# How do I forecast quarterly public expenses based on annual budgets and potentially other variables?

I have some time series data from 2008 and forward (see below) on quarterly public expenses and annual public budgets. I would like to forecast the last two quarters of 2018 as precisely as possible, but I am unsure about what methods I should use.

I have been considering a vector autoregressive model, but there is an issue with different frequencies on the data. I guess I could split the budget into 4 equal parts.

I have also considered computing the deviation between the two series and then use a univariate model instead, but that would rule out adding additional explaining variables such as demography.

If possible I would like some suggestions on what type of models I should look into. I am not an expert in times series analysis and especially not the multivariate ones, but I hope it is possible.

I hope you can help. Thank you!

+------------+-----------------+
|    Date    |    Expenses     |
+------------+-----------------+
| 2008-01-01 | 66.386.086.765  |
| ...        | ...             |
| 2016-01-01 | 78.200.910.570  |
| 2016-04-01 | 167.604.150.482 |
| 2016-07-01 | 251.017.792.801 |
| 2016-10-01 | 337.595.471.006 |
| 2017-01-01 | 77.580.707.994  |
| 2017-04-01 | 166.599.846.864 |
| 2017-07-01 | 251.331.721.551 |
| 2017-10-01 | 337.247.375.085 |
| 2018-01-01 | 76.467.286.000  |
| 2018-04-01 | 166.634.900.000 |
| 2018-07-01 | ?               |
| 2018-10-01 | ?               |
+------------+-----------------+
+------+-----------------+
| Date |     Budget      |
+------+-----------------+
| 2008 | 295.130.222.937 |
| ...  | ...             |
| 2016 | 348.210.251.795 |
| 2017 | 346.244.633.739 |
| 2018 | 346.127.455.000 |
+------+-----------------+

• Those are cumulative quarterly expenses, not actual quarterly expenses, right? – whuber Aug 16 at 13:28
• Yes, you are right. I have change it to actual quarterly expenses in my model now – Frederik Aug 21 at 10:31