Business Context

StreamWave is a subscription video streaming company with ~8M paying subscribers and meaningful seasonality: Q4 is boosted by holiday promotions and new device activations, while Q1 typically sees elevated churn. Finance needs a next-quarter (next 3 months) revenue forecast to set content spend and cash-flow targets. The stakes are high: a 2% forecasting error can swing quarterly guidance by tens of millions of dollars.

You are given 24 months of historical monthly revenue (in $M) for the core subscription product. The business also ran a major price increase starting in month 19, which may have shifted the revenue level.

Problem Statement

You need to propose and execute a statistically sound approach to forecasting revenue for months 25–27, including uncertainty quantification. You will compare a baseline seasonal model against a model that accounts for a potential level shift after the price change.

Given Data

Monthly revenue (in $M):

Additional info:

Requirements

1. Baseline model: Fit a seasonal regression model with a linear trend and monthly seasonality:
   • Trend term: month index (1–24)
   • Seasonality: month-of-year fixed effects (12 categories)
2. Intervention model: Extend the regression by adding a post-price-change indicator (1 for months 19–24, else 0) to capture a level shift.
3. For both models, compute:
   • Point forecasts for months 25–27
   • 95% prediction intervals (not just confidence intervals for the mean)
4. Compare the two models using AIC (or adjusted R²) and residual diagnostics (at minimum: residual standard deviation and whether residuals look autocorrelated).
5. Make a recommendation: which model would you ship to Finance today, and what risks remain?

Assumptions & Constraints

• Treat monthly revenue as approximately Gaussian around the model mean (reasonable at $100M+ scale).
• You may assume month-of-year for month 25 is the same as month 1 (i.e., the series starts in January).
• If you detect strong autocorrelation, describe how you’d address it (e.g., GLS/ARIMA errors), but still produce forecasts from the two regression models above.