# 
# Computes the maximum likelihood ARIMA coefficients for the yield data set.
# 
# Written by:
# -- 
# John L. Weatherwax                2009-04-21
# 
# email: wax@alum.mit.edu
# 
# Please send comments and especially bug reports to the
# above email address.
# 
#-----

# get the data into an R vector: 
Y <- c(
    17400, 15000, 17047, 19159, 24185, 30420 ,
    29866, 21575, 18865, 18487, 27407, 27410 ,
    25126, 18458, 20210, 21870, 14587, 17499 ,
    23292, 18691, 17007, 14870, 26572, 27138 ,
    13357, 17809, 14477, 15831, 19393, 17070 ,
    17874, 14883, 19013, 13886, 16468, 11019 ,
    10889, 16658, 14616, 16159, 17202, 12464 ,
    10193, 11322,  9971, 11611, 11619, 12401 ,
     9196, 12443, 11677, 11185, 11015,  9738 
)

Y <- log(Y)

# construct a ARIMA(2,1,1) model on this data ... explicitly considering the mean
fit <- arima( Y, order=c(2,1,1), method="ML" )

print(fit)

# drop the AR(2) components and reestimate the model:
fit <- arima( Y, order=c(0,1,1), method="ML" )

# predict the next four months: 
predict( fit, n.ahead=4 )