Diagnostics

Stationarity (Augmented Dickey-Fuller test)

A series is stationary if its statistical properties (mean, variance) don't drift over time. Non-stationary series get differenced before modeling. See ADF test in Learn mode.

Series	ADF statistic	p-value	Verdict	Differencing
cpi_all_items	-15.205	0.0000	cpi_all_items is stationary (ADF p-value = 0.0000).	log_difference
overnight_rate	-21.226	0.0000	overnight_rate is stationary (ADF p-value = 0.0000).	first_difference_bp
spread_10y_2y	-15.497	0.0000	spread_10y_2y is stationary (ADF p-value = 0.0000).	first_difference_bp
usdcad	-17.234	0.0000	usdcad is stationary (ADF p-value = 0.0000).	log_difference
yield_10y	-80.349	0.0000	yield_10y is stationary (ADF p-value = 0.0000).	first_difference_bp
yield_2y	-35.354	0.0000	yield_2y is stationary (ADF p-value = 0.0000).	first_difference_bp
yield_5y	-31.172	0.0000	yield_5y is stationary (ADF p-value = 0.0000).	first_difference_bp

Cointegration (Johansen test)

Tests whether the level series share a stable long-run relationship. See Johansen test in Learn mode.

Trace statistic	95% critical value	Cointegration rank	Verdict
193.833	95.754	1	Use VECM

The trace statistic (193.83) exceeds the 95% critical value (95.75), indicating a stable long-run relationship among the series. Use VECM for forecasting.

Lag order selection (AIC / BIC)

See AIC and BIC in Learn mode.

Lag	AIC	BIC	Selected
0	-7.778	-7.771
1	-42.692	-42.647
2	-42.699	-42.616	✓
3	-42.693	-42.572
4	-42.686	-42.527
5	-42.684	-42.487
6	-42.682	-42.447
7	-42.688	-42.415
8	-42.693	-42.380
9	-42.687	-42.337
10	-42.682	-42.294