Statistical significance approximation for local similarity analysis of dependent time series data

BMC Bioinformatics

Table 3 The empirical type I error rates for the six different methods (the third to ninth column): PCC, SRCC, TLSA, permutation, LSAres (AR), LSAres (ARMA), and DDLSA, based on the ARMA(1,1)-TAR(1) model

ρ₁,ρ₂	n	PCC	SRCC	TLSA	permutation	LSAres(AR)	LSAres(ARMA)	DDLSA
-0.5 -0.5	100	0.0490	0.0509	0.0295	0.0492	0.0273	0.0292	0.0309
	200	0.0511	0.0511	0.0369	0.0515	0.0341	0.0372	0.0387
	300	0.0495	0.0499	0.0393	0.0529	0.0383	0.0393	0.0400
	500	0.0511	0.0517	0.0414	0.0519	0.0388	0.0405	0.0407
	1000	0.0493	0.0508	0.0440	0.0496	0.0401	0.0419	0.0426
0 0	100	0.0494	0.0494	0.0294	0.0502	0.0283	0.0304	0.0329
	200	0.0532	0.0518	0.0330	0.0499	0.0323	0.0341	0.0359
	300	0.0487	0.0466	0.0368	0.0510	0.0368	0.0360	0.0377
	500	0.0776	0.0778	0.0841	0.0989	0.0373	0.0387	0.0445
	1000	0.0813	0.0813	0.0901	0.1005	0.0447	0.0400	0.0454
0.3 0.3	100	0.1172	0.1121	0.0955	0.1391	0.0280	0.0321	0.0431
	200	0.1181	0.1149	0.1191	0.1549	0.0329	0.0327	0.0438
	300	0.1181	0.1136	0.1277	0.1557	0.0349	0.0373	0.0460
	500	0.1135	0.1106	0.1436	0.1683	0.0411	0.0416	0.0469
	1000	0.1186	0.1122	0.1585	0.1748	0.0430	0.0460	0.0486
0.3 0.5	100	0.1245	0.1196	0.1098	0.1586	0.0336	0.0310	0.0396
	200	0.1369	0.1259	0.1400	0.1778	0.0315	0.0356	0.0449
	300	0.1350	0.1275	0.1545	0.1839	0.0421	0.0390	0.0454
	500	0.1355	0.1281	0.1690	0.1940	0.0423	0.0423	0.0466
	1000	0.1336	0.1339	0.1823	0.2014	0.0422	0.0407	0.0518
0.5 0.5	100	0.1584	0.1527	0.1527	0.2091	0.0280	0.0347	0.0423
	200	0.1589	0.1520	0.1827	0.2258	0.0352	0.0365	0.0433
	300	0.1604	0.1516	0.2004	0.2391	0.0382	0.0383	0.0429
	500	0.1545	0.1500	0.2203	0.2484	0.0358	0.0405	0.0472
	1000	0.1601	0.1507	0.2396	0.2609	0.0422	0.0425	0.0471
0.5 0.8	100	0.2160	0.2031	0.2282	0.2985	0.0312	0.0335	0.0401
	200	0.2157	0.2075	0.2858	0.3361	0.0351	0.0346	0.0399
	300	0.2194	0.2064	0.3158	0.3595	0.0391	0.0367	0.0431
	500	0.2144	0.2032	0.3221	0.3582	0.0402	0.0376	0.0444
	1000	0.2257	0.2083	0.3643	0.3920	0.0410	0.0423	0.0506

The first and second columns represent different autoregressive coefficients and number of time points, respectively. Note that we used the residuals from the estimated AR(p) or ARMA(p,q) models by maximum likelihood estimate and the order selection was based on the Akaike Information criterion (AIC). The number of permutations was 1000. The pre-specified type I error was 0.05 and the number of replications was 10000

ISSN: 1471-2105