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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: Sun, 19 Dec 2010 16:25:45 +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/19/t129277588075bux1koen2yqce.htm/, Retrieved Sun, 19 Dec 2010 17:24:41 +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/19/t129277588075bux1koen2yqce.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 «

5124 4742 5434 5684 6332 6334 5636 5940 6195 6022 4535 4320 4872 4662 4663 5491 6018 6393 5610 5777 6094 6478 5216 5201 4784 4205 4681 4896 5752 6452 5995 5601 6119 6569 5798 5492 5018 4773 5502 5908 5902 6125 5419 5559 5962 6023 5346 5379 4859 5156 5010 5508 6426 6043 5499 5191 5790 5949 5219 4729

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.429057	2.9726	0.002303
2	0.162306	1.1245	0.133198
3	0.019495	0.1351	0.446564
4	0.052272	0.3622	0.359413
5	0.019919	0.138	0.445408
6	-0.157589	-1.0918	0.140183
7	-0.325169	-2.2528	0.014439
8	-0.158602	-1.0988	0.138662
9	-0.070511	-0.4885	0.313704
10	-0.130098	-0.9013	0.185952
11	-0.084472	-0.5852	0.280565
12	-0.109552	-0.759	0.225782
13	0.156677	1.0855	0.141564
14	0.162028	1.1226	0.133604
15	0.212237	1.4704	0.073986
16	0.120257	0.8332	0.20444
17	0.193697	1.342	0.092959
18	0.033224	0.2302	0.409465
19	-0.115929	-0.8032	0.212915
20	-0.23611	-1.6358	0.05421
21	-0.22117	-1.5323	0.066006
22	-0.185893	-1.2879	0.101977
23	-0.187414	-1.2984	0.100169
24	-0.232902	-1.6136	0.056586
25	-0.236995	-1.6419	0.053569
26	0.029533	0.2046	0.41937
27	-0.036285	-0.2514	0.401294
28	0.028484	0.1973	0.422195
29	0.004928	0.0341	0.486453
30	0.089177	0.6178	0.269803
31	0.149595	1.0364	0.152598
32	0.075706	0.5245	0.301169
33	-0.0358	-0.248	0.402584
34	0.026011	0.1802	0.428874
35	-0.022904	-0.1587	0.437293
36	-0.042422	-0.2939	0.385046
37	-0.03847	-0.2665	0.395487
38	-0.074608	-0.5169	0.3038
39	0.03022	0.2094	0.417522
40	-0.000529	-0.0037	0.498547
41	0.038321	0.2655	0.395881
42	0.013013	0.0902	0.46427
43	0.041665	0.2887	0.387042
44	0.028438	0.197	0.422322
45	0.061115	0.4234	0.33694
46	0.007862	0.0545	0.478393
47	0.018186	0.126	0.450129
48	NA	NA	NA
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	0.429057	2.9726	0.002303
2	-0.026699	-0.185	0.427015
3	-0.049732	-0.3446	0.365967
4	0.080936	0.5607	0.288791
5	-0.029763	-0.2062	0.418752
6	-0.206803	-1.4328	0.079202
7	-0.225145	-1.5598	0.062683
8	0.114761	0.7951	0.215239
9	-0.019215	-0.1331	0.447326
10	-0.16176	-1.1207	0.133994
11	0.080166	0.5554	0.290598
12	-0.081853	-0.5671	0.286646
13	0.199756	1.384	0.086388
14	-0.043608	-0.3021	0.381931
15	0.179001	1.2402	0.110474
16	-0.036632	-0.2538	0.400368
17	0.104092	0.7212	0.237151
18	-0.178917	-1.2396	0.110579
19	-0.184199	-1.2762	0.104019
20	-0.048915	-0.3389	0.368084
21	-0.077599	-0.5376	0.296661
22	-0.051512	-0.3569	0.36137
23	-0.0278	-0.1926	0.424041
24	-0.093078	-0.6449	0.261043
25	-0.101546	-0.7035	0.242563
26	0.126674	0.8776	0.19226
27	-0.162366	-1.1249	0.133112
28	-0.030659	-0.2124	0.416344
29	-0.000683	-0.0047	0.498121
30	-0.087694	-0.6076	0.273171
31	-0.019471	-0.1349	0.446628
32	-0.141661	-0.9815	0.165644
33	0.06562	0.4546	0.325712
34	-4.5e-05	-3e-04	0.499877
35	-0.033822	-0.2343	0.407863
36	0.044718	0.3098	0.379021
37	0.01948	0.135	0.446604
38	0.075804	0.5252	0.300936
39	-0.06824	-0.4728	0.319257
40	0.012936	0.0896	0.464481
41	0.025919	0.1796	0.429121
42	-0.042551	-0.2948	0.384708
43	-0.109216	-0.7567	0.226472
44	-0.040663	-0.2817	0.389683
45	0.020977	0.1453	0.442528
46	-0.086306	-0.5979	0.276343
47	-0.021482	-0.1488	0.441154
48	NA	NA	NA
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/2010/Dec/19/t129277588075bux1koen2yqce/13x4a1292775941.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t129277588075bux1koen2yqce/13x4a1292775941.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t129277588075bux1koen2yqce/2d63u1292775941.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t129277588075bux1koen2yqce/2d63u1292775941.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t129277588075bux1koen2yqce/36xkx1292775941.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t129277588075bux1koen2yqce/36xkx1292775941.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 (par8 != '') par8 <- as.numeric(par8)

ox <- x

if (par8 == '') {

if (par2 == 0) {

x <- log(x)

} else {

x <- (x ^ par2 - 1) / par2

}

} else {

x <- log(x,base=par8)

}

if (par3 > 0) x <- diff(x,lag=1,difference=par3)

if (par4 > 0) x <- diff(x,lag=par5,difference=par4)

bitmap(file='picts.png')

op <- par(mfrow=c(2,1))

plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')

if (par8=='') {

mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')

mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')

} else {

mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')

mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')

}

plot(x,type='l', main=mytitle,xlab='time',ylab='value')

par(op)

dev.off()

bitmap(file='pic1.png')

racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)

dev.off()

bitmap(file='pic2.png')

rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)

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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