Forecast the Next Year
and See How Far to Trust It

ARIMA (AutoRegressive Integrated Moving Average) is a classical statistical method that excels at capturing linear patterns, autocorrelations, and trends in stationary data. It requires parameter tuning (p, d, q) and works best with clean, regularly-spaced data.

Prophet, developed by Facebook/Meta, is designed for business time series with strong seasonal effects and holiday patterns. Prophet handles missing data better, requires less manual tuning, and provides intuitive decomposition of trends and seasonality.

Which is better depends on your data, and the honest way to decide is a backtest on your own history. The standard forecast report here uses Holt-Winters first and ARIMA(1,1,1) as a fallback; it does not run Prophet. See the ARIMA and Prophet comparison.

Seasonality is a recurring pattern at fixed intervals (daily, weekly, monthly, or yearly) that significantly impacts forecast accuracy. Modeling seasonality when it is really there usually helps, and the backtest shows by how much on your data.

Common seasonal patterns include: weekly retail sales peaks on weekends, monthly billing cycles, quarterly business reporting, and yearly holiday shopping spikes.

Seasonal Holt-Winters, used here when there are at least two full cycles of history, models one repeating pattern and separates it from the underlying trend.

The amount of historical data needed depends on your forecasting horizon and seasonality:

• Daily forecasts: At least 2-3 weeks of data
• Weekly forecasts: 3-6 months of weekly data
• Monthly forecasts with yearly seasonality: 2-3 years (24-36 months) to capture seasonal patterns
• Quarterly business forecasting: 3-5 years for robust results

The key is having at least 2-3 complete cycles of your dominant seasonal pattern. More data generally improves accuracy, but data older than 5 years may not reflect current market conditions.

Confidence intervals represent the range of likely outcomes for a forecast, quantifying uncertainty. A 95% range is built so that, if the model's assumptions hold, about 95 of 100 future values land inside it. If the checks in the report are strained, the real coverage may be lower.

They matter because:

• They enable risk-aware planning by showing best and worst-case scenarios
• They widen as forecasts extend further into the future, reflecting increasing uncertainty
• They help set appropriate inventory buffers and safety stock levels
• They inform scenario planning for budgets and resource allocation

Narrow intervals indicate high confidence, while wide intervals suggest more volatility or uncertainty in the data.

Simple Exponential Smoothing: Use for data with no clear trend or seasonality, when you need fast, reactive forecasts.

Holt-Winters (Triple Exponential Smoothing): Use for data with both trend AND seasonality, like monthly sales with yearly patterns. It is fast and works well on regular monthly or weekly data.

ARIMA: Use when you need statistical rigor, your data has complex autocorrelation patterns, or you want to incorporate external variables (ARIMAX). Requires more expertise but captures subtle patterns.

For seasonal business data, Holt-Winters is a sound starting point. Compare against ARIMA when the leftover errors still show a pattern.

Anomaly detection in time series involves identifying data points that deviate significantly from expected patterns. Detection methods include:

• Statistical approaches using z-scores or IQR to flag points beyond 2-3 standard deviations
• Decomposition methods that separate trend and seasonality to identify unusual residuals
• Machine learning approaches like Isolation Forest or autoencoders

Once detected, handle anomalies by: investigating if they represent real events (promotions, outages) or data errors; deciding whether to correct, remove, or adjust them; using robust forecasting methods less sensitive to outliers.

Check your history for these before you upload, since one-off spikes can pull a forecast off course.

Traditional time series forecasting cannot predict unprecedented events (black swans) because models learn from historical patterns. However, you can improve resilience by:

• Using confidence intervals to plan for uncertainty
• Implementing scenario analysis with multiple forecast paths
• Monitoring forecast errors in real-time to detect regime changes quickly
• Combining quantitative forecasts with qualitative business intelligence
• Building adaptive models that quickly incorporate new data

After a disruption, refit models with recent data and consider structural breaks. The report's ranges show uncertainty, and the backtest shows whether recent months are drifting away from the forecast.