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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: Fri, 27 Nov 2009 19:11:06 -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/28/t12593743579u48uqfmu9wyqmp.htm/, Retrieved Sat, 28 Nov 2009 03:12:39 +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/28/t12593743579u48uqfmu9wyqmp.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 «

94.6 95.9 104.7 102.8 98.1 113.9 80.9 95.7 113.2 105.9 108.8 102.3 99 100.7 115.5 100.7 109.9 114.6 85.4 100.5 114.8 116.5 112.9 102 106 105.3 118.8 106.1 109.3 117.2 92.5 104.2 112.5 122.4 113.3 100 110.7 112.8 109.8 117.3 109.1 115.9 96 99.8 116.8 115.7 99.4 94.3 91 93.2 103.1 94.1 91.8 102.7 82.6 89.1

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	-0.630537	-4.1347	8.1e-05
2	0.018298	0.12	0.452527
3	0.403703	2.6473	0.005648
4	-0.408306	-2.6774	0.005231
5	0.171082	1.1219	0.134074
6	0.091826	0.6021	0.27512
7	-0.247588	-1.6235	0.055892
8	0.23446	1.5375	0.065754
9	-0.165165	-1.0831	0.142409
10	-0.010325	-0.0677	0.473167
11	0.167436	1.0979	0.139168
12	-0.219559	-1.4397	0.07859
13	0.114445	0.7505	0.228531
14	0.00635	0.0416	0.483489
15	-0.010024	-0.0657	0.473947
16	-0.064454	-0.4227	0.337328
17	0.096673	0.6339	0.264744
18	-0.026781	-0.1756	0.43071
19	-0.082418	-0.5405	0.295836
20	0.1171	0.7679	0.223379
21	0.017057	0.1118	0.455732
22	-0.252373	-1.6549	0.052611
23	0.370211	2.4276	0.009729
24	-0.271849	-1.7826	0.040854
25	0.045055	0.2954	0.384537
26	0.161112	1.0565	0.148324
27	-0.238526	-1.5641	0.06256
28	0.143889	0.9435	0.175337
29	0.006255	0.041	0.483737
30	-0.10633	-0.6972	0.2447
31	0.138239	0.9065	0.184863
32	-0.103725	-0.6802	0.250021
33	-0.002928	-0.0192	0.492385
34	0.114096	0.7482	0.229213
35	-0.157781	-1.0346	0.153311
36	0.113259	0.7427	0.230855
37	-0.033046	-0.2167	0.414734
38	-0.020163	-0.1322	0.447714
39	0.025509	0.1673	0.433969
40	-0.011629	-0.0763	0.469786
41	0.00667	0.0437	0.482659
42	0.000784	0.0051	0.49796
43	NA	NA	NA
44	NA	NA	NA
45	NA	NA	NA
46	NA	NA	NA
47	NA	NA	NA
48	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.630537	-4.1347	8.1e-05
2	-0.62959	-4.1285	8.2e-05
3	0.070194	0.4603	0.323813
4	0.119182	0.7815	0.219387
5	0.101254	0.664	0.255128
6	0.05501	0.3607	0.360035
7	-0.120049	-0.7872	0.217738
8	-0.032448	-0.2128	0.416253
9	-0.199344	-1.3072	0.099048
10	-0.23874	-1.5655	0.062395
11	-0.037705	-0.2472	0.402947
12	0.041295	0.2708	0.393924
13	0.037859	0.2483	0.402559
14	-0.112773	-0.7395	0.23181
15	0.155029	1.0166	0.157516
16	-0.056084	-0.3678	0.357426
17	-0.091188	-0.598	0.276502
18	-0.068732	-0.4507	0.327233
19	-0.101455	-0.6653	0.25471
20	-0.039237	-0.2573	0.399089
21	0.205849	1.3498	0.092065
22	-0.19906	-1.3053	0.099362
23	0.024001	0.1574	0.43784
24	-0.060926	-0.3995	0.345744
25	0.04587	0.3008	0.382511
26	-0.037459	-0.2456	0.403566
27	0.001483	0.0097	0.496142
28	-0.09337	-0.6123	0.271793
29	-0.124136	-0.814	0.210062
30	0.013966	0.0916	0.463729
31	0.034671	0.2274	0.410613
32	-0.001283	-0.0084	0.496664
33	0.000227	0.0015	0.49941
34	-0.082364	-0.5401	0.295959
35	-0.066633	-0.4369	0.332169
36	-0.05017	-0.329	0.371881
37	-0.032591	-0.2137	0.41589
38	-0.047347	-0.3105	0.378851
39	0.042547	0.279	0.390791
40	-0.043268	-0.2837	0.38899
41	-0.04333	-0.2841	0.388835
42	0.024957	0.1637	0.435386
43	NA	NA	NA
44	NA	NA	NA
45	NA	NA	NA
46	NA	NA	NA
47	NA	NA	NA
48	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/28/t12593743579u48uqfmu9wyqmp/19v2m1259374264.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/28/t12593743579u48uqfmu9wyqmp/19v2m1259374264.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/28/t12593743579u48uqfmu9wyqmp/2qv7o1259374264.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/28/t12593743579u48uqfmu9wyqmp/2qv7o1259374264.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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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