ARIMA forecasting model predicts average monthly revenue of $44073 (95% CI: $24287–$63860) for the next 3 months. The model explains historical variation with RMSE of $9954 and demonstrates seasonal patterns with peak-to-trough amplitude of $31775. Ljung-Box test (p=NA) indicates residuals are independent, validating forecast reliability.

Historical revenue spans $39427 to $74799 over 36 months (89.7% growth). Average monthly revenue is $44073, with peak of $74799. The trajectory reveals growth momentum, guiding inventory and staffing decisions.

The deseasonalized trend shows underlying revenue momentum after removing seasonal oscillations. Trend increases $331 per month from $39467 to $51060, indicating accelerating growth. This underlying growth pattern is critical for planning—strong trend supports aggressive marketing, weak or negative trend suggests caution.

Month 12 shows strongest seasonal uplift (+$21274 above trend), while Month 11 shows strongest downlift ($10501 below trend). Total seasonal swing of $31775 indicates promotions and holiday demand drive significant revenue variation. Plan inventory buildup for peak months and promotional support for troughs.

Forecast for next 3 months projects average revenue of $44073 (range $44073–$44073). Confidence bands (95%) span $39573, reflecting both model uncertainty and genuine randomness. Wider bands in later months indicate increasing forecast uncertainty—use as planning range, not point targets.

ARIMA model fits historical revenue with R² = -0.000 and RMSE = $9954. Most points cluster near the diagonal (perfect fit line), indicating strong alignment. Bias of $0 suggests slight overprediction. Points below the diagonal indicate periods where model underestimated revenue, suggesting external drivers (promotions, supply shocks) not captured by pure time series.

Residuals are approximately centered at $-0 (ideal: 0) with standard deviation $10095, ranging from $-17987 to $30726. Distribution is roughly bell-shaped, suggesting ARIMA adequately captures the data generation process. Normality test p-value = 0.3478 supports assumption of normally distributed errors. No large outliers detected—model is robust.

Model ARIMA order auto-selected by AIC criterion. RMSE ($9954) and MAE ($7905) indicate typical forecast error magnitude. MAPE (18.8%) shows percentage-based error. Ljung-Box test supports residual independence. Monthly observations (36) provide sufficient data for stable parameter estimation. Forecast confidence level of 95% balances precision vs. uncertainty.