I’ve been working on the church budget committee for the last 3-4 years. I’ve always wanted to fit a time series model to the church income, so I finally did it. The first model you see here is a more of a model that the church uses. If the church does any prediction, they just think the average of the previous tithes would be the best model. I also incorporated what the church leaders also think in their minds that last year’s month probably has some implication of what will happen the next month. This is called a moving average in time series.
Differencing of 1 for stationairity.
I next adjusted the series for seasonaility. I believe it is a wide known belief that certain months relate to one another in peoples giving. Less people are in church during the summers producing a slightly lower tithing rate. Other things such as holidays also play a part in peoples normal giving. The following model is an ARMA process with differencing of 1 and 12 to produce a stationary process.
The last model I have here to show is a Classical Fit with a seasonal component of 11 and a linear trend component for the average.
It is interesting to see the confidence bounds for each of these models. The first two models had two months that income went well over the expected rate. The last model seems to stay within the bounds. When I looked at the residual plots of each of these models there was also some interesting characteristics. All of the model residuals showed some dependence on the economic downturn and upturn the last year. I believe it will be interesting to see how these predictions hold as the economy seemingly improves.
*I should probably put a disclaimer here at the bottom concerning what really happens at our budget meetings. We really never look at forecasting titheing habits of the church. We do however discuss what’s best to do with what God has and is giving us. We seek input of our church leaders and prayerfully seek God’s council in the congregations budget allocations.