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autocorrelation

*The author of this computation has been verified*

R Software Module: rwasp_autocorrelation.wasp (opens new window with default values)

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Thu, 11 Dec 2008 09:35:54 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/11/t1229013393htnqzepab2v3q0o.htm/, Retrieved Thu, 11 Dec 2008 16:36:36 +0000

BibTeX entries for LaTeX users:

@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2008/Dec/11/t1229013393htnqzepab2v3q0o.htm/},
    year = {2008},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2008},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

1375.06 1334.38 1335.61 1307.24 1183.2 1187.79 1270.81 1238.67 1204.45 1178.5 1044.64 1076.59 1129.68 1144.93 1140.21 1100.29 1153.79 1114.2 1079.27 1014.05 903.69 912.55 867.81 854.54 911.17 899.26 895.87 837.61 846.62 890.19 935.96 988 992.55 989.53 1019.44 1038.73 1049.9 1080.64 1132.52 1143.37 1123.98 1133.07 1102.78 1132.76 1105.85 1088.93 1117.66 1118.07 1168.94 1199.21 1181.4 1199.63 1194.9 1164.42 1178.28 1202.25 1222.24 1224.27 1225.91 1191.96 1237.37 1262.07 1278.72 1276.65 1293.83 1302.18 1290 1253.12 1260.24 1287.15 1317.81 1363.38 1388.63 1416.42 1424.16 1444.65 1406.95 1463.65 1511.14 1514.49 1520.98 1454.62 1497.12 1539.66 1463.39 1479.23 1378.76 1354.87 1316.94 1370.47 1403.22 1341.25 1257.33 1281.47 1216.93 969.13 883.04

Output produced by software:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.939431	9.2523	0
2	0.872758	8.5957	0
3	0.832148	8.1957	0
4	0.791561	7.796	0
5	0.755225	7.4381	0
6	0.718024	7.0717	0
7	0.680642	6.7035	0
8	0.635185	6.2559	0
9	0.57919	5.7044	0
10	0.524331	5.1641	1e-06
11	0.470961	4.6384	5e-06
12	0.423867	4.1746	3.3e-05
13	0.373105	3.6747	0.000195
14	0.331862	3.2685	0.000748
15	0.287787	2.8344	0.002794
16	0.241439	2.3779	0.009686
17	0.200797	1.9776	0.025405
18	0.161277	1.5884	0.057726
19	0.124059	1.2218	0.112364
20	0.083935	0.8267	0.205227
21	0.050101	0.4934	0.311411
22	0.028702	0.2827	0.389013
23	0.008293	0.0817	0.467535
24	-0.011315	-0.1114	0.455748
25	-0.031925	-0.3144	0.376937
26	-0.054315	-0.5349	0.296957
27	-0.075006	-0.7387	0.230928
28	-0.092564	-0.9116	0.182107
29	-0.109709	-1.0805	0.141298
30	-0.128031	-1.261	0.105173
31	-0.141148	-1.3901	0.083834
32	-0.153093	-1.5078	0.067429
33	-0.168626	-1.6608	0.049994
34	-0.181944	-1.7919	0.03813
35	-0.194822	-1.9188	0.028976
36	-0.20634	-2.0322	0.022433
37	-0.220675	-2.1734	0.016093
38	-0.241241	-2.376	0.009734
39	-0.254947	-2.5109	0.006847
40	-0.268674	-2.6461	0.00475
41	-0.281615	-2.7736	0.003325
42	-0.296711	-2.9223	0.002162
43	-0.316124	-3.1135	0.001215
44	-0.337822	-3.3272	0.00062
45	-0.353304	-3.4796	0.000377
46	-0.363994	-3.5849	0.000265
47	-0.37454	-3.6888	0.000186
48	-0.377368	-3.7166	0.000169
49	-0.384833	-3.7902	0.000131
50	-0.400286	-3.9424	7.6e-05
51	-0.409837	-4.0364	5.4e-05
52	-0.419515	-4.1317	3.8e-05
53	-0.422151	-4.1577	3.5e-05
54	-0.416715	-4.1042	4.2e-05
55	-0.413761	-4.0751	4.7e-05
56	-0.405229	-3.991	6.4e-05
57	-0.393549	-3.876	9.7e-05
58	-0.370607	-3.6501	0.000212
59	-0.342483	-3.3731	0.000535
60	-0.319294	-3.1447	0.001104

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.939431	9.2523	0
2	-0.083191	-0.8193	0.207302
3	0.190269	1.8739	0.031975
4	-0.049365	-0.4862	0.313966
5	0.06498	0.64	0.261847
6	-0.044109	-0.4344	0.332474
7	0.007019	0.0691	0.472513
8	-0.105219	-1.0363	0.151323
9	-0.10055	-0.9903	0.162244
10	-0.049408	-0.4866	0.313816
11	-0.056871	-0.5601	0.288346
12	0.013632	0.1343	0.446737
13	-0.08672	-0.8541	0.197579
14	0.084061	0.8279	0.204878
15	-0.094461	-0.9303	0.177253
16	0.023326	0.2297	0.409393
17	-0.013706	-0.135	0.44645
18	-0.002307	-0.0227	0.490961
19	-0.013312	-0.1311	0.447982
20	-0.060544	-0.5963	0.276184
21	0.038722	0.3814	0.351883
22	0.038276	0.377	0.353509
23	0.01729	0.1703	0.432569
24	-0.005355	-0.0527	0.479025
25	-0.011656	-0.1148	0.45442
26	-0.048185	-0.4746	0.318079
27	0.001197	0.0118	0.49531
28	-0.017516	-0.1725	0.431696
29	-0.041412	-0.4079	0.342137
30	-0.039924	-0.3932	0.347514
31	0.003726	0.0367	0.4854
32	-0.015928	-0.1569	0.437837
33	-0.042179	-0.4154	0.339379
34	0.007079	0.0697	0.472282
35	-0.026789	-0.2638	0.396231
36	-0.007637	-0.0752	0.4701
37	-0.053972	-0.5316	0.298121
38	-0.067159	-0.6614	0.254949
39	0.020089	0.1979	0.421788
40	-0.056878	-0.5602	0.288323
41	0.007854	0.0774	0.46925
42	-0.067294	-0.6628	0.254524
43	-0.041226	-0.406	0.342806
44	-0.06568	-0.6469	0.259621
45	0.035043	0.3451	0.365372
46	-0.025678	-0.2529	0.40044
47	-0.009622	-0.0948	0.462349
48	0.050615	0.4985	0.309632
49	-0.080638	-0.7942	0.21451
50	-0.041322	-0.407	0.342462
51	-0.016331	-0.1608	0.436276
52	-0.023557	-0.232	0.408509
53	0.009756	0.0961	0.461827
54	0.028142	0.2772	0.391121
55	-0.04196	-0.4133	0.340164
56	0.0514	0.5062	0.306921
57	0.008145	0.0802	0.468112
58	0.120562	1.1874	0.118986
59	0.026166	0.2577	0.398591
60	-0.014771	-0.1455	0.442318

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t1229013393htnqzepab2v3q0o/1rihw1229013353.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t1229013393htnqzepab2v3q0o/1rihw1229013353.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t1229013393htnqzepab2v3q0o/2uynn1229013353.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t1229013393htnqzepab2v3q0o/2uynn1229013353.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

R code (references can be found in the software module):

if (par1 == 'Default') {

par1 = 10*log10(length(x))

} else {

par1 <- as.numeric(par1)

}

par2 <- as.numeric(par2)

par3 <- as.numeric(par3)

par4 <- as.numeric(par4)

par5 <- as.numeric(par5)

if (par2 == 0) {

x <- log(x)

} else {

x <- (x ^ par2 - 1) / par2

}

if (par3 > 0) x <- diff(x,lag=1,difference=par3)

if (par4 > 0) x <- diff(x,lag=par5,difference=par4)

bitmap(file='pic1.png')

racf <- acf(x,par1,main='Autocorrelation',xlab='lags',ylab='ACF')

dev.off()

bitmap(file='pic2.png')

rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')

dev.off()

(myacf <- c(racf$acf))

(mypacf <- c(rpacf$acf))

lengthx <- length(x)

sqrtn <- sqrt(lengthx)

load(file='createtable')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,'Autocorrelation Function',4,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Time lag k',header=TRUE)

a<-table.element(a,hyperlink('http://www.xycoon.com/basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),header=TRUE)

a<-table.element(a,'T-STAT',header=TRUE)

a<-table.element(a,'P-value',header=TRUE)

a<-table.row.end(a)

for (i in 2:(par1+1)) {

a<-table.row.start(a)

a<-table.element(a,i-1,header=TRUE)

a<-table.element(a,round(myacf[i],6))

mytstat <- myacf[i]*sqrtn

a<-table.element(a,round(mytstat,4))

a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))

a<-table.row.end(a)

}

a<-table.end(a)

table.save(a,file='mytable.tab')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,'Partial Autocorrelation Function',4,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Time lag k',header=TRUE)

a<-table.element(a,hyperlink('http://www.xycoon.com/basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),header=TRUE)

a<-table.element(a,'T-STAT',header=TRUE)

a<-table.element(a,'P-value',header=TRUE)

a<-table.row.end(a)

for (i in 1:par1) {

a<-table.row.start(a)

a<-table.element(a,i,header=TRUE)

a<-table.element(a,round(mypacf[i],6))

mytstat <- mypacf[i]*sqrtn

a<-table.element(a,round(mytstat,4))

a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))

a<-table.row.end(a)

}

a<-table.end(a)

table.save(a,file='mytable1.tab')

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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