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

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Fri, 30 Apr 2010 11:52:38 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Apr/30/t1272628457ot2dxjznigntd4i.htm/, Retrieved Fri, 30 Apr 2010 13:54:19 +0200

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/2010/Apr/30/t1272628457ot2dxjznigntd4i.htm/},
    year = {2010},
}
@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 = {2010},
    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:

KDGP2W21

Dataseries X:

» Textbox « » Textfile « » CSV «

4.50 4.65 4.71 15.80 14.99 15.26 17.21 16.94 16.80 18.37 18.53 18.48 18.73 18.63 19.15 19.76 20.02 20.26 20.32 20.52 20.81 21.26 22.15 23.05 24.01 24.69 25.38 26.33 27.36 28.55 30.10 32.20 36.28 40.91 44.66 47.83 49.97 52.20 55.67 59.92 65.15 70.14 74.60 78.23 79.24 80.47 81.41 83.94 86.83 89.61 91.79 94.32 96.56 97.98 100.00 101.63 102.60 103.75 106.39 109.02 110.81 112.57 114.93 118.13 120.25 122.44 127.94 127.87

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	0.240399	1.9678	0.026619
2	0.218039	1.7847	0.039416
3	0.335724	2.748	0.003848
4	0.144066	1.1792	0.121238
5	0.132309	1.083	0.141346
6	0.247871	2.0289	0.023222
7	0.208214	1.7043	0.046479
8	0.191191	1.565	0.061151
9	0.162051	1.3264	0.094598
10	0.092302	0.7555	0.226292
11	0.065304	0.5345	0.297369
12	0.004731	0.0387	0.484613
13	-0.063051	-0.5161	0.303743
14	-0.05938	-0.4861	0.314259
15	-0.06409	-0.5246	0.300796
16	-0.065145	-0.5332	0.297818
17	-0.066641	-0.5455	0.293618
18	-0.076547	-0.6266	0.266538
19	-0.087547	-0.7166	0.238055
20	-0.131079	-1.0729	0.143577
21	-0.136145	-1.1144	0.134545
22	-0.169822	-1.3901	0.084556
23	-0.119983	-0.9821	0.164792
24	-0.114521	-0.9374	0.17596
25	-0.112706	-0.9225	0.179779
26	-0.103986	-0.8512	0.198856
27	-0.124266	-1.0172	0.156367
28	-0.128085	-1.0484	0.149106
29	-0.056169	-0.4598	0.323586
30	-0.024015	-0.1966	0.42238
31	-0.045043	-0.3687	0.356759
32	-0.056749	-0.4645	0.321894
33	-0.077487	-0.6343	0.264036
34	-0.082263	-0.6734	0.25152
35	-0.059733	-0.4889	0.313243
36	-0.018253	-0.1494	0.44084
37	0.02371	0.1941	0.423354
38	0.011885	0.0973	0.461398
39	0.009988	0.0818	0.467543
40	-0.003434	-0.0281	0.488829
41	-0.096776	-0.7921	0.215535
42	-0.055461	-0.454	0.325659
43	-0.066483	-0.5442	0.294058
44	-0.0089	-0.0728	0.471072
45	0.000757	0.0062	0.497539
46	-0.011291	-0.0924	0.463318
47	-0.046338	-0.3793	0.352835
48	-0.013567	-0.1111	0.455953
49	-0.006663	-0.0545	0.478335
50	-0.056038	-0.4587	0.32397
51	-0.022015	-0.1802	0.428771
52	-0.028516	-0.2334	0.408076
53	-0.064794	-0.5304	0.298807
54	-0.052703	-0.4314	0.333785
55	-0.001089	-0.0089	0.496457
56	0.005605	0.0459	0.481773
57	-0.011732	-0.096	0.461891
58	-0.055401	-0.4535	0.325836
59	-0.012463	-0.102	0.459525
60	0.063897	0.523	0.301342

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.240399	1.9678	0.026619
2	0.170076	1.3921	0.084243
3	0.274699	2.2485	0.013919
4	0.00189	0.0155	0.493851
5	0.013547	0.1109	0.45602
6	0.138179	1.131	0.131035
7	0.115678	0.9469	0.173555
8	0.076843	0.629	0.265749
9	-0.013293	-0.1088	0.456839
10	-0.06073	-0.4971	0.310375
11	-0.048159	-0.3942	0.347344
12	-0.092612	-0.7581	0.225535
13	-0.137668	-1.1269	0.13191
14	-0.109596	-0.8971	0.186443
15	-0.069825	-0.5715	0.284771
16	-0.022246	-0.1821	0.42803
17	-0.018768	-0.1536	0.439183
18	-0.010142	-0.083	0.467042
19	0.009592	0.0785	0.468828
20	-0.01757	-0.1438	0.443038
21	-0.003227	-0.0264	0.489502
22	-0.050461	-0.413	0.340447
23	0.025407	0.208	0.417945
24	0.009972	0.0816	0.467595
25	0.001154	0.0094	0.496245
26	-0.026589	-0.2176	0.414184
27	-0.052617	-0.4307	0.334038
28	-0.035147	-0.2877	0.387235
29	0.056699	0.4641	0.32204
30	0.084553	0.6921	0.245636
31	0.023782	0.1947	0.423123
32	-0.044931	-0.3678	0.357101
33	-0.074734	-0.6117	0.271395
34	-0.051412	-0.4208	0.337614
35	-0.027307	-0.2235	0.411907
36	0.007455	0.061	0.475763
37	0.033507	0.2743	0.392361
38	-0.001011	-0.0083	0.496711
39	-0.007931	-0.0649	0.474215
40	-0.028808	-0.2358	0.407151
41	-0.125514	-1.0274	0.15397
42	-0.047923	-0.3923	0.348053
43	-0.051376	-0.4205	0.337722
44	0.059184	0.4844	0.314827
45	0.017867	0.1462	0.442084
46	-0.017996	-0.1473	0.441667
47	-0.076403	-0.6254	0.26692
48	-0.00153	-0.0125	0.495022
49	0.058259	0.4769	0.317504
50	0.009086	0.0744	0.470466
51	0.026532	0.2172	0.414367
52	-0.003857	-0.0316	0.487455
53	-0.049697	-0.4068	0.34273
54	-0.08261	-0.6762	0.250622
55	-0.025373	-0.2077	0.418051
56	0.022866	0.1872	0.426048
57	0.027751	0.2272	0.410498
58	-0.052403	-0.4289	0.334672
59	-0.003598	-0.0294	0.488297
60	0.100786	0.825	0.206158

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Apr/30/t1272628457ot2dxjznigntd4i/1t7or1272628356.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Apr/30/t1272628457ot2dxjznigntd4i/1t7or1272628356.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Apr/30/t1272628457ot2dxjznigntd4i/2t7or1272628356.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Apr/30/t1272628457ot2dxjznigntd4i/2t7or1272628356.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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