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Paper ACF 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: Tue, 28 Dec 2010 22:24:37 +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/28/t1293575073ibi2em2h8j8o2jd.htm/, Retrieved Tue, 28 Dec 2010 23:24:33 +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/28/t1293575073ibi2em2h8j8o2jd.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 «

1203 1319 1328 1260 1286 1274 1389 1255 1244 1336 1214 1239 1174 1061 1116 1123 1086 1074 965 1035 1016 941 1003 998 891 828 833 887 842 793 778 699 686 727 641 619 627 593 535 536 504 487 477 435 433 393 389 377 339 370 350 341 367 396 408 405 391 396 368 356

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.283583	-2.1782	0.016698
2	-0.213243	-1.638	0.053377
3	0.293416	2.2538	0.01397
4	-0.189454	-1.4552	0.075454
5	0.281496	2.1622	0.017334
6	-0.081756	-0.628	0.26622
7	-0.09309	-0.715	0.238702
8	0.251924	1.9351	0.02889
9	-0.277226	-2.1294	0.018701
10	0.085085	0.6536	0.25797
11	0.101459	0.7793	0.219452
12	-0.332707	-2.5556	0.006599
13	0.272241	2.0911	0.020416
14	0.089727	0.6892	0.246698
15	-0.231362	-1.7771	0.040351
16	0.041591	0.3195	0.37525
17	-0.020933	-0.1608	0.436403
18	0.108355	0.8323	0.2043
19	-0.047797	-0.3671	0.357417
20	-0.169407	-1.3012	0.099118
21	0.180632	1.3875	0.08526
22	0.043489	0.334	0.369765
23	-0.208182	-1.5991	0.057573
24	0.042115	0.3235	0.373734
25	-0.030147	-0.2316	0.40884
26	-0.029127	-0.2237	0.411871
27	0.130448	1.002	0.160221
28	-0.08878	-0.6819	0.248976
29	-0.110257	-0.8469	0.200237
30	0.028941	0.2223	0.412424
31	-0.003039	-0.0233	0.490728
32	-0.000282	-0.0022	0.499139
33	-0.023214	-0.1783	0.429544
34	-0.056402	-0.4332	0.333213
35	0.080781	0.6205	0.268662
36	-0.079357	-0.6096	0.272249
37	-0.068424	-0.5256	0.300577
38	0.094551	0.7263	0.235276
39	-0.120235	-0.9235	0.179743
40	0.033893	0.2603	0.397755
41	-0.016701	-0.1283	0.449182
42	-0.083819	-0.6438	0.261091
43	0.049267	0.3784	0.353235
44	-0.035937	-0.276	0.391743
45	0.01595	0.1225	0.451454
46	-0.002322	-0.0178	0.492914
47	-0.009832	-0.0755	0.470027
48	0.078382	0.6021	0.274719

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.283583	-2.1782	0.016698
2	-0.319343	-2.4529	0.008573
3	0.149034	1.1448	0.128468
4	-0.133236	-1.0234	0.155148
5	0.372898	2.8643	0.00289
6	-0.051807	-0.3979	0.346056
7	0.145078	1.1144	0.134821
8	0.055723	0.428	0.335099
9	-0.14249	-1.0945	0.139095
10	-0.054108	-0.4156	0.339601
11	-0.059875	-0.4599	0.323635
12	-0.281076	-2.159	0.017465
13	0.076755	0.5896	0.278867
14	0.211437	1.6241	0.054845
15	0.041421	0.3182	0.375744
16	-0.066222	-0.5087	0.306444
17	0.068666	0.5274	0.299935
18	-0.006872	-0.0528	0.47904
19	-0.11459	-0.8802	0.191167
20	-0.117355	-0.9014	0.185514
21	-0.054471	-0.4184	0.338587
22	0.142431	1.094	0.139194
23	-0.074601	-0.573	0.284405
24	-0.071057	-0.5458	0.293631
25	-0.082086	-0.6305	0.265396
26	-0.01351	-0.1038	0.458851
27	0.0122	0.0937	0.462828
28	0.041252	0.3169	0.376234
29	-0.083707	-0.643	0.261368
30	-0.002744	-0.0211	0.491627
31	-0.060945	-0.4681	0.32071
32	-0.137421	-1.0555	0.147739
33	0.022274	0.1711	0.432369
34	-0.007334	-0.0563	0.477634
35	-0.069062	-0.5305	0.298888
36	-0.070423	-0.5409	0.295297
37	0.07189	0.5522	0.29145
38	0.004751	0.0365	0.485506
39	-0.139894	-1.0745	0.143476
40	-0.089996	-0.6913	0.246053
41	-0.177411	-1.3627	0.089075
42	-0.018178	-0.1396	0.444715
43	-0.089316	-0.6861	0.247684
44	0.009921	0.0762	0.469757
45	0.075358	0.5788	0.282452
46	0.074144	0.5695	0.285585
47	0.080035	0.6148	0.270538
48	-0.000374	-0.0029	0.498859

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293575073ibi2em2h8j8o2jd/1qr341293575074.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293575073ibi2em2h8j8o2jd/1qr341293575074.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293575073ibi2em2h8j8o2jd/210371293575074.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293575073ibi2em2h8j8o2jd/210371293575074.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293575073ibi2em2h8j8o2jd/310371293575074.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293575073ibi2em2h8j8o2jd/310371293575074.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 (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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