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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: Tue, 15 Dec 2009 07:28:42 -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/15/t1260887374r0lzys9sqxdxyot.htm/, Retrieved Tue, 15 Dec 2009 15:29:36 +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/15/t1260887374r0lzys9sqxdxyot.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 «

122.36 123.33 123.04 124.53 125.13 125.85 126.50 126.53 127.07 124.55 124.90 124.32 122.84 123.31 123.31 124.87 124.64 124.73 124.90 124.04 123.28 123.86 122.29 124.09 124.54 125.65 125.70 125.53 125.61 125.55 125.41 127.60 124.68 124.41 126.43 126.38 125.78 124.70 125.07 125.25 126.58 127.13 125.82 123.70 124.39 123.70 124.42 121.05 121.02 123.23 121.32 120.91 120.72 123.31 119.58 119.53 120.59 118.63 118.47 111.81 114.71 117.34 115.77 118.38 117.84 118.83 120.02 116.21 117.08 120.20 119.83 118.92 118.03 117.71 119.55 116.13 115.97 115.99 114.96 116.46 116.55 113.05 117.44 118.84 117.06 117.54 119.31 118.72 121.55 122.61 121.53 123.31 124.07 123.59 122.97 123.22 123.04 122.96 122.81 122.81 122.62 120.82 119.41 121.56 121.59 118.50 118.77 118.86 117.60 119.90 121.83 121.84 122.12 122.12 121.36 119.66 119.32 120.36 117.06 117.48 115.60 113.86 116.92 117.75 117.75 115.31 116.28 115.22 etc...

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	-0.244633	-4.8558	1e-06
2	-0.008103	-0.1608	0.436148
3	-0.080074	-1.5894	0.056384
4	0.070287	1.3952	0.081878
5	-0.041361	-0.821	0.206073
6	-0.031344	-0.6222	0.267098
7	-0.070907	-1.4075	0.080039
8	0.097957	1.9444	0.02628
9	-0.090878	-1.8039	0.036007
10	-0.034888	-0.6925	0.244513
11	0.121223	2.4062	0.008289
12	-0.044001	-0.8734	0.191492
13	0.043689	0.8672	0.19318
14	-0.103068	-2.0458	0.020717
15	-0.013061	-0.2592	0.397791
16	0.105481	2.0937	0.018461
17	-0.003066	-0.0609	0.475754
18	0.005863	0.1164	0.453708
19	0.005427	0.1077	0.457135
20	-0.041723	-0.8282	0.204033
21	0.075769	1.504	0.066694
22	-0.069852	-1.3865	0.083187
23	0.016321	0.324	0.373068
24	0.030346	0.6023	0.273645
25	0.020204	0.401	0.344304
26	-0.025613	-0.5084	0.305725
27	0.030009	0.5957	0.275872
28	-0.069223	-1.374	0.085104
29	0.06002	1.1914	0.117114
30	-0.025954	-0.5152	0.303362
31	0.035651	0.7077	0.23979
32	-0.00412	-0.0818	0.467429
33	-0.124989	-2.481	0.00676
34	0.061463	1.22	0.111597
35	-0.025854	-0.5132	0.304053
36	0.034833	0.6914	0.244854
37	-0.069631	-1.3821	0.083857
38	0.040325	0.8004	0.211974
39	0.007973	0.1583	0.43717
40	0.054161	1.0751	0.141501
41	-0.037336	-0.7411	0.229539
42	0.026874	0.5334	0.297018
43	0.033822	0.6714	0.251194
44	-0.052403	-1.0402	0.149449
45	-0.000945	-0.0188	0.49252
46	-0.004298	-0.0853	0.466028
47	0.090132	1.7891	0.037185
48	-0.02887	-0.573	0.283471

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.244633	-4.8558	1e-06
2	-0.072274	-1.4346	0.076098
3	-0.106795	-2.1198	0.017323
4	0.023498	0.4664	0.320584
5	-0.027558	-0.547	0.292344
6	-0.054339	-1.0786	0.140714
7	-0.096221	-1.9099	0.028434
8	0.046602	0.925	0.177758
9	-0.073548	-1.4599	0.072558
10	-0.085864	-1.7043	0.044553
11	0.105528	2.0947	0.018419
12	-0.021943	-0.4356	0.331698
13	0.037392	0.7422	0.229199
14	-0.074854	-1.4858	0.069065
15	-0.077143	-1.5312	0.063256
16	0.078088	1.55	0.060972
17	0.037304	0.7405	0.229732
18	0.04619	0.9168	0.179893
19	0.009776	0.1941	0.423118
20	-0.031753	-0.6303	0.264439
21	0.059931	1.1896	0.11746
22	-0.039872	-0.7914	0.214582
23	0.011021	0.2188	0.413473
24	0.020262	0.4022	0.34388
25	0.060864	1.2081	0.113863
26	0.018646	0.3701	0.355752
27	0.018736	0.3719	0.355081
28	-0.055401	-1.0997	0.136072
29	-0.005145	-0.1021	0.459355
30	0.028703	0.5697	0.284592
31	0.054226	1.0764	0.141213
32	0.009903	0.1966	0.422131
33	-0.131516	-2.6105	0.004693
34	-0.008113	-0.161	0.43607
35	-0.034541	-0.6856	0.246678
36	0.016848	0.3344	0.369119
37	-0.071024	-1.4098	0.079696
38	0.001131	0.0225	0.491049
39	0.031819	0.6316	0.264012
40	0.032688	0.6488	0.258411
41	0.012375	0.2456	0.403048
42	-0.041512	-0.824	0.205222
43	0.048911	0.9709	0.166109
44	-0.003515	-0.0698	0.472207
45	0.001331	0.0264	0.489471
46	0.002653	0.0527	0.479014
47	0.053658	1.0651	0.143747
48	0.028174	0.5592	0.288159

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260887374r0lzys9sqxdxyot/10zjp1260887321.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260887374r0lzys9sqxdxyot/10zjp1260887321.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260887374r0lzys9sqxdxyot/25ykg1260887321.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260887374r0lzys9sqxdxyot/25ykg1260887321.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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

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 (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='lags',ylab='ACF')

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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