Stationarity

ECON 3209 · Week 19, Lecture 1 · Kerala Agricultural University

Department of Development Economics, KAU

Autumn 2026

Learning Outcomes

By the end of this lecture, you should be able to:

  1. define strict and weak stationarity in time-series analysis
  2. distinguish trend, seasonality, cycles, and white noise
  3. recognise why nonstationarity complicates estimation and forecasting
  4. use Python plots and rolling statistics to inspect time-series behaviour
  5. apply these ideas to paddy production and related Kerala examples

Why Stationarity Matters

  • Many time-series tools assume the process has stable statistical properties over time.
  • Without stationarity, past relationships may not help forecast the future.
  • Before fitting ARIMA or other models, we inspect whether the series is roughly stable in mean, variance, and dependence structure.

Strict versus Weak Stationarity

  • Strict stationarity: the full probability distribution is unchanged by time shifts.
  • Weak stationarity (covariance stationarity):
    • constant mean,
    • constant variance,
    • autocovariance depends only on lag, not calendar time.
  • In most applied work, weak stationarity is the practical target.

Trend, Seasonality, White Noise

  • Trend: long-run upward or downward movement.
  • Seasonality: regular pattern that repeats every fixed period.
  • Cycle: broader medium-run fluctuation.
  • White noise: zero mean, constant variance, no serial correlation.

A nonstationary series often contains trend or changing variance.

Simulating White Noise and Trend

Visual Comparison

Kerala Paddy Example

Annual paddy production in Kerala from 2000 to 2024 may show a downward long-run trend, climate shocks, and policy effects.

A trending series is usually not weakly stationary in levels, so we may need detrending or differencing before modelling.

Plotting Paddy Production

Rolling Mean and Variance

Common Fixes for Nonstationarity

  • Remove deterministic trend with a trend term.
  • Difference the series to eliminate stochastic trend or unit roots.
  • Model seasonal patterns explicitly.
  • Transform the variance, for example using logs when appropriate.

What Comes Next

  • Visual inspection is helpful but not enough.
  • Next we use formal tests such as the Augmented Dickey-Fuller (ADF) test and the KPSS test.
  • Together, they help us judge whether a series is stationary or contains a unit root.

Exercise

Use the starter code to compute a rolling mean for the paddy series. Does the rolling mean look stable? What does that suggest about stationarity in levels?

Summary

  • ✅ Stationarity means the series has stable properties over time, especially mean and variance.
  • ✅ Trend and seasonality are common reasons a series fails to be stationary.
  • ✅ White noise is the benchmark stationary process with no serial dependence.
  • ✅ Visual plots and rolling statistics are useful first checks before formal tests.

Next Lecture

  • We study unit roots with the ADF test and compare it with KPSS.
  • You will learn how to interpret apparently contradictory test outcomes.
  • Stationarity intuition now becomes formal testing practice.