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*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, 29 Dec 2010 13:28:49 +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/29/t1293630141omscumo4ju7iuqs.htm/, Retrieved Wed, 29 Dec 2010 14:42:21 +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/29/t1293630141omscumo4ju7iuqs.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 «

60178 53200 59909 55970 47682 50173 43090 36031 42143 48478 36046 31060 54874 60051 71622 66526 50140 55973 40393 38483 42879 47875 40578 31027 62027 56493 65566 62653 53470 59600 42542 42018 44038 44988 43309 26843 69770 64886 79354 63025 54003 55926 45629 40361 43039 44570 43269 25563 68707 60223 74283 61232 61531 65305 51699 44599 35221 55066 45335 28702 69517 69240 71525 77740 62107 65450 51493 43067 49172 54483 38158 27898 58648 56000 62381 59849 48345 55376 45400 38389 44098 48290 41267 31238

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	0.428518	3.9274	8.8e-05
2	0.221761	2.0325	0.022632
3	0.029517	0.2705	0.39371
4	-0.193686	-1.7752	0.039747
5	-0.307742	-2.8205	0.002991
6	-0.528413	-4.843	3e-06
7	-0.347911	-3.1887	0.001004
8	-0.2587	-2.371	0.010014
9	-0.060572	-0.5551	0.290134
10	0.119705	1.0971	0.137863
11	0.313291	2.8714	0.002586
12	0.790149	7.2418	0
13	0.337272	3.0911	0.001352
14	0.17945	1.6447	0.051886
15	0.031943	0.2928	0.385212
16	-0.178789	-1.6386	0.052516
17	-0.291351	-2.6703	0.004549
18	-0.527265	-4.8325	3e-06
19	-0.344831	-3.1604	0.001096
20	-0.289364	-2.6521	0.004781
21	-0.11236	-1.0298	0.153031
22	0.051563	0.4726	0.318868
23	0.229188	2.1005	0.01934
24	0.63229	5.795	0
25	0.292376	2.6797	0.004433
26	0.140653	1.2891	0.10045
27	0.036713	0.3365	0.368674
28	-0.12823	-1.1752	0.121609
29	-0.221807	-2.0329	0.02261
30	-0.404151	-3.7041	0.000189
31	-0.268346	-2.4594	0.007984
32	-0.243031	-2.2274	0.014297
33	-0.115455	-1.0582	0.146507
34	0.022434	0.2056	0.418798
35	0.148133	1.3577	0.089103
36	0.479276	4.3926	1.6e-05
37	0.243788	2.2344	0.014058
38	0.126294	1.1575	0.125174
39	0.050163	0.4598	0.323441
40	-0.063331	-0.5804	0.281588
41	-0.165906	-1.5205	0.066064
42	-0.29453	-2.6994	0.004199
43	-0.208812	-1.9138	0.029526
44	-0.198599	-1.8202	0.036146
45	-0.11398	-1.0446	0.149593
46	-0.011525	-0.1056	0.458063
47	0.073175	0.6707	0.252139
48	0.321887	2.9501	0.002057

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.428518	3.9274	8.8e-05
2	0.046711	0.4281	0.334831
3	-0.099546	-0.9124	0.182096
4	-0.226405	-2.075	0.020521
5	-0.17891	-1.6397	0.0524
6	-0.390362	-3.5777	0.000289
7	-0.003795	-0.0348	0.486168
8	-0.104499	-0.9577	0.170469
9	0.038056	0.3488	0.36406
10	0.006566	0.0602	0.476077
11	0.168957	1.5485	0.062629
12	0.679538	6.2281	0
13	-0.405553	-3.717	0.000181
14	-0.138659	-1.2708	0.103648
15	-0.018155	-0.1664	0.434123
16	-0.045148	-0.4138	0.34004
17	-0.03739	-0.3427	0.366347
18	-0.064246	-0.5888	0.278781
19	0.071271	0.6532	0.257704
20	-0.082885	-0.7597	0.224793
21	-0.029371	-0.2692	0.394221
22	-0.05082	-0.4658	0.321291
23	-0.039236	-0.3596	0.360023
24	-0.047393	-0.4344	0.33257
25	0.033665	0.3085	0.379216
26	-0.15503	-1.4209	0.079527
27	-0.024553	-0.225	0.411251
28	0.072862	0.6678	0.25305
29	0.040308	0.3694	0.356369
30	0.18542	1.6994	0.046472
31	-0.106695	-0.9779	0.165471
32	-0.013129	-0.1203	0.452256
33	-0.098108	-0.8992	0.185565
34	-0.033412	-0.3062	0.380096
35	-0.120623	-1.1055	0.136044
36	-0.060987	-0.559	0.28884
37	0.099867	0.9153	0.181327
38	0.062206	0.5701	0.285058
39	-0.037675	-0.3453	0.365368
40	0.017406	0.1595	0.436817
41	-0.099045	-0.9078	0.183301
42	-0.01693	-0.1552	0.43853
43	-0.049183	-0.4508	0.326659
44	-0.06329	-0.5801	0.281713
45	-0.021806	-0.1999	0.421037
46	-0.041885	-0.3839	0.351017
47	-0.00063	-0.0058	0.497704
48	-0.072916	-0.6683	0.252893

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630141omscumo4ju7iuqs/1ii0u1293629325.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630141omscumo4ju7iuqs/1ii0u1293629325.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630141omscumo4ju7iuqs/2s90x1293629325.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630141omscumo4ju7iuqs/2s90x1293629325.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630141omscumo4ju7iuqs/3s90x1293629325.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293630141omscumo4ju7iuqs/3s90x1293629325.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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