All projects
Forecasting/Time series /Project 05 of 10 M.S. coursework

Revenue Forecasting with ARIMA

I used 731 daily hospital revenue observations to evaluate an ARIMA forecast against a no-change baseline and project revenue for the next 30 days.

Python Forecasting Time series ARIMA Statistics M.S. coursework

Business impact

The primary evaluation tests whether an ARIMA forecast improves on assuming no daily revenue change. For the 146 forecasts issued together, the simpler baseline had slightly lower error.

0.4887Daily-change RMSE ($ millions)
0.4860No-change RMSE ($ millions)
30 daysForward projection

Business question

Can daily revenue history support an accurate short-term forecast for a hospital in its first two years of operation?

Approach

How the work was done

  • Reviewed 731 daily observations for continuity, visualized the series, and ran an Augmented Dickey-Fuller stationarity test.
  • First-differenced the series; the post-difference ADF p-value was 5.11e-30, compared with 0.1997 before differencing.
  • Fit an AR(1) model to 584 daily changes. From day 585, forecast changes for days 586–731 and compare them with assuming zero change each day.

Results

What the analysis shows

  • On the 146 held-out days, ARIMA had MAE of 0.3765 and RMSE of 0.4887 million dollars of daily change. The no-change forecast had MAE of 0.3746 and RMSE of 0.4860 million.
  • For the 30-day projection, the notebook refits the model on all 731 revenue observations. It forecasts daily revenue levels for days 732–761 with model-based 95% prediction intervals.

From the project

Forecast error and uncertainty

Observed daily revenue changes and ARIMA predictions for days 586 through 731, with individual 95 percent prediction intervals.

The forecasts issued together

These are the 146 forecasts used for evaluation, all issued at day 585. Assuming no daily change gave slightly lower MAE and RMSE. Values are in millions of dollars.

View the source Open full size
Revenue forecast for days 732 through 761 with widening 95 percent prediction intervals after the final observed day.

The next 30 days

The notebook refits through day 731 before projecting revenue levels. The widening interval shows how uncertainty grows over the month.

View the source Open full size

Additional comparison

Forecasts updated each day

A separate evaluation refits ARIMA before predicting each next day, using only observations available at that point. On the same 146 test days, MAE was 0.3531 and RMSE 0.4408 million dollars of daily change, versus 0.3746 and 0.4860 for no change. The update schedule changes which method performs better.

Business relevance

What this makes easier to decide

For a forecast issued once at the training cutoff, no change performed slightly better. The additional daily-update comparison favored ARIMA. Monthly budgeting needs further tests of revenue levels and totals at several historical cutoffs.