Introduction

The data used for this analysis is the quarterly iron production (thousand tonnes) in Australia from 1956 to 1994.

I have changed the name of the variable of interest to something that is easier to read.

## # A tibble: 6 x 2
##   Quarter `Iron Production (thousand tonnes)`
##   <chr>                                 <dbl>
## 1 1956Q1                                  513
## 2 1956Q2                                  530
## 3 1956Q3                                  519
## 4 1956Q4                                  549
## 5 1957Q1                                  545
## 6 1957Q2                                  531

Data Analysis

Iron production seems to have grown at a relatively stable pace from 1956 to about 1970-72. After these years, iron production varied significantly, with no growing or decreasing production (1972-1982). In the year 1982, iron production started to increase again after a huge dip in 1981, although this time with more variability between quarters than the 1956-72 period.

Transformation

If we wish to predict future values beyond 1994, we would have to use a log transformation of the data in order to stabilize variance. Given that there exists a trend, we could also use a differencing of the data to make it stationary.

Once these methods are applied, the data appears to be stationary with constant variance - for the exception of 1980-81 and 1991-92.

When looking at the ACF and PACF, they cut off at lag 1, which suggests that an ARIMA(1, 0, 1) would be an appropriate model.

Modeling

Here, I have created an ARIMA(1, 1, 1) to simulate the iron production in the years 1985 to 1995. It seems to do a decent job in predicting the trend but not very good at predicting the actual values, althought the observed values are within the 95% confidence interval.

Model Improvement

Perhaps, the model can be improved if seasonality is taken into account. We can see that, for the most part, iron production has a seasonal component of 4.

The SARIMA(1, 1, 1)x(1, 0, 1)_4 is very similar to the ARIMA(1, 1, 1) and so significant improvement is done.

A last attempt at improving the model is by creating another SARIMA with seasonality of 12, since values of last year are very similar to values next year. In this case, there is some noticeable improvement in the prediction capability of the model.