An Independence Test Based on Symbolic Time Series

Table 2

Size of the BDS and runs tests.

Test	𝛼=1%	𝛼=5%	𝛼=10%	𝛼=1%	𝛼=5%	𝛼=10%	𝛼=1%	𝛼=5%	𝛼=10%	𝛼=1%	𝛼=5%	𝛼=10%
	𝑇=50			𝑇=200			𝑇=500			𝑇=2000
BDS [36]	9.30	19.83	27.83	2.57	8.82	15.55	1.27	6.16	12.07	1.22	5.56	10.55
BDS [37]	4.07	10.80	16.79	1.12	4.86	8.95	0.58	3.53	7.36	0.61	3.05	6.30
BDS [36] small sample	0.76	4.69	9.45	1.03	4.74	9.99	0.83	4.82	10.37	1.25	5.33	10.48
Runs test	0.59	3.25	6.65	0.93	4.23	8.99	0.95	4.41	9.31	0.88	4.50	9.38

Note: 10,000 Monte Carlo simulations were conducted applying the normally distributed pseudorandom numbers from MatLab R2010a.
Bold values refer to reasonable percentage of rejections considering the process and the critical values.