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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: Mon, 20 Dec 2010 08:06:42 +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/20/t12928322736ltcivfau6y31nr.htm/, Retrieved Mon, 20 Dec 2010 09:04:33 +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/20/t12928322736ltcivfau6y31nr.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 «

116.1 107.5 116.7 112.5 113 126.4 114.1 112.5 112.4 113.1 116.3 111.7 118.8 116.5 125.1 113.1 119.6 114.4 114 117.8 117 120.9 115 117.3 119.4 114.9 125.8 117.6 117.6 114.9 121.9 117 106.4 110.5 113.6 114.2 125.4 124.6 120.2 120.8 111.4 124.1 120.2 125.5 116 117 105.7 102 106.4 96.9 107.6 98.8 101.1 105.7 104.6 103.2 101.6 106.7 99.5 101

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	0.601333	4.6579	9e-06
2	0.601075	4.6559	9e-06
3	0.459607	3.5601	0.000366
4	0.35378	2.7404	0.004036
5	0.37052	2.87	0.00283
6	0.2603	2.0163	0.024127
7	0.318433	2.4666	0.008258
8	0.132048	1.0228	0.155246
9	0.119737	0.9275	0.178696
10	0.025448	0.1971	0.422199
11	-0.020853	-0.1615	0.43611
12	-0.003011	-0.0233	0.490735
13	-0.116399	-0.9016	0.18543
14	-0.051216	-0.3967	0.346491
15	-0.083066	-0.6434	0.2612
16	-0.058184	-0.4507	0.326918
17	-0.039078	-0.3027	0.381584
18	-0.087851	-0.6805	0.249407
19	-0.081654	-0.6325	0.264736
20	-0.120385	-0.9325	0.177408
21	-0.092413	-0.7158	0.238437
22	-0.073952	-0.5728	0.28445
23	-0.079264	-0.614	0.270776
24	-0.003919	-0.0304	0.487941
25	-0.068177	-0.5281	0.299691
26	-0.090939	-0.7044	0.241951
27	-0.108817	-0.8429	0.201319
28	-0.192163	-1.4885	0.07093
29	-0.119601	-0.9264	0.178968
30	-0.174648	-1.3528	0.090595
31	-0.074835	-0.5797	0.282153
32	-0.155023	-1.2008	0.117274
33	-0.176646	-1.3683	0.088162
34	-0.120266	-0.9316	0.177643
35	-0.222295	-1.7219	0.045121
36	-0.100985	-0.7822	0.218578
37	-0.133526	-1.0343	0.152577
38	-0.095893	-0.7428	0.230256
39	-0.089315	-0.6918	0.245856
40	-0.089865	-0.6961	0.244529
41	-0.092169	-0.7139	0.239016
42	-0.146042	-1.1312	0.131228
43	-0.078702	-0.6096	0.272208
44	-0.131667	-1.0199	0.155938
45	-0.070633	-0.5471	0.293162
46	-0.071648	-0.555	0.290484
47	-0.061154	-0.4737	0.318718
48	0.003019	0.0234	0.490709

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.601333	4.6579	9e-06
2	0.375116	2.9056	0.002563
3	0.014903	0.1154	0.454242
4	-0.086466	-0.6698	0.252789
5	0.144	1.1154	0.134559
6	-0.035729	-0.2768	0.39146
7	0.115122	0.8917	0.188051
8	-0.227829	-1.7648	0.041347
9	-0.054407	-0.4214	0.337472
10	-0.061345	-0.4752	0.318193
11	-0.002951	-0.0229	0.490921
12	0.016017	0.1241	0.450837
13	-0.121352	-0.94	0.175496
14	0.03614	0.2799	0.390243
15	0.108691	0.8419	0.201589
16	0.028682	0.2222	0.412468
17	0.018108	0.1403	0.444462
18	-0.086457	-0.6697	0.252811
19	-0.06881	-0.533	0.298001
20	0.015821	0.1226	0.451436
21	-0.01055	-0.0817	0.467571
22	0.017611	0.1364	0.445976
23	-0.057287	-0.4437	0.329414
24	0.101855	0.789	0.216619
25	-0.032732	-0.2535	0.40036
26	-0.13599	-1.0534	0.148196
27	-0.034771	-0.2693	0.394299
28	-0.137055	-1.0616	0.146331
29	0.083789	0.649	0.259399
30	-0.014951	-0.1158	0.454094
31	0.072387	0.5607	0.288544
32	-0.130686	-1.0123	0.157732
33	-0.087269	-0.676	0.250824
34	0.135081	1.0463	0.149801
35	-0.061427	-0.4758	0.317968
36	0.013716	0.1062	0.457871
37	0.047424	0.3673	0.357327
38	-0.082464	-0.6388	0.262704
39	0.020336	0.1575	0.437682
40	0.019697	0.1526	0.439624
41	-0.183706	-1.423	0.07996
42	-0.053411	-0.4137	0.340278
43	0.043876	0.3399	0.367575
44	0.047124	0.365	0.35819
45	0.014189	0.1099	0.456425
46	-0.083656	-0.648	0.259731
47	0.034981	0.271	0.393674
48	0.07411	0.5741	0.284038

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/20/t12928322736ltcivfau6y31nr/1ly7c1292832398.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t12928322736ltcivfau6y31nr/1ly7c1292832398.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t12928322736ltcivfau6y31nr/26zrs1292832399.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t12928322736ltcivfau6y31nr/26zrs1292832399.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t12928322736ltcivfau6y31nr/36zrs1292832399.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t12928322736ltcivfau6y31nr/36zrs1292832399.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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