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*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, 26 Nov 2009 03:35:41 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/26/t1259231889mukocaqv71np88l.htm/, Retrieved Thu, 26 Nov 2009 11:38:12 +0100

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/2009/Nov/26/t1259231889mukocaqv71np88l.htm/},
    year = {2009},
}
@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 = {2009},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

785.8 819.3 849.4 880.4 900.1 937.2 948.9 952.6 947.3 974.2 1000.8 1032.8 1050.7 1057.3 1075.4 1118.4 1179.8 1227 1257.8 1251.5 1236.3 1170.6 1213.1 1265.5 1300.8 1348.4 1371.9 1403.3 1451.8 1474.2 1438.2 1513.6 1562.2 1546.2 1527.5 1418.7 1448.5 1492.1 1395.4 1403.7 1316.6 1274.5 1264.4 1323.9 1332.1 1250.2 1096.7 1080.8 1039.2 792 746.6 688.8 715.8 672.9 629.5 681.2 755.4 760.6 765.9 836.8 904.9

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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.370752	-2.8478	0.003025
2	-0.194303	-1.4925	0.070452
3	0.060562	0.4652	0.321757
4	-0.000143	-0.0011	0.499563
5	0.196916	1.5125	0.067867
6	-0.177961	-1.3669	0.088415
7	-0.121244	-0.9313	0.177748
8	0.199016	1.5287	0.065845
9	0.0725	0.5569	0.289857
10	-0.33276	-2.556	0.006592
11	0.300796	2.3105	0.012189
12	-0.10409	-0.7995	0.213596
13	-0.053592	-0.4117	0.341043
14	0.119923	0.9211	0.180362
15	-0.121027	-0.9296	0.178176
16	0.167327	1.2853	0.101862
17	-0.091669	-0.7041	0.242063
18	-0.181354	-1.393	0.084422
19	0.214919	1.6508	0.052044
20	-0.000473	-0.0036	0.498557
21	-0.042045	-0.323	0.373935
22	-0.048768	-0.3746	0.354654
23	-0.00241	-0.0185	0.492646
24	-0.021978	-0.1688	0.433258
25	0.086255	0.6625	0.255103
26	-0.103109	-0.792	0.215768
27	-0.00811	-0.0623	0.475271
28	0.148636	1.1417	0.129096
29	-0.083559	-0.6418	0.261736
30	0.023942	0.1839	0.427362
31	-0.052765	-0.4053	0.343364
32	0.040364	0.31	0.378811
33	0.001442	0.0111	0.495599
34	0.012596	0.0968	0.461626
35	-0.063373	-0.4868	0.314111
36	0.026574	0.2041	0.41948
37	0.011472	0.0881	0.46504
38	0.003448	0.0265	0.48948
39	0.00237	0.0182	0.492767
40	-0.022158	-0.1702	0.432719
41	0.020187	0.1551	0.438653
42	-0.001618	-0.0124	0.495063
43	0.01321	0.1015	0.459761
44	-0.0318	-0.2443	0.403937
45	0.026981	0.2072	0.418267
46	-0.008649	-0.0664	0.47363
47	0.012076	0.0928	0.463206
48	-0.021783	-0.1673	0.433847
49	-0.004372	-0.0336	0.486661
50	0.012478	0.0958	0.461985
51	0.002274	0.0175	0.493061
52	-0.007144	-0.0549	0.478211
53	-0.004532	-0.0348	0.486175
54	0.004032	0.031	0.487699
55	-0.002067	-0.0159	0.493693
56	0.000234	0.0018	0.499286
57	-0.000974	-0.0075	0.497029
58	5.1e-05	4e-04	0.499846
59	NA	NA	NA
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.370752	-2.8478	0.003025
2	-0.384631	-2.9544	0.002247
3	-0.247351	-1.8999	0.031166
4	-0.223785	-1.7189	0.045436
5	0.117864	0.9053	0.184487
6	-0.028375	-0.2179	0.41411
7	-0.15525	-1.1925	0.11892
8	0.008161	0.0627	0.475114
9	0.145674	1.1189	0.133849
10	-0.300691	-2.3096	0.012213
11	0.179706	1.3803	0.086344
12	-0.021334	-0.1639	0.435198
13	-0.126134	-0.9689	0.168287
14	0.037089	0.2849	0.388364
15	0.08966	0.6887	0.246859
16	0.051645	0.3967	0.346513
17	0.01707	0.1311	0.448064
18	-0.113818	-0.8742	0.192764
19	0.006695	0.0514	0.47958
20	-0.110524	-0.849	0.199669
21	0.166635	1.2799	0.102786
22	-0.094183	-0.7234	0.236135
23	-0.002589	-0.0199	0.492101
24	-0.18052	-1.3866	0.085391
25	-0.066198	-0.5085	0.306508
26	-0.104216	-0.8005	0.213316
27	-0.110248	-0.8468	0.200257
28	0.010944	0.0841	0.466646
29	0.148828	1.1432	0.128793
30	-0.071283	-0.5475	0.293038
31	0.079058	0.6073	0.273006
32	0.015698	0.1206	0.452218
33	-0.008532	-0.0655	0.473983
34	-0.022464	-0.1726	0.431798
35	0.01397	0.1073	0.457455
36	-0.096095	-0.7381	0.231684
37	-0.069993	-0.5376	0.296427
38	0.126655	0.9729	0.167299
39	0.003525	0.0271	0.489246
40	-0.060209	-0.4625	0.322722
41	0.056886	0.4369	0.331872
42	-0.079811	-0.613	0.271104
43	-0.026692	-0.205	0.419128
44	-0.021293	-0.1636	0.43532
45	0.025524	0.1961	0.42262
46	-0.009616	-0.0739	0.470686
47	0.006478	0.0498	0.480242
48	-0.033887	-0.2603	0.397773
49	-0.08392	-0.6446	0.260842
50	-0.024998	-0.192	0.424196
51	0.022312	0.1714	0.432254
52	0.010496	0.0806	0.468009
53	0.022535	0.1731	0.431585
54	-0.030961	-0.2378	0.406424
55	0.042829	0.329	0.37167
56	-0.009012	-0.0692	0.472523
57	-0.080074	-0.6151	0.27044
58	-0.011968	-0.0919	0.463532
59	NA	NA	NA
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259231889mukocaqv71np88l/1iysb1259231739.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259231889mukocaqv71np88l/1iysb1259231739.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259231889mukocaqv71np88l/2dr5x1259231739.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259231889mukocaqv71np88l/2dr5x1259231739.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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 (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'

par7 <- as.numeric(par7)

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='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))

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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