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paper

*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: Wed, 09 Dec 2009 12:58:12 -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/Dec/09/t1260388748pnmd8lh4x6tq1t1.htm/, Retrieved Wed, 09 Dec 2009 20:59:10 +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/Dec/09/t1260388748pnmd8lh4x6tq1t1.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 «

595 591 612 595 597 589 584 573 567 569 621 629 628 593 588 566 557 590 580 574 573 573 620 626 620 561 527 510 514 549 532 526 511 499 555 565 542 517 506 502 516 508 493 490 469 478 528 534 518 528 533 536 537 524 536 587 597 581 564 558

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	0.189137	1.4528	0.07579
2	-0.210198	-1.6146	0.055871
3	-0.349468	-2.6843	0.00471
4	-0.266018	-2.0433	0.022747
5	0.151133	1.1609	0.125184
6	0.20919	1.6068	0.056717
7	0.018707	0.1437	0.443118
8	-0.178918	-1.3743	0.087274
9	-0.175865	-1.3508	0.090952
10	-0.037839	-0.2906	0.386171
11	0.128531	0.9873	0.163773
12	0.467651	3.5921	0.000335
13	-0.026787	-0.2058	0.418845
14	-0.169126	-1.2991	0.099484
15	-0.165027	-1.2676	0.104961
16	-0.134219	-1.031	0.153384
17	0.154766	1.1888	0.119645
18	0.078759	0.605	0.273762
19	-0.089836	-0.69	0.246437
20	-0.030092	-0.2311	0.409002
21	-0.047735	-0.3667	0.357593
22	-0.038303	-0.2942	0.384815
23	0.017835	0.137	0.44575
24	0.117314	0.9011	0.185597
25	-0.009809	-0.0753	0.470097
26	-0.006744	-0.0518	0.479431
27	-0.015825	-0.1216	0.451834
28	-0.047206	-0.3626	0.3591
29	-0.014327	-0.11	0.456373
30	-0.090454	-0.6948	0.244958
31	-0.105227	-0.8083	0.211092
32	0.091191	0.7005	0.243199
33	0.084111	0.6461	0.26037
34	-0.01699	-0.1305	0.448307
35	0.010457	0.0803	0.468127
36	0.029775	0.2287	0.409944
37	-0.006893	-0.0529	0.478977
38	0.042583	0.3271	0.372379
39	0.000757	0.0058	0.497691
40	-0.049345	-0.379	0.353014
41	-0.034935	-0.2683	0.394686
42	-0.076149	-0.5849	0.28042
43	-0.035933	-0.276	0.391754
44	0.091182	0.7004	0.243221
45	0.131396	1.0093	0.158482
46	0.00949	0.0729	0.471067
47	-0.038849	-0.2984	0.383221
48	-0.052664	-0.4045	0.343646
49	-0.024003	-0.1844	0.427176
50	0.002319	0.0178	0.492925
51	-0.005595	-0.043	0.482934
52	-0.009355	-0.0719	0.47148
53	0.035857	0.2754	0.391976
54	0.01086	0.0834	0.466902
55	-0.004085	-0.0314	0.487537
56	-0.007654	-0.0588	0.476657
57	-0.002178	-0.0167	0.493354
58	0.000647	0.005	0.498025
59	NA	NA	NA
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.189137	1.4528	0.07579
2	-0.255096	-1.9594	0.027396
3	-0.278787	-2.1414	0.018191
4	-0.234411	-1.8005	0.038443
5	0.115066	0.8838	0.190184
6	-0.016431	-0.1262	0.449997
7	-0.12097	-0.9292	0.178289
8	-0.159264	-1.2233	0.113034
9	-0.059317	-0.4556	0.325166
10	-0.085273	-0.655	0.257509
11	-0.039395	-0.3026	0.38163
12	0.412801	3.1708	0.001206
13	-0.210343	-1.6157	0.05575
14	0.069266	0.532	0.298348
15	0.061107	0.4694	0.320268
16	-0.014594	-0.1121	0.455562
17	-0.02468	-0.1896	0.425147
18	-0.065955	-0.5066	0.307159
19	-0.056493	-0.4339	0.332962
20	0.101235	0.7776	0.219955
21	-0.053884	-0.4139	0.340228
22	-0.139134	-1.0687	0.144778
23	-0.026165	-0.201	0.420705
24	-0.100367	-0.7709	0.221911
25	0.032223	0.2475	0.402688
26	-0.044826	-0.3443	0.365916
27	0.010217	0.0785	0.468856
28	0.046551	0.3576	0.360972
29	-0.167146	-1.2839	0.102103
30	-0.106472	-0.8178	0.208374
31	-0.042097	-0.3234	0.373785
32	-0.02904	-0.2231	0.412129
33	-0.031675	-0.2433	0.404308
34	-0.062042	-0.4766	0.317721
35	0.074445	0.5718	0.284807
36	0.081348	0.6248	0.26724
37	-0.126637	-0.9727	0.167332
38	0.009992	0.0768	0.46954
39	0.071791	0.5514	0.291707
40	-0.075125	-0.577	0.283051
41	0.016833	0.1293	0.448783
42	-0.015304	-0.1176	0.453411
43	0.021072	0.1619	0.435985
44	-0.038878	-0.2986	0.383137
45	0.039128	0.3005	0.382409
46	0.021645	0.1663	0.434262
47	-0.036468	-0.2801	0.390184
48	-0.063107	-0.4847	0.31483
49	0.03934	0.3022	0.38179
50	-0.136342	-1.0473	0.149625
51	-0.03102	-0.2383	0.406249
52	-0.015029	-0.1154	0.454243
53	-0.040465	-0.3108	0.378518
54	0.077356	0.5942	0.27733
55	-0.013971	-0.1073	0.457453
56	-0.082249	-0.6318	0.264991
57	-0.051794	-0.3978	0.346093
58	0.022013	0.1691	0.433154
59	NA	NA	NA
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/09/t1260388748pnmd8lh4x6tq1t1/1wi2y1260388691.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/09/t1260388748pnmd8lh4x6tq1t1/1wi2y1260388691.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/09/t1260388748pnmd8lh4x6tq1t1/24va31260388691.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/09/t1260388748pnmd8lh4x6tq1t1/24va31260388691.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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