Stationarity & ADF Test

Stationarity & the ADF Test

A time series is stationary if its statistical properties (mean, variance) do not change over time. Most forecasting models assume stationarity.

Variance-Ratio Test

A simple check: split the series in half and compare the variances of both halves. If the ratio is close to 1, the series may be stationary.

is_stationary(xs, threshold=0.5):
    half = len(xs) // 2
    ratio = variance(xs[:half]) / variance(xs[half:])
    return |ratio - 1| < threshold

Augmented Dickey-Fuller (ADF) Statistic

The ADF test regresses the first-difference Δxs[t] on xs[t-1]:

Δxs[t] = intercept + slope * xs[t-1] + ε[t]

The t-statistic of slope is the ADF statistic. A very negative value (e.g., < -3) suggests stationarity.

Task

Implement is_stationary(xs, threshold=0.5) and adf_statistic(xs).