ARIMA models in R

Question

I am using the forecast package in R to implement ARIMA models. I'm having problems with fitting the model and the resulting residuals.

This an ARIMA model fitted to the training data:

m1_shattuck_train <- Arima(training_set_shattuck, order = c(0,1,1), seasonal = list(order = c(0,1,1), period = 7))

Then after i test several models on the test set suppose the one above performs the best, so i fit it on the entire data as so: (time_shattuck is the entire data set)

m1_shattuck_full <- Arima(time_shattuck, model = m1_shattuck_train)

When doing that, i get extremely low p-values for the Ljung-Box test indicating serial correlation in the residuals, which isn't at all apparent in the ACF plots.

Yet if i do this:

m1_shattuck_full <- Arima(time_shattuck, order = c(0,1,1), seasonal = list(order = c(0,1,1), period = 7))

i get different figures for the forecasts, and the p-values become high. The same ARIMA model is being applied in both cases. Does anyone know why the results are different? Thanks

Answer 1

You're fitting the same model, but the coefficients for each fitted model will be different because their input data are different. I don't have your data, so I'll be using the AirPassengers dataset.

library(forecast)

data("AirPassengers")

fit_same_model <- function(x) {
  Arima(x, order = c(0, 1, 1), seasonal = list(order = c(0, 1, 1), period = 12))
}

fit_same_model(AirPassengers)
# Series: x 
# ARIMA(0,1,1)(0,1,1)[12] 
# 
# Coefficients:
#           ma1     sma1
#       -0.3087  -0.1074
# s.e.   0.0890   0.0828
# 
# sigma^2 estimated as 137.5:  log likelihood=-507.5
# AIC=1021   AICc=1021.19   BIC=1029.63

training <- window(AirPassengers, end = c(1955, 12))
fit_same_model(training)
# Series: x 
# ARIMA(0,1,1)(0,1,1)[12] 
# 
# Coefficients:
#           ma1     sma1
#       -0.2436  -0.2393
# s.e.   0.1308   0.1161
# 
# sigma^2 estimated as 97.62:  log likelihood=-262.74
# AIC=531.48   AICc=531.84   BIC=538.27

Both models are ARIMA(0, 1, 1)(0, 1, 1)[12], but you can see the difference in how they were fitted.