Forecast the Future
With Confidence

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.

For most business forecasting, Prophet is easier to use, while ARIMA offers more statistical rigor when properly configured. MCP Analytics supports both methods and can automatically select the best approach for your data.

Seasonality is a recurring pattern at fixed intervals (daily, weekly, monthly, or yearly) that significantly impacts forecast accuracy. Properly identifying and modeling seasonality can improve forecast accuracy by 20-40%.

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

Modern forecasting tools like Prophet and Seasonal ARIMA (SARIMA) automatically detect and model multiple seasonal patterns simultaneously, separating them from underlying trends for more accurate predictions.

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% confidence interval means there's a 95% probability the actual value will fall within that range.

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's computationally efficient and great for automated forecasting.

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 most business applications, start with Holt-Winters for seasonal data or Prophet for its ease of use, then compare with ARIMA for complex cases.

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.

MCP Analytics automatically flags anomalies and provides recommendations for handling them in your forecasts.

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. MCP Analytics provides uncertainty quantification and anomaly detection to help identify when patterns are shifting, enabling faster response to market changes.