[HFT 시스템 트레이딩]자기상관관계 분석3

15개 통화쌍 2009년 5월부터 2013년 9월까지 통계치입니다.

위에 통계치는 bid와 ask의 중간 값에 대한 통계치이고,

아래의 통계치는 return 값입니다. 다시 말해서 price(t) - price(t-1) 값입니다. 1초면 1초의 변화량 1분이면 1분의 변화량입니다.

첨도가 엄청나게 높게 나오는 것은 값의 변화가 없이 0이 매우 많이 나왔기 때문입니다.

또한 자기상관이 1로 나온 것도 비슷한 이유네요. 값이 변화가 없었던 구간이 많아서 그렇게 나온 것으로 생각됩니다.

다른 나머지들은 각 통화쌍의 움직임에 대해서 재미있는 특징들을 보여주네요. 재밌다고 생각하는 것은 저만인 것은 아니겠죠 ^^;;;;

과거 통계치에서는 10분안에 return값이 음의 자기상관관계가 있었다고 하는데, 이제는 그런게 보이지를 않네요. 거래 빈도가 상당히 올라가고 자동화가 많이 된 영향이 아닌가 추측이 됩니다.

다음 글에서는 FX에서 중요한 개념중 하나인 seasonality에 대해서 다루도록 하겠습니다.

seasonality는 시간대마다 변동폭 등의 통계치가 다르다는 것입니다. 요일 이나 24시간의 변화에 따른 통계치를 분석해보도록 하겠습니다.

EURUSD	n	mean	variance	skewness	kurtosis	autocorrelation
1s	92435574	1.34832	0.00477103	0.252181	-0.654648	1
1m	1541154	1.3483	0.00477156	0.252444	-0.65481	0.999993
5m	308311	1.3483	0.00477161	0.252376	-0.654873	0.999967
1h	25760	1.34831	0.00476939	0.252542	-0.653792	0.999617
1d	1245	1.35	0.00501715	-0.0100677	0.399693	0.962074
1w	224	1.3478	0.00556242	-0.72897	4.21549	0.812631
EURUSD	n	mean	variance	skewness	kurtosis	autocorrelation
1s	92435573	3.02048e-10	1.08072e-09	151.206	575521	-0.0335426
1m	1541153	1.80871e-08	6.6626e-08	19.2124	9166.36	-0.0572718
5m	308310	8.81094e-08	3.17088e-07	9.73167	2121.94	-0.0651078
1h	25759	1.06895e-06	3.6338e-06	3.16826	198.98	-0.0620681
1d	1244	0.000359164	0.000221784	18.3327	514.925	-0.0195289
1w	223	0.00200359	0.0012085	7.87992	93.7056	0.0443753
GBPUSD	n	mean	variance	skewness	kurtosis	autocorrelation
1s	92418558	1.58039	0.00226547	-0.418154	-0.0869121	1
1m	1540883	1.58039	0.00226533	-0.417985	-0.0867141	0.999973
5m	308260	1.58039	0.0022655	-0.418296	-0.0855756	0.999869
1h	25761	1.58038	0.00226686	-0.421661	-0.0712679	0.998501
1d	1243	1.58093	0.00234134	-0.506634	0.220385	0.970265
1w	224	1.5799	0.00250805	-0.799782	1.28501	0.860075
GBPUSD	n	mean	variance	skewness	kurtosis	autocorrelation
1s	92418557	1.49505e-09	1.12432e-09	82.0471	296392	0.0243908
1m	1540882	1.72771e-07	8.77012e-08	59.5925	25601.1	-0.0339555
5m	308259	8.63543e-07	4.21724e-07	28.2599	5549.19	-0.0494909
1h	25760	1.03556e-05	4.71794e-06	8.3489	480.966	-0.0478517
1d	1242	0.000210616	9.63278e-05	2.63729	38.0651	-0.058002
1w	223	0.00117303	0.000465216	1.34967	7.16594	0.0801616
USDJPY	n	mean	variance	skewness	kurtosis	autocorrelation
1s	92356482	86.7082	53.5769	0.356698	-1.16436	1
1m	1539595	86.7071	53.581	0.355862	-1.15271	0.999895
5m	307986	86.7067	53.596	0.351681	-1.10649	0.999477
1h	25728	86.7024	53.8025	0.294746	-0.477866	0.993758
1d	1243	86.5184	57.6535	-0.786835	11.1203	0.879454
1w	224	86.4446	86.4397	-3.16993	28.961	0.552933
USDJPY	n	mean	variance	skewness	kurtosis	autocorrelation
1s	92356481	-5.41922e-09	5.85861e-06	99.2686	375117	-0.0341302
1m	1539594	6.28671e-05	0.00644565	1155.16	1.39931e+06	-0.00108802
5m	307985	0.000314304	0.0321518	518.509	281257	0.000806071
1h	25727	0.00375988	0.385061	150.101	23542.9	-0.00262694
1d	1242	0.0778074	7.98571	33.0251	1135.86	0.0024483
1w	223	0.433349	44.408	13.9426	200.634	-0.0108091
EURJPY	n	mean	variance	skewness	kurtosis	autocorrelation
1s	92332308	116.928	136.5	0.1002	-1.2401	1
1m	1539310	116.927	136.522	0.100121	-1.24019	0.999992
5m	307940	116.927	136.513	0.100148	-1.24011	0.999963
1h	25736	116.928	136.412	0.100476	-1.23907	0.999562
1d	1243	116.939	134.984	0.124546	-1.20891	0.990891
1w	224	117.125	136.703	0.0864748	-1.2192	0.951902
EURJPY	n	mean	variance	skewness	kurtosis	autocorrelation
1s	92332307	2.25707e-08	1.76165e-05	348.103	1.19492e+06	-0.0398272
1m	1539309	2.25494e-05	0.0017055	341.407	259890	-0.037163
5m	307939	0.000112745	0.00824148	161.844	56173.6	-0.0354321
1h	25735	0.00134506	0.0962063	48.5677	4954.61	-0.0402721
1d	1242	0.0277709	1.97836	11.0012	252.037	-0.0351671
1w	223	0.15467	10.4858	4.83754	47.2807	-0.0172492
GBPJPY	n	mean	variance	skewness	kurtosis	autocorrelation
1s	92317456	136.93	122.571	0.383677	-1.02253	1
1m	1539012	136.928	122.575	0.383923	-1.02243	0.999993
5m	307889	136.928	122.565	0.383951	-1.02227	0.999965
1h	25728	136.929	122.467	0.383978	-1.02099	0.999604
1d	1242	136.814	120.756	0.416894	-0.962273	0.991936
1w	224	137.14	122.025	0.400799	-0.989022	0.960197
GBPJPY	n	mean	variance	skewness	kurtosis	autocorrelation
1s	92317455	1.39215e-07	2.30785e-05	248.647	726113	-0.0294336
1m	1539011	1.70535e-05	0.00145636	57.5118	20671.8	-0.0436399
5m	307888	8.52761e-05	0.00687141	28.0902	4672.26	-0.0544082
1h	25727	0.00101842	0.0771571	8.28977	435.367	-0.0561696
1d	1241	0.020913	1.54057	2.35291	28.8254	-0.0346278
1w	223	0.116381	7.51757	0.886633	4.38016	-0.0493046
NZDUSD	n	mean	variance	skewness	kurtosis	autocorrelation
1s	92313670	0.766314	0.00350738	-0.675463	-0.058813	1
1m	1539269	0.766421	0.0198214	926.442	1.04286e+06	0.175852
5m	307930	0.766831	0.0850618	520.953	283063	0.0400077
1h	25721	0.772454	0.979882	159.509	25532.4	0.00230294
1d	1242	0.89142	20.2243	35.1902	1236.57	-0.00103928
1w	224	1.47327	112.118	14.8655	218.99	-0.00121739
NZDUSD	n	mean	variance	skewness	kurtosis	autocorrelation
1s	92313669	2.8538e-09	7.89836e-10	267.689	822983	-0.0470349
1m	1539268	-0.000102912	0.0163564	-1240.67	1.53926e+06	-1.3362e-07
5m	307929	-0.000514434	0.0817619	-554.909	307922	-2.75455e-06
1h	25720	-0.00615901	0.978911	-160.365	25714.9	3.24161e-06
1d	1241	-0.127647	20.2863	-35.1851	1236	-9.40788e-06
1w	223	-0.71036	112.895	-14.8325	218.004	-0.000215086
AUDJPY	n	mean	variance	skewness	kurtosis	autocorrelation
1s	92335574	83.6673	40.7628	1.03404	0.831669	1
1m	1539183	83.6674	40.7657	1.03242	0.849135	0.999897
5m	307905	83.6671	40.7817	1.02624	0.919639	0.999485
1h	25724	83.6641	41.0064	0.941629	1.87359	0.993906
1d	1243	83.3252	43.8764	-0.651956	19.5513	0.882148
1w	224	83.3009	71.3028	-3.66774	39.33	0.596103
AUDJPY	n	mean	variance	skewness	kurtosis	autocorrelation
1s	92335573	2.1274e-07	1.04978e-05	84.3684	115748	0.0414622
1m	1539182	5.90591e-05	0.00393289	952.808	1.08148e+06	0.000550671
5m	307904	0.000295211	0.0195054	431.148	219743	0.00115733
1h	25723	0.00352965	0.230613	126.571	18745.5	-0.00397597
1d	1242	0.0730367	4.80657	27.9355	908.96	0.00774417
1w	223	0.406779	26.7481	11.7252	159.214	0.0317603
EURGBP	n	mean	variance	skewness	kurtosis	autocorrelation
1s	92312400	0.852999	0.00098821	-0.231467	-0.451494	1
1m	1539109	0.853052	0.00635278	962.649	1.09746e+06	0.155962
5m	307895	0.853289	0.0278041	525.558	286391	0.0359898
1h	25727	0.85654	0.321913	159.649	25564.4	0.00355007
1d	1242	0.927151	6.64854	35.1916	1236.63	0.000535819
1w	224	1.25933	36.8596	14.8656	218.993	0.000399223
EURGBP	n	mean	variance	skewness	kurtosis	autocorrelation
1s	92312399	-6.41192e-10	3.37829e-10	10.3457	27166.4	-0.0243427
1m	1539108	-5.90488e-05	0.00535953	-1240.6	1.53909e+06	-7.63148e-07
5m	307894	-0.000295175	0.0267912	-554.877	307887	3.63102e-06
1h	25726	-0.00353272	0.320628	-160.383	25720.9	3.30456e-07
1d	1241	-0.0732314	6.64774	-35.1851	1235.99	-5.91453e-06
1w	223	-0.407534	36.9947	-14.8325	218.003	-8.54473e-05
AUDNZD	n	mean	variance	skewness	kurtosis	autocorrelation
1s	91929516	1.26486	0.00216842	-0.562949	0.870266	0.999998
1m	1532507	1.26486	0.00216899	-0.563783	0.8779	0.999923
5m	306590	1.26486	0.00216985	-0.567183	0.91217	0.999638
1h	25624	1.26489	0.00218179	-0.615045	1.37626	0.99585
1d	1239	1.26598	0.00240252	-1.49888	9.62123	0.925687
1w	224	1.26253	0.00301358	-2.38982	15.5539	0.672804
AUDNZD	n	mean	variance	skewness	kurtosis	autocorrelation
1s	91929515	3.13267e-09	4.85332e-09	2954.36	1.92125e+07	-0.0643228
1m	1532506	1.88094e-07	1.98764e-07	675.281	685589	-0.0571594
5m	306589	9.40461e-07	9.05933e-07	346.347	164635	-0.0435883
1h	25623	1.12596e-05	1.01387e-05	112.904	16145.5	-0.028162
1d	1238	0.000234228	0.000191523	26.8266	863.336	-0.0140708
1w	223	0.00130034	0.00107313	11.1998	149.87	-0.0362816
AUDUSD	n	mean	variance	skewness	kurtosis	autocorrelation
1s	92355740	0.969116	0.00641465	-0.676047	-0.453127	1
1m	1539590	0.969117	0.00641414	-0.676062	-0.453006	0.999987
5m	307990	0.969117	0.00641406	-0.675962	-0.453161	0.999935
1h	25728	0.969141	0.0064111	-0.675973	-0.452017	0.99924
1d	1243	0.967602	0.0066234	-0.635892	-0.514457	0.984908
1w	224	0.968728	0.0067958	-0.617793	-0.527935	0.917121
AUDUSD	n	mean	variance	skewness	kurtosis	autocorrelation
1s	92355739	-2.06955e-09	2.55984e-09	-5109.42	4.00045e+07	0.0104981
1m	1539589	-1.2426e-07	1.52132e-07	-669.845	680499	-0.0047852
5m	307989	-6.21629e-07	7.49896e-07	-306.219	140155	-0.0116753
1h	25727	-7.45637e-06	8.76572e-06	-92.5159	12426.6	-0.00134808
1d	1242	-0.00015442	0.00017944	-20.2424	593.533	-0.0156007
1w	223	-0.000860045	0.00101677	-8.35069	100.761	-0.0797497
CADJPY	n	mean	variance	skewness	kurtosis	autocorrelation
1s	92276912	84.7678	35.0861	0.550481	-0.31749	0.999998
1m	1538325	84.7666	35.0955	0.54685	-0.267045	0.999863
5m	307751	84.7662	35.1281	0.531469	-0.0642676	0.999317
1h	25730	84.7601	35.5975	0.324951	2.63382	0.991988
1d	1243	84.4689	44.4303	-2.75901	38.3638	0.866904
1w	224	84.4295	65.9273	-4.60138	48.1647	0.501144
CADJPY	n	mean	variance	skewness	kurtosis	autocorrelation
1s	92276911	1.02259e-06	8.32464e-05	7855.55	7.04139e+07	-0.00336305
1m	1538324	6.13536e-05	0.00497148	1021.29	1.18483e+06	-0.00292386
5m	307750	0.000306683	0.0247678	460.368	239511	-0.00218877
1h	25729	0.00366653	0.29301	135.363	20487.2	-0.00726348
1d	1242	0.0760051	6.11246	30.0849	1002.29	-0.00148468
1w	223	0.423311	33.953	12.6913	176.766	0.0102077
CHFJPY	n	mean	variance	skewness	kurtosis	autocorrelation
1s	92058449	89.8186	57.2942	0.98045	-0.0970355	1
1m	1534698	89.8173	57.292	0.980639	-0.0966155	0.999992
5m	307032	89.8171	57.2852	0.980706	-0.0962907	0.999965
1h	25661	89.8155	57.2221	0.981067	-0.0940363	0.999606
1d	1242	89.5699	53.5637	1.03705	0.135228	0.991247
1w	224	89.9214	57.3991	0.963286	-0.121046	0.955405
CHFJPY	n	mean	variance	skewness	kurtosis	autocorrelation
1s	92058448	1.44979e-07	2.50152e-05	-17.8159	1.19544e+06	-0.109644
1m	1534697	8.72159e-06	0.00067637	-14.2808	13683.4	-0.0519587
5m	307031	4.35917e-05	0.0027749	-9.3254	2992.64	-0.0294719
1h	25660	0.000520401	0.0300709	-3.74962	323.454	-0.0108347
1d	1241	0.0107668	0.618144	-1.36714	20.9045	-0.0064058
1w	223	0.0599173	3.42789	-0.882395	4.08511	-0.105998
EURCHF	n	mean	variance	skewness	kurtosis	autocorrelation
1s	92229567	1.30482	0.0140418	8.76482	7299.15	0.99112
1m	1537808	1.30493	0.0288997	327.621	206710	0.741244
5m	307651	1.3055	0.0888153	303.784	109396	0.579141
1h	25713	1.3132	0.910044	110.785	12461.5	0.508583
1d	1242	1.48166	18.5511	24.8311	615.056	0.501304
1w	224	1.78612	51.4467	14.8601	218.883	0.00212103
EURCHF	n	mean	variance	skewness	kurtosis	autocorrelation
1s	92229566	-1.1647e-06	0.000124451	-9603.52	9.22282e+07	-1.15462e-06
1m	1537807	-6.98514e-05	0.00746387	-1240.07	1.53778e+06	-1.96626e-05
5m	307650	-0.000349156	0.0373083	-554.654	307641	-2.63686e-05
1h	25712	-0.00417775	0.446398	-160.339	25706.7	-4.56937e-05
1d	1241	-0.0865571	9.24929	-35.1849	1235.99	-0.00086071
1w	223	-0.481692	51.4695	-14.8324	218.002	-4.04081e-05
USDCAD	n	mean	variance	skewness	kurtosis	autocorrelation
1s	92317789	1.02259	0.00174029	1.20174	2.19596	1
1m	1539085	1.02258	0.0017401	1.20193	2.19702	0.99998
5m	307902	1.02258	0.00174033	1.20224	2.19858	0.999901
1h	25733	1.02259	0.00174221	1.20611	2.21841	0.998953
1d	1243	1.0235	0.00187213	1.23934	2.34392	0.980985
1w	224	1.02432	0.00200324	1.33804	2.82169	0.899142
USDCAD	n	mean	variance	skewness	kurtosis	autocorrelation
1s	92317788	-2.08194e-09	6.78414e-10	-296.972	752929	0.00235886
1m	1539084	-1.24792e-07	4.34014e-08	-29.5357	12420.1	-0.0164734
5m	307901	-6.2348e-07	2.10893e-07	-13.6	2606.83	-0.0326544
1h	25732	-7.4693e-06	2.05962e-06	-2.12623	74.5067	-0.0572307
1d	1242	-0.000154868	3.86068e-05	-0.348275	6.23995	-0.0612282
1w	223	-0.000862539	0.000224332	-0.434653	1.70495	-0.04961
USDCHF	n	mean	variance	skewness	kurtosis	autocorrelation
1s	92242015	0.968367	0.00600732	0.156274	-0.04052	1
1m	1537755	0.968367	0.00600649	0.156313	-0.0401176	0.999996
5m	307626	0.968369	0.00600681	0.156227	-0.0402823	0.999979
1h	25705	0.9684	0.00600336	0.155892	-0.0414238	0.999765
1d	1242	0.96988	0.00624621	0.10628	-0.164945	0.995221
1w	224	0.969083	0.00614422	0.142641	-0.185853	0.974218
USDCHF	n	mean	variance	skewness	kurtosis	autocorrelation
1s	92242014	-1.37464e-09	8.28399e-10	548.898	2.11371e+06	-0.00762003
1m	1537754	-8.24644e-08	4.63805e-08	78.8712	40367.4	-0.0159318
5m	307625	-4.11914e-07	2.22865e-07	38.628	8789.87	-0.023654
1h	25704	-4.94553e-06	2.50371e-06	13.2009	887.093	-0.0109216
1d	1241	-0.000101898	5.32942e-05	3.18166	42.7819	-0.0216929
1w	223	-0.000567063	0.000281909	1.71276	9.94314	-0.0567077