Overview

Time Series Analysis is studying data that changes over time. It’s not just a snapshot; it’s a movie. The goal is usually forecasting: predicting the future based on the past.

Core Idea

The core idea is dependence. In most stats, data points are independent. In time series, today depends on yesterday. (If it rained yesterday, it’s more likely to rain today).

Formal Definition

A sequence of data points indexed in time order. Decomposed into:

  1. Trend: Long-term direction (Global warming).
  2. Seasonality: Repeating patterns (Ice cream sales in summer).
  3. Noise: Random variation.

Intuition

  • Signal vs. Noise: Trying to hear the music (Trend) through the static (Noise).
  • Lag: The delay between cause and effect. (Advertising today increases sales next week).

Examples

  • Stock Market: The ultimate time series. (Random Walk Hypothesis says it’s unpredictable).
  • ECG: Heartbeat monitoring.
  • Climate Change: Analyzing temperature anomalies over 100 years.

Common Misconceptions

  • Misconception: Past performance guarantees future results.
    • Correction: Structural breaks (like a pandemic) can ruin any model.
  • Misconception: You can predict far into the future.
    • Correction: Errors compound. Weather forecasts are good for 3 days, useless for 3 weeks.
  • Regression: Often used, but needs modification for time (Autoregression).
  • Chaos Theory: Why long-term prediction is impossible.

Applications

  • Supply Chain: Predicting demand to stock inventory.
  • Epidemiology: Predicting COVID waves.

Criticism and Limitations

  • Black Swans: Models trained on stable times fail during crises.

Further Reading

  • Forecasting: Principles and Practice by Hyndman and Athanasopoulos