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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: Sat, 04 Dec 2010 16:06:05 +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/Dec/04/t129147873277pfgddxermi2m5.htm/, Retrieved Sat, 04 Dec 2010 17:05:34 +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/2010/Dec/04/t129147873277pfgddxermi2m5.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

0.4754 0.4531 0.469 0.4716 0.4824 0.527 0.5172 0.515 0.5245 0.53 0.4836 0.4663 0.4592 0.4553 0.4217 0.4366 0.4532 0.4743 0.4776 0.4949 0.5069 0.498 0.5213 0.5394 0.6075 0.5919 0.5758 0.5916 0.6474 0.6704 0.7553 0.7891 0.784 0.7007 0.668 0.6102 0.5238 0.4237 0.3983 0.3879 0.3733 0.394 0.3945 0.4324 0.4233 0.455 0.4344 0.4388 0.4561 0.4512 0.4756 0.4704 0.5107 0.5472 0.5537 0.5539 0.5313 0.5371 0.5459 0.5461

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	5 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.455103	3.4957	0.000452
2	0.340132	2.6126	0.00569
3	0.128446	0.9866	0.163931
4	0.106491	0.818	0.208331
5	-0.169297	-1.3004	0.099261
6	-0.239675	-1.841	0.035327
7	-0.148276	-1.1389	0.129668
8	-0.193123	-1.4834	0.071645
9	-0.214242	-1.6456	0.05258
10	-0.137769	-1.0582	0.147134
11	0.000975	0.0075	0.497025
12	-0.087723	-0.6738	0.25153
13	-0.109773	-0.8432	0.201267
14	-0.151934	-1.167	0.123947
15	-0.077936	-0.5986	0.275853
16	-0.244779	-1.8802	0.032511
17	-0.197986	-1.5208	0.066831
18	-0.179201	-1.3765	0.086939
19	0.002969	0.0228	0.490942
20	-0.095635	-0.7346	0.232751
21	0.015638	0.1201	0.452399
22	0.133082	1.0222	0.155425
23	0.233673	1.7949	0.038898
24	0.130126	0.9995	0.160813
25	0.163138	1.2531	0.107559
26	0.168401	1.2935	0.100438
27	0.04403	0.3382	0.368205
28	0.01405	0.1079	0.457213
29	-0.02685	-0.2062	0.418657
30	0.013143	0.101	0.459966
31	-0.086513	-0.6645	0.254473
32	-0.078527	-0.6032	0.27435
33	-0.038725	-0.2975	0.383582
34	-0.001106	-0.0085	0.496626
35	0.006049	0.0465	0.48155
36	0.058048	0.4459	0.328659
37	0.013019	0.1	0.460341
38	-0.000252	-0.0019	0.49923
39	-0.022003	-0.169	0.433183
40	-0.012772	-0.0981	0.461091
41	-0.014999	-0.1152	0.454334
42	-0.04048	-0.3109	0.378474
43	-0.003543	-0.0272	0.48919
44	-0.019291	-0.1482	0.441353
45	0.034742	0.2669	0.395255
46	0.008998	0.0691	0.472566
47	0.005172	0.0397	0.484223
48	0.028162	0.2163	0.414745

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.455103	3.4957	0.000452
2	0.16776	1.2886	0.101285
3	-0.099575	-0.7648	0.223706
4	0.040796	0.3134	0.377556
5	-0.284076	-2.182	0.016551
6	-0.147229	-1.1309	0.13134
7	0.144951	1.1134	0.135028
8	-0.125498	-0.964	0.169498
9	-0.090025	-0.6915	0.245982
10	0.053269	0.4092	0.34195
11	0.026931	0.2069	0.418416
12	-0.148244	-1.1387	0.129718
13	-0.084187	-0.6467	0.260181
14	-0.168568	-1.2948	0.100218
15	-0.009253	-0.0711	0.47179
16	-0.184772	-1.4193	0.080543
17	-0.088329	-0.6785	0.250064
18	-0.081686	-0.6274	0.266395
19	0.096695	0.7427	0.230296
20	-0.168385	-1.2934	0.100458
21	-0.054262	-0.4168	0.33917
22	0.054432	0.4181	0.338697
23	0.054405	0.4179	0.33877
24	-0.112731	-0.8659	0.195026
25	0.019786	0.152	0.43986
26	-0.07341	-0.5639	0.287488
27	-0.106334	-0.8168	0.208675
28	0.066544	0.5111	0.305583
29	-0.094362	-0.7248	0.235716
30	-0.099572	-0.7648	0.223711
31	0.028179	0.2164	0.414693
32	-0.148696	-1.1422	0.129001
33	-0.039807	-0.3058	0.380429
34	-0.028092	-0.2158	0.414952
35	0.020112	0.1545	0.438877
36	0.016003	0.1229	0.451293
37	-0.111465	-0.8562	0.197682
38	-0.104	-0.7988	0.213794
39	0.086385	0.6635	0.254785
40	-0.037222	-0.2859	0.387976
41	-0.032921	-0.2529	0.400623
42	-0.055885	-0.4293	0.334648
43	0.036602	0.2811	0.389791
44	-0.059682	-0.4584	0.324164
45	-0.005406	-0.0415	0.483511
46	-0.051847	-0.3982	0.345943
47	-0.122811	-0.9433	0.17468
48	0.040617	0.312	0.378076

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/04/t129147873277pfgddxermi2m5/1g4tj1291478759.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/04/t129147873277pfgddxermi2m5/1g4tj1291478759.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/04/t129147873277pfgddxermi2m5/2g4tj1291478759.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/04/t129147873277pfgddxermi2m5/2g4tj1291478759.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; 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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