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Time Series Forecasting • Statistical Models (ARIMA, Exponential Smoothing)Easy⏱️ ~3 min

What is Statistical Time Series Forecasting?

Definition
Statistical time series forecasting predicts future values using mathematical formulas that capture patterns in historical data—trends, cycles, and momentum that will likely continue.
THE PROBLEM IT SOLVES
Businesses need predictions: next month sales, tomorrow server load, next quarter inventory. The simplest approach—use last month value—fails when data has trends or seasonal patterns. Statistical models capture these patterns mathematically, enabling forecasts that adapt to growth and cycles.
WHY STATISTICAL MODELS STILL MATTER
Despite deep learning hype, statistical models dominate production. They train in milliseconds (vs hours for neural networks), need minimal data (20-50 points vs thousands), produce interpretable outputs, and often outperform complex models on single time series. For millions of SKUs or servers, speed and simplicity win.
💡 Insight: Statistical models are the right tool for fast, interpretable forecasts at scale. Deep learning shines with complex multivariate data; statistical models shine with millions of univariate series.
TWO MAIN APPROACHES
Exponential Smoothing (ETS): Averages past values, weighting recent observations more heavily. Best when data has clear trend and seasonal patterns. ARIMA: Models how each value relates to previous values (momentum) and previous errors (shocks). Best when knowing yesterday strongly helps predict today.
PREDICTION INTERVALS
Both produce point forecasts (single value) and prediction intervals (uncertainty range). A 95% interval means the true value falls in this range 95% of the time. Wider intervals = more uncertainty. As horizon extends, intervals widen because uncertainty compounds.

💡 Key Takeaways

✓Statistical models predict future values using mathematical formulas that capture patterns in historical data

✓They train in milliseconds, need minimal data (20-50 points), and produce interpretable outputs

✓ETS averages past values with recent data weighted more; ARIMA models momentum and shock patterns

✓Both produce point forecasts plus prediction intervals showing uncertainty

✓Statistical models often outperform deep learning on single univariate time series

📌 Interview Tips

1When asked about forecasting approach, explain why statistical models are often preferred over deep learning at scale

2Mention the interpretability advantage—you can explain WHY the forecast is a specific value

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