Time Series & Trends

Lesson 2: Identifying Cycles in History

Quantitative Methods for Causal Inference

Temporal Analysis

History as a Sequence

History is not a set of independent observations. Observations are autocorrelated—what happens today is heavily dependent on what happened yesterday.

Key Question

How do we distinguish a "blip" (short-term shock) from a "trend" (long-term structural shift)?

01

Trend Analysis

02

Cyclical Variation

03

Seasonal Adjustment

04

Stochastic Noise

The Components of Change

Trend (\(T_t\))

The long-term movement in the data. Think: Population growth or Industrialization.

Seasonality (\(S_t\))

Periodic fluctuations within a year. Think: Agricultural harvest cycles.

Cyclical (\(C_t\))

Multi-year waves. Think: Business cycles or dynastic rise/fall periods.

Noise (\(I_t\))

Irregular, unpredictable shocks. Think: Fires, plagues, or data recording errors.

\(Y_t = T_t + S_t + C_t + I_t\)

The Moving Average

Historical datasets are often "spiky" due to measurement errors and local crises. Moving Averages (MA) help us see the underlying signal.

MA = (Sum of 'n' periods) / n

Reduces impact of outliers
Reveals structural breaks
Trade-off: Loses information on shocks!

Visualization Challenge

If we smooth a plague year, we might miss the very causal event we are looking for.

Case Study Prep

"You are looking at the price of wheat in London from 1500 to 1800. You see a massive price spike in 1666. Is this the end of an old economic trend, or just the Great Fire of London creating a one-year supply shock?"

Shock identification

Trend extrapolation

Time Series Analysis and Trends

Time Series Trends Slides

Trend Hunter Lab Activity