A Fast Screen and Shape Recognition Algorithm for Multiple Change-Point Detection

Table 1

Distribution of for the various competing algorithms and sample sizes (100 simulated sample paths), with BIC values and run times (normal error case).

Sample Size		Method		-2	-1	0	1	2		BIC	Time
n=500	N=5	FSSR	6	20	48	23	3	0	0	0.0662×	0.0113
		SaRa	0	1	5	14	22	32	26	0.1495	0.0231
		mSaRa	48	30	11	10	0	1	0	0.1644	0.3802
n=3000	N=10	FSSR	1	5	37	45	10	2	0	0.1445	0.0583
		SaRa	0	0	2	13	7	2	76	0.6343	0.1339
		mSaRa	31	8	11	9	12	8	21	0.6626	1.3432
	N=15	FSSR	20	22	29	24	5	0	0	0.2644	0.0593
		SaRa	5	3	9	15	6	8	54	0.9871	0.1101
		mSaRa	88	6	2	1	1	0	2	0.8995	1.0129
n=5000	N=10	FSSR	0	1	19	67	10	3	0	0.1357	0.0794
		SaRa	0	0	1	10	4	2	83	0.9874	0.1869
		mSaRa	11	2	5	10	7	5	60	0.8727	2.3090
	N=20	FSSR	15	22	28	27	6	1	1	0.3125	0.1280
		SaRa	7	3	4	24	6	6	50	1.5053	0.2049
		mSaRa	86	1	2	2	1	0	8	1.4307	2.0621
	N=30	FSSR	44	6	9	16	7	9	9	0.5242	0.1317
		SaRa	30	8	12	20	10	5	15	3.1588	0.1973
		mSaRa	100	0	0	0	0	0	0	1.9524	1.4564
n=8000	N=10	FSSR	0	0	25	55	17	3	0	0.1759	0.0920
		SaRa	0	0	6	9	5	6	74	1.9034	0.3024
		mSaRa	2	1	1	7	5	3	81	1.0359	2.3814
	N=20	FSSR	13	11	28	37	10	1	0	0.3645	0.2373
		SaRa	7	4	3	18	6	4	58	2.2859	0.4487
		mSaRa	64	8	7	3	2	0	16	1.8060	3.2446
	N=30	FSSR	12	4	19	11	12	7	35	0.5457	0.2480
		SaRa	17	3	11	32	5	3	29	3.9068	0.3850
		mSaRa	95	0	1	0	1	0	3	2.7051	2.5822
	N=50	FSSR	95	3	1	0	1	0	0	1.0258	0.3051
		SaRa	51	12	14	14	2	4	3	6.9394	0.3918
		mSaRa	99	1	0	0	0	0	0	3.3326	3.0239