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Autocorrelation function D=d=1

*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 12:57:51 +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/t12927635178otqnpnaews2tg7.htm/, Retrieved Sun, 19 Dec 2010 13:58:37 +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/t12927635178otqnpnaews2tg7.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 «

206010 198112 194519 185705 180173 176142 203401 221902 197378 185001 176356 180449 180144 173666 165688 161570 156145 153730 182698 200765 176512 166618 158644 159585 163095 159044 155511 153745 150569 150605 179612 194690 189917 184128 175335 179566 181140 177876 175041 169292 166070 166972 206348 215706 202108 195411 193111 195198 198770 194163 190420 189733 186029 191531 232571 243477 227247 217859 208679 213188 216234 213586 209465 204045 200237 203666 241476 260307 243324 244460 233575 237217 235243 230354 227184 221678 217142 219452 256446 265845 248624 241114 229245 231805 219277 219313 212610 214771 211142 211457 240048 240636 230580 208795 197922 194596 194581 185686 178106 172608 167302 168053 202300 202388 182516 173476 166444 171297 169701 164182 161914 159612 151001 158114 186530 187069 174330 169362 166827 178037 186413 189226 191563 188906 186005 195309 223532 226899 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	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.025997	-0.2964	0.383693
2	0.226464	2.5821	0.005464
3	0.015892	0.1812	0.428249
4	0.165699	1.8893	0.030542
5	0.129585	1.4775	0.070981
6	0.038005	0.4333	0.33275
7	0.096292	1.0979	0.13714
8	-0.000309	-0.0035	0.498598
9	0.162435	1.852	0.033144
10	-0.002752	-0.0314	0.487507
11	0.104969	1.1968	0.116776
12	-0.275431	-3.1404	0.001045
13	0.055059	0.6278	0.265628
14	0.084149	0.9594	0.169559
15	-0.041229	-0.4701	0.319543
16	-0.055564	-0.6335	0.263751
17	-0.103555	-1.1807	0.119938
18	0.05618	0.6405	0.261471
19	-0.018641	-0.2125	0.416009
20	0.014444	0.1647	0.434725
21	-0.038242	-0.436	0.331771
22	-0.07331	-0.8359	0.202382
23	-0.093117	-1.0617	0.145172
24	-0.148312	-1.691	0.046615
25	-0.025843	-0.2947	0.384363
26	-0.195339	-2.2272	0.013827
27	-0.077996	-0.8893	0.187745
28	-0.068761	-0.784	0.217235
29	-0.071968	-0.8206	0.206698
30	-0.159171	-1.8148	0.035928
31	-0.123897	-1.4126	0.080076
32	-0.063795	-0.7274	0.234153
33	0.028018	0.3195	0.374946
34	-0.046966	-0.5355	0.296612
35	0.080756	0.9208	0.17944
36	-0.021862	-0.2493	0.401774
37	0.008385	0.0956	0.46199
38	-0.087389	-0.9964	0.160457
39	0.022747	0.2594	0.397887
40	-0.087291	-0.9953	0.160727
41	0.050013	0.5702	0.284751
42	0.008686	0.099	0.460631
43	0.039845	0.4543	0.325186
44	-0.031583	-0.3601	0.359677
45	-0.063797	-0.7274	0.234146
46	0.034832	0.3972	0.345954
47	-0.106806	-1.2178	0.112758
48	-0.008885	-0.1013	0.459731

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.025997	-0.2964	0.383693
2	0.225941	2.5761	0.005554
3	0.027758	0.3165	0.376071
4	0.121938	1.3903	0.083405
5	0.136599	1.5575	0.060895
6	-0.014493	-0.1652	0.434505
7	0.042226	0.4815	0.315501
8	-0.024637	-0.2809	0.389613
9	0.105033	1.1976	0.116633
10	-0.008122	-0.0926	0.463181
11	0.03618	0.4125	0.340321
12	-0.310453	-3.5397	0.000278
13	-0.028368	-0.3234	0.373438
14	0.189975	2.1661	0.016066
15	-0.062509	-0.7127	0.23865
16	-0.083488	-0.9519	0.171455
17	-0.032328	-0.3686	0.356515
18	0.037746	0.4304	0.333819
19	0.044503	0.5074	0.306363
20	0.011221	0.1279	0.449196
21	0.045845	0.5227	0.30103
22	-0.084	-0.9578	0.169983
23	-0.121266	-1.3826	0.084573
24	-0.259604	-2.9599	0.001829
25	0.012246	0.1396	0.444585
26	0.016614	0.1894	0.425026
27	-0.110376	-1.2585	0.105237
28	-0.041531	-0.4735	0.318314
29	-0.031713	-0.3616	0.359127
30	-0.07849	-0.8949	0.186241
31	-0.015488	-0.1766	0.430052
32	0.042194	0.4811	0.315634
33	0.216184	2.4649	0.007505
34	0.004625	0.0527	0.479013
35	0.098384	1.1217	0.132019
36	-0.061732	-0.7039	0.24139
37	0.040337	0.4599	0.323172
38	-0.133387	-1.5208	0.065364
39	-0.109979	-1.254	0.106054
40	-0.103939	-1.1851	0.119072
41	0.034265	0.3907	0.348337
42	-0.048607	-0.5542	0.290196
43	0.000531	0.0061	0.497589
44	-0.00977	-0.1114	0.455736
45	0.060087	0.6851	0.247249
46	-0.02749	-0.3134	0.377227
47	-0.055133	-0.6286	0.265351
48	-0.0551	-0.6282	0.265475

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927635178otqnpnaews2tg7/1hrzl1292763467.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927635178otqnpnaews2tg7/1hrzl1292763467.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927635178otqnpnaews2tg7/290g51292763467.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927635178otqnpnaews2tg7/290g51292763467.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927635178otqnpnaews2tg7/32sgq1292763467.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927635178otqnpnaews2tg7/32sgq1292763467.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 1 ; 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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