels "1931-01","1931-02",..: 1 2 3 4 5 6 7 8 9 10 ...
##  $ Monthly.reported.number.of.chickenpox..New.York.city..1931.1972: int  956 927 1585 1536 1448 1272 303 68 62 116 ...

names(chickenpox)[2]<-c("reported.incidents")
head(chickenpox)

##     Month reported.incidents
## 1 1931-01                956
## 2 1931-02                927
## 3 1931-03               1585
## 4 1931-04               1536
## 5 1931-05               1448
## 6 1931-06               1272

tail(chickenpox)

##       Month reported.incidents
## 493 1972-01                320
## 494 1972-02                463
## 495 1972-03                690
## 496 1972-04                847
## 497 1972-05               1121
## 498 1972-06               1048

attach(chickenpox)

plot(chickenpox$reported.incidents,type="l",xlab="Month",ylab="Reported # of Chicken Pox in NYC")

Time series

pox.ts <- ts(chickenpox$reported.incidents,frequency=12,start=c(1931,1))
plot(pox.ts)

Decompose

decAdd<-decompose(pox.ts,type="additive")  
decMult<-decompose(pox.ts,type="multiplicative")

#plot
plot(decAdd)

plot(decMult)

Error

error1<-na.omit(decAdd$random)  
error2<-na.omit(decMult$random)  
error1<-as.vector(error1)      
error2<-as.vector(error2)     
abserror1<-abs(error1)  
abserror2<-abs(error2)
sqerror1<-error1^2
sqerror2<-error2^2

#Calculate Statisics
#mean error (bias)
me<-c(mean(error1),mean(error2))
#mean absolute deviation (variance)
mad<-c(mean(abserror1), mean(abserror2))
#mean square error (variance)
mse<-c(mean(sqerror1),mean(sqerror2))
#root mean square error (variance)
rmse<-sqrt(mse)
all<-c(me,mad,rmse)
all

## [1]   0.4211107   0.9958124 174.8686218   0.9958124 226.5805330   1.0393789