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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: Wed, 30 Dec 2009 09:59:53 -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/30/t1262192540hmyu11t57l58z09.htm/, Retrieved Wed, 30 Dec 2009 18:02:23 +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/30/t1262192540hmyu11t57l58z09.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 «

4223,4 4627,3 5175,3 4550,7 4639,3 5498,7 5031,0 4033,3 4643,5 4873,2 4608,7 4733,5 3955,6 4590,9 5127,5 5257,3 5416,9 5813,3 5261,9 4669,2 5855,8 5274,6 5516,7 5819,5 5156,0 5377,3 6386,8 5144,0 6138,5 5567,8 5822,6 5145,5 5706,6 6078,5 6074,5 5577,6 5727,5 6067,0 7069,9 5490,0 5948,3 6177,5 6890,1 5756,2 6528,8 6792,0 6657,4 5753,7 5750,9 5968,4 5871,7 7004,9 6363,4 6694,7 7101,6 5364,0 6958,6 6503,3 5316,0 5312,7 4478,0

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	0.251757	1.7623	0.042128
2	0.281763	1.9723	0.027114
3	0.158031	1.1062	0.137017
4	0.019317	0.1352	0.446495
5	0.152338	1.0664	0.145742
6	-0.04233	-0.2963	0.384123
7	-0.09467	-0.6627	0.255317
8	0.124303	0.8701	0.194239
9	-0.002524	-0.0177	0.492989
10	0.193139	1.352	0.091296
11	0.003429	0.024	0.490473
12	-0.111055	-0.7774	0.220335
13	-0.084051	-0.5884	0.279498
14	-0.084149	-0.589	0.27927
15	-0.014036	-0.0983	0.461067
16	-0.174243	-1.2197	0.114208
17	-0.044852	-0.314	0.377439
18	0.111712	0.782	0.218993
19	0.008528	0.0597	0.476319
20	0.074303	0.5201	0.302662
21	0.041783	0.2925	0.385576
22	-0.035903	-0.2513	0.401309
23	0.108537	0.7598	0.225519
24	-0.181039	-1.2673	0.105523
25	-0.002424	-0.017	0.493266
26	-0.01223	-0.0856	0.466063
27	-0.046035	-0.3222	0.374319
28	0.049028	0.3432	0.366458
29	-0.016205	-0.1134	0.455074
30	-0.121131	-0.8479	0.200304
31	0.020662	0.1446	0.442798
32	-0.146225	-1.0236	0.155531
33	-0.112536	-0.7878	0.217317
34	-0.246175	-1.7232	0.045577
35	-0.178933	-1.2525	0.108161
36	-0.090045	-0.6303	0.265708
37	-0.091242	-0.6387	0.262997
38	-0.114756	-0.8033	0.212842
39	-0.127847	-0.8949	0.1876
40	-0.093406	-0.6538	0.258134
41	-0.02162	-0.1513	0.440165
42	-0.026287	-0.184	0.427382
43	-0.016172	-0.1132	0.455166
44	-0.010367	-0.0726	0.471221
45	0.036244	0.2537	0.40039
46	0.100642	0.7045	0.242231
47	0.055947	0.3916	0.348515
48	0.051024	0.3572	0.361249
49	NA	NA	NA
50	NA	NA	NA
51	NA	NA	NA
52	NA	NA	NA
53	NA	NA	NA
54	NA	NA	NA
55	NA	NA	NA
56	NA	NA	NA
57	NA	NA	NA
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.251757	1.7623	0.042128
2	0.23316	1.6321	0.054533
3	0.050734	0.3551	0.362006
4	-0.096252	-0.6738	0.251814
5	0.131472	0.9203	0.180961
6	-0.095265	-0.6669	0.253997
7	-0.144951	-1.0147	0.157627
8	0.212332	1.4863	0.0718
9	0.023195	0.1624	0.435844
10	0.122822	0.8598	0.197055
11	-0.0978	-0.6846	0.24841
12	-0.167417	-1.1719	0.123448
13	-0.125313	-0.8772	0.192331
14	0.060403	0.4228	0.337138
15	0.08757	0.613	0.271358
16	-0.189974	-1.3298	0.094868
17	0.11969	0.8378	0.203098
18	0.177518	1.2426	0.109959
19	-0.119601	-0.8372	0.20327
20	-0.062001	-0.434	0.333093
21	0.172167	1.2052	0.116963
22	-0.058496	-0.4095	0.34199
23	0.011571	0.081	0.467886
24	-0.169373	-1.1856	0.120747
25	0.032057	0.2244	0.411691
26	0.089807	0.6286	0.266249
27	0.003581	0.0251	0.490051
28	-0.137708	-0.964	0.169901
29	0.007771	0.0544	0.478419
30	-0.047791	-0.3345	0.3697
31	-0.008118	-0.0568	0.477458
32	-0.117043	-0.8193	0.20829
33	-0.095539	-0.6688	0.253389
34	-0.043308	-0.3032	0.381528
35	0.002824	0.0198	0.492154
36	-0.07754	-0.5428	0.29487
37	-0.047874	-0.3351	0.369483
38	0.002249	0.0157	0.493752
39	-0.055519	-0.3886	0.349616
40	-0.10087	-0.7061	0.241738
41	0.014945	0.1046	0.458555
42	0.181045	1.2673	0.105517
43	-0.017291	-0.121	0.452079
44	-0.027036	-0.1892	0.42534
45	0.068617	0.4803	0.316569
46	-0.035752	-0.2503	0.401716
47	0.025538	0.1788	0.429428
48	0.002372	0.0166	0.493409
49	NA	NA	NA
50	NA	NA	NA
51	NA	NA	NA
52	NA	NA	NA
53	NA	NA	NA
54	NA	NA	NA
55	NA	NA	NA
56	NA	NA	NA
57	NA	NA	NA
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/30/t1262192540hmyu11t57l58z09/14i4k1262192390.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/30/t1262192540hmyu11t57l58z09/14i4k1262192390.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/30/t1262192540hmyu11t57l58z09/21c3b1262192390.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/30/t1262192540hmyu11t57l58z09/21c3b1262192390.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; 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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