R Notebook

#download data
library(readr)
mydata <- read_csv("IOWA Farm Data.csv")

Parsed with column specification:
cols(
  DATE = col_character(),
  A045RC1Q027SBEA = col_double()
)

View(mydata)

#libraries needed
library(forecast)
library(xts)
library(tseries)
library(fpp)
library(fpp2)

#view data
str(mydata)

Classes ‘spec_tbl_df’, ‘tbl_df’, ‘tbl’ and 'data.frame':    129 obs. of  2 variables:
 $ DATE           : chr  "1/1/1947" "4/1/1947" "7/1/1947" "10/1/1947" ...
 $ A045RC1Q027SBEA: num  20.2 20.9 19.8 20 21.9 ...
 - attr(*, "spec")=
  .. cols(
  ..   DATE = col_character(),
  ..   A045RC1Q027SBEA = col_double()
  .. )

head(mydata)

summary(mydata)

     DATE           A045RC1Q027SBEA 
 Length:129         Min.   : 19.80  
 Class :character   1st Qu.: 32.74  
 Mode  :character   Median : 44.57  
                    Mean   : 56.16  
                    3rd Qu.: 67.23  
                    Max.   :156.30  

names(mydata)

[1] "DATE"            "A045RC1Q027SBEA"

#set up time series and plot
myts=ts(mydata$A045RC1Q027SBEA,frequency=4,start=c(1947))
plot(myts, main="Quarterly Iowa NONFarm Income (1948-1979)",ylab="Nonfarm Income (Billions)")

#model 1 - Auto selection ETS
par(mfrow=c(2,2))

model1<-ets(myts,model = "ZZZ")
model1

ETS(M,A,N) 

Call:
 ets(y = myts, model = "ZZZ") 

  Smoothing parameters:
    alpha = 0.9999 
    beta  = 0.1019 

  Initial states:
    l = 19.7697 
    b = 0.432 

  sigma:  0.0193

     AIC     AICc      BIC 
615.4408 615.9286 629.7399 

#MAN was picked automatic

model1.pred=forecast(model1,h=8)
plot(forecast(model1,h=8), ylab="Nonfarm Income",main="Model1 Auto-select: MAN")
model1$par

     alpha       beta          l          b 
 0.9999000  0.1019448 19.7696663  0.4319821 

summary(model1)

ETS(M,A,N) 

Call:
 ets(y = myts, model = "ZZZ") 

  Smoothing parameters:
    alpha = 0.9999 
    beta  = 0.1019 

  Initial states:
    l = 19.7697 
    b = 0.432 

  sigma:  0.0193

     AIC     AICc      BIC 
615.4408 615.9286 629.7399 

Training set error measures:
                    ME    RMSE       MAE       MPE     MAPE
Training set 0.2409512 1.00811 0.6996218 0.2307613 1.350205
                  MASE      ACF1
Training set 0.1655465 0.2917487

hist(residuals(model1))

#Model 2 with ETS ANN
model2<-ets(myts,model = "ANN")
model2

ETS(A,N,N) 

Call:
 ets(y = myts, model = "ANN") 

  Smoothing parameters:
    alpha = 0.9999 

  Initial states:
    l = 20.2415 

  sigma:  1.7852

     AIC     AICc      BIC 
780.4207 780.6127 789.0001 

model2.pred=forecast(model2,h=8)
plot(forecast(model2,h=8), ylab="Nonfarm Income",main="Model_2 ANN")
model2$par

   alpha        l 
 0.99990 20.24154 

summary(model2)

ETS(A,N,N) 

Call:
 ets(y = myts, model = "ANN") 

  Smoothing parameters:
    alpha = 0.9999 

  Initial states:
    l = 20.2415 

  sigma:  1.7852

     AIC     AICc      BIC 
780.4207 780.6127 789.0001 

Training set error measures:
                   ME     RMSE      MAE      MPE     MAPE      MASE
Training set 1.054834 1.771319 1.184007 1.554514 1.939676 0.2801631
                  ACF1
Training set 0.6671985

hist(residuals(model2))

#model 3 ets MAM

Model3 <- ets(myts, model="MAM")
Model3 

ETS(M,Ad,M) 

Call:
 ets(y = myts, model = "MAM") 

  Smoothing parameters:
    alpha = 0.9626 
    beta  = 0.161 
    gamma = 2e-04 
    phi   = 0.9797 

  Initial states:
    l = 19.7873 
    b = 0.0035 
    s = 0.9964 1 1.0024 1.0012

  sigma:  0.0201

     AIC     AICc      BIC 
630.3840 632.2484 658.9821 

Model3.pred=forecast(Model3,h=8)
plot(forecast(Model3,h=8), ylab="Nonfarm Income",main="Model_3 MAM")
Model3$par

       alpha         beta        gamma          phi            l 
9.626321e-01 1.609806e-01 1.508929e-04 9.797130e-01 1.978729e+01 
           b           s0           s1           s2 
3.459506e-03 9.963982e-01 9.999871e-01 1.002411e+00 

summary(Model3)

ETS(M,Ad,M) 

Call:
 ets(y = myts, model = "MAM") 

  Smoothing parameters:
    alpha = 0.9626 
    beta  = 0.161 
    gamma = 2e-04 
    phi   = 0.9797 

  Initial states:
    l = 19.7873 
    b = 0.0035 
    s = 0.9964 1 1.0024 1.0012

  sigma:  0.0201

     AIC     AICc      BIC 
630.3840 632.2484 658.9821 

Training set error measures:
                    ME     RMSE       MAE       MPE     MAPE
Training set 0.2763901 1.001765 0.7210062 0.3943811 1.422822
                  MASE      ACF1
Training set 0.1706065 0.2671561

hist(residuals(Model3))