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ACF ( d=0 , D=0 )

*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, 22 Dec 2010 17:19:20 +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/22/t12930382437e65dhwxyg0x8eb.htm/, Retrieved Wed, 22 Dec 2010 18:17:26 +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/22/t12930382437e65dhwxyg0x8eb.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 «

94.6 95.9 104.7 102.8 98.1 113.9 80.9 95.7 113.2 105.9 108.8 102.3 99 100.7 115.5 100.7 109.9 114.6 85.4 100.5 114.8 116.5 112.9 102 106 105.3 118.8 106.1 109.3 117.2 92.5 104.2 112.5 122.4 113.3 100 110.7 112.8 109.8 117.3 109.1 115.9 96 99.8 116.8 115.7 99.4 94.3 91 93.2 103.1 94.1 91.8 102.7 82.6 89.1 104.5 105.1 95.1 88.7

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	0.25584	1.9817	0.026048
2	0.001102	0.0085	0.496608
3	0.179307	1.3889	0.084997
4	0.162542	1.259	0.106445
5	0.349749	2.7091	0.00439
6	0.334355	2.5899	0.006016
7	0.225318	1.7453	0.043025
8	0.017693	0.137	0.445726
9	-0.049977	-0.3871	0.35002
10	-0.169631	-1.314	0.096931
11	0.065771	0.5095	0.306151
12	0.44587	3.4537	0.00051
13	-0.053699	-0.4159	0.339465
14	-0.302295	-2.3416	0.011271
15	-0.208486	-1.6149	0.055787
16	-0.081698	-0.6328	0.264625
17	0.051641	0.4	0.345284
18	-0.031003	-0.2402	0.405516
19	-0.028202	-0.2185	0.413908
20	-0.203235	-1.5743	0.060344
21	-0.220663	-1.7092	0.046287
22	-0.235976	-1.8279	0.036271
23	-0.073682	-0.5707	0.285154
24	0.202438	1.5681	0.061061
25	-0.133147	-1.0314	0.153258
26	-0.337798	-2.6166	0.005611
27	-0.201465	-1.5605	0.061946
28	-0.084203	-0.6522	0.25837
29	-0.022691	-0.1758	0.430535
30	-0.066927	-0.5184	0.303038
31	-0.040949	-0.3172	0.3761
32	-0.196487	-1.522	0.066634
33	-0.205594	-1.5925	0.058261
34	-0.108753	-0.8424	0.201455
35	-0.085879	-0.6652	0.25423
36	0.132534	1.0266	0.154364
37	-0.075571	-0.5854	0.280247
38	-0.239776	-1.8573	0.034089
39	-0.087199	-0.6754	0.250996
40	0.008333	0.0645	0.474375
41	0.020416	0.1581	0.437438
42	0.048875	0.3786	0.353166
43	0.011696	0.0906	0.464058
44	-0.069647	-0.5395	0.295775
45	0.005937	0.046	0.481738
46	0.032551	0.2521	0.400897
47	0.050379	0.3902	0.348872
48	0.155338	1.2032	0.116804

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.25584	1.9817	0.026048
2	-0.068859	-0.5334	0.297872
3	0.211396	1.6375	0.053384
4	0.064099	0.4965	0.310675
5	0.350076	2.7117	0.00436
6	0.18661	1.4455	0.076764
7	0.19526	1.5125	0.067831
8	-0.149574	-1.1586	0.125606
9	-0.160344	-1.242	0.109531
10	-0.532987	-4.1285	5.7e-05
11	-0.167004	-1.2936	0.10038
12	0.361094	2.797	0.003461
13	0.034223	0.2651	0.395924
14	-0.035057	-0.2716	0.393449
15	-0.129128	-1.0002	0.160611
16	0.064624	0.5006	0.309251
17	-0.035822	-0.2775	0.391186
18	-0.147856	-1.1453	0.128319
19	0.039888	0.309	0.379205
20	-0.02097	-0.1624	0.435756
21	0.116612	0.9033	0.184998
22	-0.035502	-0.275	0.392133
23	-0.103575	-0.8023	0.212775
24	-0.101032	-0.7826	0.218472
25	-0.105285	-0.8155	0.208996
26	-0.082097	-0.6359	0.263624
27	0.074123	0.5742	0.284006
28	-0.01725	-0.1336	0.447075
29	-0.014546	-0.1127	0.455333
30	-0.03643	-0.2822	0.389388
31	0.046019	0.3565	0.361373
32	-0.105662	-0.8185	0.208169
33	-0.132439	-1.0259	0.154536
34	0.091578	0.7094	0.240424
35	-0.086748	-0.6719	0.252099
36	0.022368	0.1733	0.431513
37	-0.03983	-0.3085	0.379376
38	0.032887	0.2547	0.399897
39	0.023428	0.1815	0.428304
40	0.00473	0.0366	0.485448
41	-0.029145	-0.2258	0.41108
42	0.103818	0.8042	0.212236
43	-0.156142	-1.2095	0.115612
44	0.008418	0.0652	0.474115
45	0.046277	0.3585	0.360628
46	0.010817	0.0838	0.466752
47	-0.005871	-0.0455	0.481938
48	-0.153951	-1.1925	0.11888

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/22/t12930382437e65dhwxyg0x8eb/1yx4f1293038357.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t12930382437e65dhwxyg0x8eb/1yx4f1293038357.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t12930382437e65dhwxyg0x8eb/286301293038357.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t12930382437e65dhwxyg0x8eb/286301293038357.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t12930382437e65dhwxyg0x8eb/386301293038357.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t12930382437e65dhwxyg0x8eb/386301293038357.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 48 ; 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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