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paper ACF ruw

*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: Mon, 27 Dec 2010 12:07:41 +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/27/t1293451650ztqc5qyytdl3gvd.htm/, Retrieved Mon, 27 Dec 2010 13:07:33 +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/27/t1293451650ztqc5qyytdl3gvd.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 «

5,2 7,9 8,7 8,9 15,3 15,4 18,1 19,7 13 12,6 6,2 3,5 3,4 0 9,5 8,9 10,4 13,2 18,9 19 16,3 10,6 5,8 3,6 2,6 5 7,3 9,2 15,7 16,8 18,4 18,1 14,6 7,8 7,6 3,8 5,6 2,2 6,8 11,8 14,9 16,7 16,7 15,9 13,6 9,2 2,8 2,5 4,8 2,8 7,8 9 12,9 16,4 21,8 17,8 13,5 10 10,4 5,5 4 6,8 5,7 9,1 13,6 15 20,9 20,4 14 13,7 7,1 0,8 2,1 1,3 3,9 10,7 11,1 16,4 17,1 17,3 12,9 10,9 5,3 0,7 -0,2 6,5 8,6 8,5 13,3 16,2 17,5 21,2 14,8 10,3 7,3 5,1 4,4 6,2 7,7 9,3 15,6 16,3 16,6 17,4 15,3 9,7 3,7 4,6 5,4 3,1 7,9 10,1 15 15,6 19,7 18,1 17,7 10,7 6,2 4,2 4 5,9 7,1 10,5 15,1 16,8 15,3 18,4 16,1 11,3 7,9 5,6 3,4 4,8 6,5 8,5 15,1 15,7 18,7 19,2 12,9 14,4 6,2 3,3 4,6 7,2 7,8 9,9 13,6 17,1 17,8 18,6 14,7 10,5 8,6 4,4 2,3 2,8 8,8 10,7 13,9 19,3 19,5 20,4 15,3 7,9 8,3 4,5 3,2 5 6,6 11,1 12,8 16,3 17,4 18,9 15,8 11,7 6,4 2,9 4,7 2,4 7,2 10,7 13,4 18,5 18,3 16,8 16,6 14, 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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.794173	12.3033	0
2	0.454465	7.0405	0
3	0.007596	0.1177	0.453214
4	-0.45077	-6.9833	0
5	-0.767012	-11.8825	0
6	-0.884261	-13.6989	0
7	-0.769578	-11.9223	0
8	-0.441433	-6.8387	0
9	0.005036	0.078	0.46894
10	0.434302	6.7282	0
11	0.753757	11.6772	0
12	0.863554	13.3781	0
13	0.743054	11.5113	0
14	0.415755	6.4409	0
15	-0.017171	-0.266	0.395228
16	-0.425378	-6.5899	0
17	-0.736902	-11.416	0
18	-0.837057	-12.9676	0
19	-0.714266	-11.0654	0
20	-0.408209	-6.3239	0
21	0.002088	0.0323	0.487113
22	0.428769	6.6425	0
23	0.705794	10.9341	0
24	0.81782	12.6696	0
25	0.70821	10.9715	0
26	0.385471	5.9717	0
27	-0.006617	-0.1025	0.459222
28	-0.413996	-6.4136	0
29	-0.693841	-10.7489	0
30	-0.782663	-12.125	0
31	-0.665554	-10.3107	0
32	-0.388391	-6.0169	0
33	0.017941	0.2779	0.390649
34	0.411942	6.3818	0
35	0.68953	10.6822	0
36	0.787649	12.2022	0
37	0.674528	10.4497	0
38	0.382339	5.9232	0
39	-0.012091	-0.1873	0.425785
40	-0.393172	-6.091	0
41	-0.661552	-10.2487	0
42	-0.757721	-11.7386	0
43	-0.650333	-10.0749	0
44	-0.374083	-5.7953	0
45	-0.009145	-0.1417	0.44373
46	0.375249	5.8133	0
47	0.646201	10.0109	0
48	0.725172	11.2343	0
49	0.63247	9.7982	0
50	0.365357	5.6601	0
51	-0.004481	-0.0694	0.472359
52	-0.357381	-5.5365	0
53	-0.610848	-9.4632	0
54	-0.703367	-10.8965	0
55	-0.599246	-9.2835	0
56	-0.35111	-5.4394	0
57	-0.005382	-0.0834	0.466812
58	0.339589	5.2609	0
59	0.598371	9.2699	0
60	0.698088	10.8147	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.794173	12.3033	0
2	-0.477255	-7.3936	0
3	-0.513919	-7.9616	0
4	-0.508875	-7.8835	0
5	-0.28912	-4.479	6e-06
6	-0.229543	-3.5561	0.000227
7	-0.145841	-2.2594	0.012379
8	0.01521	0.2356	0.40696
9	0.13733	2.1275	0.017199
10	0.063517	0.984	0.163054
11	0.1066	1.6514	0.049979
12	0.04851	0.7515	0.226539
13	0.035571	0.5511	0.291051
14	-0.093999	-1.4562	0.073318
15	-0.066581	-1.0315	0.151681
16	0.078449	1.2153	0.112716
17	-0.068744	-1.065	0.143978
18	-0.011447	-0.1773	0.429695
19	-0.009441	-0.1463	0.441923
20	-0.026778	-0.4148	0.339316
21	-0.084345	-1.3067	0.096287
22	0.118568	1.8368	0.033734
23	-0.087045	-1.3485	0.089385
24	0.087221	1.3512	0.088949
25	0.046359	0.7182	0.236667
26	-0.094364	-1.4619	0.072541
27	0.053973	0.8361	0.201954
28	-0.06062	-0.9391	0.174308
29	0.060772	0.9415	0.173703
30	0.052495	0.8132	0.208443
31	0.041663	0.6454	0.25963
32	-0.13709	-2.1238	0.017355
33	0.103795	1.608	0.054577
34	0.085407	1.3231	0.093529
35	0.052909	0.8197	0.206609
36	0.045074	0.6983	0.242838
37	0.105416	1.6331	0.05188
38	-0.009228	-0.143	0.443219
39	0.026094	0.4042	0.343197
40	0.020542	0.3182	0.37529
41	0.10015	1.5515	0.061047
42	0.028934	0.4482	0.327191
43	-0.018648	-0.2889	0.386457
44	-0.028119	-0.4356	0.331751
45	-0.064399	-0.9977	0.159722
46	0.047916	0.7423	0.229313
47	-0.037811	-0.5858	0.279292
48	-0.037312	-0.578	0.281889
49	-0.041258	-0.6392	0.261665
50	0.07684	1.1904	0.117534
51	-0.048137	-0.7457	0.228281
52	0.021603	0.3347	0.369082
53	0.050295	0.7792	0.218324
54	0.052183	0.8084	0.209826
55	0.01748	0.2708	0.393391
56	-0.052429	-0.8122	0.208734
57	0.042259	0.6547	0.256654
58	-0.041304	-0.6399	0.261431
59	0.106818	1.6548	0.049635
60	0.070754	1.0961	0.137064

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293451650ztqc5qyytdl3gvd/17d3h1293451658.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293451650ztqc5qyytdl3gvd/17d3h1293451658.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293451650ztqc5qyytdl3gvd/2i42k1293451658.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293451650ztqc5qyytdl3gvd/2i42k1293451658.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293451650ztqc5qyytdl3gvd/3i42k1293451658.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293451650ztqc5qyytdl3gvd/3i42k1293451658.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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