. 2022 Apr 2;2677(4):463–477. doi: 10.1177/03611981221084698

Table 4.

Time Series Model for all Four Subway Stations before and after Change Points

Subway station	Fitted model	Estimated parameters	Performance errors	Li-McLeod’s test p-values
South Ferry station (before change point)	ARIMA (0,0,1)	$θ_{2}$ = 0.2677	AIC = 563.07	>=0.05
			AICC = 563.1
			BIC = 571.23
South Ferry station (after change point)	ARIMA (3,1,3)	$ϕ_{1}$ = 1.3867	AIC = −34.28	>=0.05
		$ϕ_{1}$ = 1.3867	AICC = −33.03
		$ϕ_{2}$ = −1.0280	BIC = −16.26
		$ϕ_{3}$ = 0.0795
		$θ_{1}$ = −1.9053
		$θ_{2}$ = 1.5240
		$θ_{3}$ = −0.370
137 Street, City College (before change point)	ARIMA (1,0,1)	$ϕ_{1}$ = 0.310	AIC = 486.4	<0.05
		$θ_{1}$ = 0.492	AICC = 486.5
		$θ_{1}$ = 0.492	BIC = 498.7
137 Street, City College (after change point)	ARIMA (5,0,1)	$ϕ_{1}$ = 0.0536	AIC = 531.2	>=0.05
		$ϕ_{1}$ = 0.0536	AICC = 531.53
		$ϕ_{2}$ = −0.8238	BIC = 563.84
		$ϕ_{3}$ = 0.4975
		$ϕ_{4}$ = −0.1208
		$ϕ_{5}$ = 0.2307
		$θ_{1}$ = 0.4355
Bronx East Park station (before change point)	ARIMA (0,0,2)	$θ_{1}$ = 0.1761	AIC = 491.35	>=0.05
		$θ_{1}$ = 0.1761	AICC = 491.4
		$θ_{2}$ = 0.1947	BIC = 503.58
Bronx East Park station (after change point)	ARIMA (2,1,1)	$ϕ_{1}$ = 0.7612	AIC = −15.55	>=0.05
		$ϕ_{2}$ = −0.1742	AICC = −15.12
		$θ_{1}$ = −0.8191	BIC = −5.25
Crescent Street, Brooklyn (before change point)	ARIMA (0,0,2)	$θ_{1}$ = 0.5124	AIC = 659.27	>=0.05
		$θ_{1}$ = 0.5124	AICC = 659.32
		$θ_{2}$ = 0.1316	BIC = 671.58
Crescent Street, Brooklyn (after change point)	ARIMA (0,1,0)		AIC = 4.83	>=0.05
		AICC = 4.87
		BIC = 7.42
Hunts Point (before change point)	ARIMA (0,0,1)	$θ_{1}$ = 0.2199	AIC = 178.2	>=0.05
			AICC = 178.27
			BIC = 184.57
Hunts Point (after change point, 2 models)	ARIMA (3,0,0)	$ϕ_{1}$ = 0.4740	AIC = 262.91	>=0.05
	ARIMA (2,1,1)	$ϕ_{2}$ = −0.0671	AICC = 263.07	>=0.05
		$ϕ_{3}$ = 0.0522	BIC = 277.14
		$ϕ_{1}$ = 0.3942	AIC = 64.67
		$ϕ_{2}$ = 0.2132	AICC = 65.1
		$θ_{1}$ = −0.9014	BIC = 74.96
President station (before change point)	ARIMA (1,0,0)	$θ_{1}$ = 0.6636	AIC = 394.15	>=0.05
			AICC = 394.18
			BIC = 402.31
President station (after change point)	ARIMA (6,1,0)	$ϕ_{1}$ = 0.1121	AIC = −140.1	>=0.05
		$ϕ_{2}$ = −0.6223	AICC = −138.48
		$ϕ_{3}$ = −0.3153	BIC = −119.42
		$ϕ_{4}$ = −0.1176
		$ϕ_{5}$ = −0.5350
		$ϕ_{6}$ = 0.3523
Grand Newton station (before change point)	ARIMA (1,0,0)	$ϕ_{1}$ = 0.3244	AIC = 270.06	<0.05
			AICC = 270.09
			BIC = 278.23
Grand Newton station (after change point)	ARIMA (2,1,2)	$ϕ_{1}$ = 1.3181	AIC = −52.96	<0.05
		$ϕ_{1}$ = 1.3181	AICC = −52.3
		$ϕ_{2}$ = −0.9618	BIC = −40.09
		$θ_{1}$ = −1.4192
		$θ_{2}$ = 0.8813

Note: AIC = Akaike information criterion; AICC = corrected AIC; ARIMA = autoregressive integrated moving average; BIC = Bayesian information criterion.