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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 10:56:59 -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/t12290183005d7zjfs5qakqesv.htm/, Retrieved Thu, 11 Dec 2008 17:58:20 +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/t12290183005d7zjfs5qakqesv.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	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.215585	2.1123	0.018629
2	-0.012303	-0.1205	0.452153
3	0.105871	1.0373	0.151096
4	0.010059	0.0986	0.460848
5	0.121207	1.1876	0.118964
6	0.02244	0.2199	0.413223
7	0.087633	0.8586	0.196344
8	0.092987	0.9111	0.182266
9	0.058282	0.571	0.284653
10	0.121593	1.1914	0.118224
11	0.034765	0.3406	0.367066
12	-0.008621	-0.0845	0.46643
13	-0.026514	-0.2598	0.397792
14	-0.009856	-0.0966	0.461634
15	0.009959	0.0976	0.461235
16	-0.020875	-0.2045	0.419184
17	0.014275	0.1399	0.444529
18	0.000215	0.0021	0.499163
19	0.032625	0.3197	0.374961
20	-0.062187	-0.6093	0.271882
21	-0.10801	-1.0583	0.146292
22	0.004291	0.042	0.483276
23	-0.000636	-0.0062	0.49752
24	-0.05969	-0.5848	0.280015
25	0.006083	0.0596	0.476297
26	-0.073165	-0.7169	0.237597
27	-0.029221	-0.2863	0.387632
28	-0.041909	-0.4106	0.341133
29	-0.023116	-0.2265	0.41065
30	-0.04926	-0.4826	0.315223
31	-0.03569	-0.3497	0.36367
32	0.034671	0.3397	0.367409
33	-0.046318	-0.4538	0.325489
34	-0.02412	-0.2363	0.40684
35	-0.053411	-0.5233	0.30098
36	-0.004865	-0.0477	0.481041
37	-0.005053	-0.0495	0.480308
38	-0.085716	-0.8398	0.201541
39	-0.012841	-0.1258	0.45007
40	-0.000209	-0.002	0.499186
41	-0.008685	-0.0851	0.466183
42	0.044229	0.4334	0.332863
43	-0.016054	-0.1573	0.437669
44	-0.022083	-0.2164	0.414581
45	-0.04507	-0.4416	0.32989
46	-0.051794	-0.5075	0.306494
47	-0.079719	-0.7811	0.218336
48	-0.024766	-0.2427	0.404394
49	0.005184	0.0508	0.479799
50	-0.069823	-0.6841	0.247773
51	-0.058444	-0.5726	0.284117
52	-0.072482	-0.7102	0.239659
53	-0.051598	-0.5056	0.307163
54	-0.025949	-0.2543	0.399923
55	-0.057974	-0.568	0.285672
56	-0.076352	-0.7481	0.228115
57	-0.129174	-1.2656	0.104353
58	-0.090849	-0.8901	0.187808
59	0.0122	0.1195	0.452552
60	-0.121558	-1.191	0.118291

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.215585	2.1123	0.018629
2	-0.061644	-0.604	0.273637
3	0.12841	1.2582	0.105693
4	-0.046898	-0.4595	0.323456
5	0.150916	1.4787	0.071251
6	-0.062061	-0.6081	0.272287
7	0.132173	1.295	0.099209
8	0.004077	0.04	0.484108
9	0.072559	0.7109	0.239427
10	0.061343	0.601	0.274616
11	0.001153	0.0113	0.495504
12	-0.037251	-0.365	0.357963
13	-0.046933	-0.4599	0.323331
14	-0.008582	-0.0841	0.466581
15	-0.022131	-0.2168	0.414398
16	-0.023198	-0.2273	0.41034
17	0.006785	0.0665	0.473566
18	-0.016404	-0.1607	0.436323
19	0.044476	0.4358	0.33199
20	-0.101048	-0.9901	0.162315
21	-0.050564	-0.4954	0.310716
22	0.022926	0.2246	0.411375
23	0.020072	0.1967	0.422253
24	-0.062852	-0.6158	0.269734
25	0.055212	0.541	0.294893
26	-0.097994	-0.9601	0.169699
27	0.036816	0.3607	0.359551
28	-0.064588	-0.6328	0.264175
29	0.053685	0.526	0.30005
30	-0.084228	-0.8253	0.205633
31	0.074244	0.7274	0.234363
32	-0.003897	-0.0382	0.484812
33	-0.021476	-0.2104	0.416894
34	-0.007868	-0.0771	0.469356
35	-0.040296	-0.3948	0.346925
36	0.044166	0.4327	0.33309
37	-0.031298	-0.3067	0.379885
38	-0.044341	-0.4345	0.332467
39	0.004181	0.041	0.483706
40	0.014951	0.1465	0.441921
41	-0.012032	-0.1179	0.453201
42	0.040593	0.3977	0.345857
43	-0.001995	-0.0195	0.492224
44	-0.024125	-0.2364	0.406824
45	-0.024574	-0.2408	0.40512
46	-0.042887	-0.4202	0.337636
47	-0.085885	-0.8415	0.201081
48	0.023392	0.2292	0.409602
49	0.001636	0.016	0.493622
50	-0.084509	-0.828	0.204857
51	-0.031351	-0.3072	0.379686
52	-0.061036	-0.598	0.275616
53	0.003863	0.0378	0.484944
54	-0.025798	-0.2528	0.400496
55	-0.00492	-0.0482	0.480827
56	-0.065733	-0.6441	0.260539
57	-0.0751	-0.7358	0.231814
58	-0.038964	-0.3818	0.351739
59	0.019146	0.1876	0.425797
60	-0.10583	-1.0369	0.15119

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t12290183005d7zjfs5qakqesv/116s21229018212.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t12290183005d7zjfs5qakqesv/116s21229018212.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t12290183005d7zjfs5qakqesv/29u0d1229018212.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t12290183005d7zjfs5qakqesv/29u0d1229018212.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; 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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