Sampling Based on Trading Probability in a Given Period

Sampling Based on Trading Probability in a Given Period: Summary statistics by group

Parameter:	alpha (α)			delta (δ)
	Period 1	Period 2	Period 3	Period 1	Period 2	Period 3
A: 1^st decile
Mean	0.500	0.418	0.217	0.243	0.142	0.310
Median	0.231	0.141	0.030	0.088	0.076	0.184
Std. dev.	0.454	0.463	0.368	0.342	0.175	0.362
Stat. sign. at 5%	32.0%	41.7%	41.7%	28.0%	54.2%	33.3%
B: 2^nd decile
Mean	0.322	0.238	0.179	0.232	0.109	0.107
Median	0.100	0.081	0.026	0.205	0.025	0.001
Std. dev.	0.409	0.356	0.332	0.273	0.214	0.149
Stat. sign. at 5%	36.0%	44.0%	43.5%	48.0%	32.0%	26.1%
C: 3^rd decile
Mean	0.236	0.300	0.236	0.314	0.104	0.127
Median	0.174	0.127	0.132	0.226	0.030	0.062
Std. dev.	0.307	0.365	0.291	0.333	0.209	0.147
Stat. sign. at 5%	60.0%	50.0%	64.0%	40.0%	25.0%	20.0%
D: 4^th decile
Mean	0.409	0.289	0.259	0.256	0.033	0.220
Median	0.291	0.032	0.073	0.167	0.000	0.104
Std. dev.	0.374	0.399	0.381	0.302	0.073	0.304
Stat. sign. at 5%	56.0%	32.0%	44.0%	24.0%	0.0%	24.0%
E: 5^th decile
Mean	0.214	0.321	0.295	0.292	0.062	0.224
Median	0.203	0.013	0.206	0.244	0.000	0.108
Std. dev.	0.244	0.422	0.323	0.303	0.202	0.307
Stat. sign. at 5%	48.0%	24.0%	60.0%	28.0%	8.0%	40.0%
F: 6^th decile
Mean	0.264	0.267	0.255	0.227	0.078	0.142
Median	0.166	0.000	0.087	0.182	0.000	0.078
Std. dev.	0.315	0.396	0.358	0.250	0.219	0.182
Stat. sign. at 5%	40.0%	20.0%	52.0%	24.0%	12.0%	44.0%
G: 7^th decile
Mean	0.200	0.188	0.234	0.290	0.116	0.157
Median	0.169	0.000	0.106	0.200	0.000	0.000
Std. dev.	0.178	0.328	0.314	0.305	0.222	0.235
Stat. sign. at 5%	44.0%	32.0%	50.0%	16.0%	20.0%	20.8%
H: 8^th decile
Mean	0.316	0.151	0.204	0.321	0.080	0.234
Median	0.275	0.003	0.171	0.100	0.000	0.150
Std. dev.	0.304	0.261	0.246	0.411	0.212	0.315
Stat. sign. at 5%	36.0%	28.0%	58.3%	4.0%	4.0%	25.0%
I: 9^th decile
Mean	0.364	0.214	0.251	0.158	0.141	0.208
Median	0.259	0.090	0.197	0.000	0.004	0.036
Std. dev.	0.377	0.287	0.267	0.299	0.274	0.326
Stat. sign. at 5%	16.0%	44.0%	48.0%	8.0%	8.0%	12.0%
J: 10^thdecile
Mean	0.239	0.219	0.315	0.414	0.180	0.334
Median	0.156	0.143	0.194	0.484	0.052	0.153
Std. dev.	0.282	0.240	0.365	0.395	0.289	0.391
Stat. sign. at 5%	8.0%	40.0%	39.1%	8.0%	8.0%	17.4%

Parameter:	epsilon (ε)			mu (μ)
	Period 1	Period 2	Period 3	Period 1	Period 2	Period 3
A: 1^st decile
Mean	2,807	2,366	397,486	5,353	13,094	94,510
Median	634	684	953	35	1,579	1,335
Std. dev.	5,282	3,545	1,833,328	12,607	28,330	234,422
Stat. sign. at 5%	100.0%	100.0%	87.5%	44.0%	62.5%	50.0%
B: 2^nd decile
Mean	522	371	5,842	7,324	5,092	25,502
Median	257	254	173	180	34	173
Std. dev.	757	366	25,872	18,504	17,031	85,982
Stat. sign. at 5%	92.0%	100.0%	100.0%	60.0%	52.0%	52.2%
C: 3^rd decile
Mean	117	287	408	719	2,033	3,452
Median	64	148	86	362	279	1,139
Std. dev.	133	286	1,091	980	4,239	6,249
Stat. sign. at 5%	96.0%	100.0%	96.0%	72.0%	62.5%	72.0%
D: 4^th decile
Mean	122	203	1,191	425	1,212	30,015
Median	48	143	290	113	0	99
Std. dev.	159	209	2,837	822	3,768	70,793
Stat. sign. at 5%	100.0%	100.0%	100.0%	72.0%	32.0%	60.0%
E: 5^th decile
Mean	116	181	174	588	490	6,846
Median	61	125	64	77	0	734
Std. dev.	243	140	218	1,770	1,247	25,547
Stat. sign. at 5%	92.0%	100.0%	100.0%	60.0%	32.0%	84.0%
F: 6^th decile
Mean	82	245	320	505	294	1,201
Median	32	167	129	138	0	204
Std. dev.	158	371	475	1,262	940	1,813
Stat. sign. at 5%	92.0%	100.0%	100.0%	64.0%	20.0%	68.0%
G: 7^th decile
Mean	75	208	222	526	1,144	1,145
Median	49	164	111	115	0	625
Std. dev.	82	171	287	931	3,312	2,030
Stat. sign. at 5%	92.0%	100.0%	100.0%	64.0%	40.0%	62.5%
H: 8^th decile
Mean	42	168	112	173	1,825	776
Median	29	163	63	60	69	86
Std. dev.	46	121	116	365	3,958	1,364
Stat. sign. at 5%	88.0%	100.0%	100.0%	60.0%	52.0%	66.7%
I: 9^th decile
Mean	48	287	116	35	8,991	439
Median	24	103	45	1	82	21
Std. dev.	60	912	156	72	42,087	867
Stat. sign. at 5%	84.0%	100.0%	84.0%	52.0%	56.0%	56.0%
J: 10^thdecile
Mean	30	165	259	3,510	8,206	1,625
Median	14	55	45	18	44	44
Std. dev.	46	494	737	17,350	39,620	4,893
Stat. sign. at 5%	72.0%	92.0%	100.0%	40.0%	56.0%	52.2%