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PAPER - ACF

*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 10:56:45 +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/t129275628816p3zjru5slpj3d.htm/, Retrieved Sun, 19 Dec 2010 11:58:08 +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/t129275628816p3zjru5slpj3d.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 «

104.37 104.89 105.15 105.72 106.38 106.40 106.47 106.59 106.76 107.35 107.81 108.03 109.08 109.86 110.29 110.34 110.59 110.64 110.83 111.51 113.32 115.89 116.51 117.44 118.25 118.65 118.52 119.07 119.12 119.28 119.30 119.44 119.57 119.93 120.03 119.66 119.46 119.48 119.56 119.43 119.57 119.59 119.50 119.54 119.56 119.61 119.64 119.60 119.71 119.72 119.66 119.76 119.80 119.88 119.78 120.08 120.22

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

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.597494	4.4712	1.9e-05
2	0.352902	2.6409	0.005348
3	0.254129	1.9017	0.031178
4	0.152134	1.1385	0.129887
5	-0.006529	-0.0489	0.480603
6	0.056877	0.4256	0.336005
7	0.136499	1.0215	0.155713
8	0.220757	1.652	0.052066
9	0.216962	1.6236	0.05504
10	0.115	0.8606	0.196569
11	0.15648	1.171	0.123281
12	0.089987	0.6734	0.25173
13	-0.031191	-0.2334	0.408147
14	-0.174251	-1.304	0.098788
15	-0.179408	-1.3426	0.092414
16	-0.142602	-1.0671	0.145246
17	-0.00121	-0.0091	0.496402
18	-0.049392	-0.3696	0.356531
19	-0.038249	-0.2862	0.387879
20	-0.003886	-0.0291	0.488453
21	-0.079548	-0.5953	0.277027
22	-0.138692	-1.0379	0.151894
23	-0.142718	-1.068	0.145051
24	-0.103287	-0.7729	0.221406
25	-0.141142	-1.0562	0.147704
26	-0.156302	-1.1697	0.123546
27	-0.152329	-1.1399	0.129584
28	-0.11051	-0.827	0.20588
29	-0.147369	-1.1028	0.137414
30	-0.124588	-0.9323	0.177584
31	-0.131234	-0.9821	0.165146
32	-0.124086	-0.9286	0.178548
33	-0.141977	-1.0625	0.146294
34	-0.086783	-0.6494	0.25936
35	-0.072442	-0.5421	0.294947
36	-0.040101	-0.3001	0.382609
37	-0.031464	-0.2355	0.407357
38	-0.044252	-0.3312	0.370883
39	-0.022134	-0.1656	0.43452
40	-0.040587	-0.3037	0.381231
41	-0.038466	-0.2879	0.387262
42	-0.031884	-0.2386	0.406145
43	-0.017117	-0.1281	0.449267
44	-0.019538	-0.1462	0.442141
45	-0.009441	-0.0706	0.471965
46	-0.00985	-0.0737	0.470753
47	-0.006223	-0.0466	0.481512
48	-0.004172	-0.0312	0.487602

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.597494	4.4712	1.9e-05
2	-0.006372	-0.0477	0.481069
3	0.071132	0.5323	0.29831
4	-0.040561	-0.3035	0.381305
5	-0.148748	-1.1131	0.135204
6	0.184948	1.384	0.085921
7	0.093601	0.7004	0.243275
8	0.160774	1.2031	0.116996
9	-0.00226	-0.0169	0.493284
10	-0.168115	-1.2581	0.106796
11	0.180724	1.3524	0.090839
12	-0.103251	-0.7727	0.221487
13	-0.053107	-0.3974	0.346284
14	-0.210498	-1.5752	0.060419
15	-0.091268	-0.683	0.248716
16	0.105364	0.7885	0.216873
17	0.177742	1.3301	0.094438
18	-0.174766	-1.3078	0.098138
19	-0.083246	-0.623	0.267922
20	-0.035392	-0.2649	0.396049
21	-0.003739	-0.028	0.488888
22	0.135744	1.0158	0.157042
23	-0.099732	-0.7463	0.229296
24	-0.018359	-0.1374	0.44561
25	-0.110463	-0.8266	0.205978
26	-0.028968	-0.2168	0.414586
27	0.11385	0.852	0.198928
28	-0.157927	-1.1818	0.121136
29	-0.116636	-0.8728	0.193243
30	0.029253	0.2189	0.413757
31	-0.011189	-0.0837	0.466784
32	0.117824	0.8817	0.19085
33	-0.129343	-0.9679	0.168624
34	-0.019135	-0.1432	0.443326
35	0.019106	0.143	0.443411
36	0.061874	0.463	0.322572
37	0.055449	0.4149	0.339886
38	-0.064143	-0.48	0.316547
39	-0.048681	-0.3643	0.358504
40	-0.010739	-0.0804	0.468119
41	0.021683	0.1623	0.435843
42	0.028174	0.2108	0.41689
43	-0.079025	-0.5914	0.278327
44	-0.075405	-0.5643	0.287408
45	-0.006714	-0.0502	0.480055
46	0.073211	0.5479	0.292983
47	-0.062889	-0.4706	0.31987
48	-0.02005	-0.15	0.440635

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/19/t129275628816p3zjru5slpj3d/1hipa1292756201.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t129275628816p3zjru5slpj3d/1hipa1292756201.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t129275628816p3zjru5slpj3d/2hipa1292756201.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t129275628816p3zjru5slpj3d/2hipa1292756201.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 1 ; 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 (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='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))

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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