A stochastic trend is a non-deterministic time-dependent component that changes a series’ statistical properties, indicating nonstationarity. The Augmented Dickey–Fuller (ADF) test detects evidence of this trend. section 7.3.7
Interpret the ADF test as follows:
- Treat nonstationarity as the null hypothesis. section 7.3.7
- Reject the null when the p-value is below 0.05, concluding that the series is stationary. section 7.3.7
- Interpret a nonsignificant gamma parameter and p-value above 0.05 as evidence of a stochastic trend. section 7.3.7
- Account for autocorrelation with lagged differences, while recognizing sensitivity to lag length and reduced power for short or noisy series. section 7.3.7
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Applying statsmodels’ adfuller function to the training series returns p = 0.5761, supporting nonstationarity. First-order differencing produces a series with p = 1.25 × 10⁻¹⁶, supporting stationarity; ACF and PACF plots compare the correlation structure before and after differencing. section 7.3.7
