# install.packages("forecast")
library("forecast")

# Read the data
data = scan('fancy.dat')
ts_data <- ts(data, frequency=12, start=c(1987,1))
ts_data

# Plot the time series
png('time_series.png')
plot.ts(ts_data)
dev.off()

# Fit the ARMA model
fit = auto.arima(ts_data)
summary(fit)
# Series: ts_data 
# ARIMA(1,1,1)(0,1,1)[12]                    
#    Coefficients:
#    ar1      ma1    sma1
# 0.2401  -0.9013  0.7499
# s.e.  0.1427   0.0709  0.1790
# 
# sigma^2 estimated as 15464184:  log likelihood=-693.69
# AIC=1395.38   AICc=1395.98   BIC=1404.43
# Training set error measures:
#                 ME     RMSE      MAE       MPE     MAPE      MASE        ACF1
# Training set 328.301 3615.374 2171.002 -2.481166 15.97302 0.4905797 -0.02521172