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Paper Auto Correlation Function 2 - Priems

*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, 15 Dec 2010 16:19:08 +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/15/t1292430082jj2j5jlbf152z88.htm/, Retrieved Wed, 15 Dec 2010 17:21:25 +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/15/t1292430082jj2j5jlbf152z88.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 «

0.397232704 0.382767296 0.396037736 0.441761006 0.445220126 0.438490566 0.467484277 0.465786164 0.402075472 0.376163522 0.37591195 0.392955975 0.34490566 0.368553459 0.390880503 0.424842767 0.426855346 0.442327044 0.474842767 0.447610063 0.480754717 0.516037736 0.580628931 0.573522013 0.578867925 0.593584906 0.645974843 0.690503145 0.782201258 0.839056604 0.847484277 0.726855346 0.635534591 0.470943396 0.346163522 0.272327044 0.286792453 0.27672956 0.297421384 0.321698113 0.365597484 0.435220126 0.412893082 0.458679245 0.428427673 0.463522013 0.487169811 0.473584906 0.491886792 0.474842767 0.502327044 0.539371069 0.484402516 0.474654088 0.473522013 0.48754717 0.493333333 0.525157233 0.542704403

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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.333234	-2.5159	0.007358
2	0.15402	1.1628	0.124873
3	-0.16519	-1.2472	0.10872
4	0.05965	0.4504	0.327083
5	-0.133428	-1.0074	0.15901
6	-0.222404	-1.6791	0.049302
7	0.095442	0.7206	0.237059
8	0.072339	0.5461	0.293548
9	-0.111054	-0.8384	0.202644
10	0.010567	0.0798	0.468347
11	0.102257	0.772	0.221644
12	-0.007395	-0.0558	0.477836
13	-0.084649	-0.6391	0.262663
14	0.017508	0.1322	0.447653
15	0.140612	1.0616	0.146448
16	-0.090587	-0.6839	0.248399
17	-0.057256	-0.4323	0.333587
18	-0.045914	-0.3466	0.365069
19	0.220602	1.6655	0.050649
20	-0.261165	-1.9718	0.026749
21	0.177831	1.3426	0.092363
22	-0.115139	-0.8693	0.19417
23	0.209399	1.5809	0.059714
24	-0.213816	-1.6143	0.055995
25	0.163871	1.2372	0.110544
26	0.011489	0.0867	0.465592
27	-0.051541	-0.3891	0.349315
28	-0.028914	-0.2183	0.413989
29	-0.032171	-0.2429	0.404482
30	0.075905	0.5731	0.284425
31	-0.127474	-0.9624	0.169954
32	-0.000601	-0.0045	0.498198
33	0.05331	0.4025	0.344417
34	-0.01676	-0.1265	0.449878
35	0.038981	0.2943	0.384798
36	-0.015813	-0.1194	0.452694
37	0.047641	0.3597	0.360206
38	-0.039742	-0.3	0.382617
39	-0.038989	-0.2944	0.384776
40	0.087717	0.6623	0.255239
41	-0.053256	-0.4021	0.344567
42	0.003497	0.0264	0.489516
43	-0.037084	-0.28	0.390254
44	0.074501	0.5625	0.288001
45	-0.006199	-0.0468	0.481419
46	-0.04672	-0.3527	0.362798
47	0.012323	0.093	0.4631
48	0.04848	0.366	0.357854

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.333234	-2.5159	0.007358
2	0.048343	0.365	0.358238
3	-0.113023	-0.8533	0.198532
4	-0.035887	-0.2709	0.393706
5	-0.120405	-0.909	0.183578
6	-0.364363	-2.7509	0.003976
7	-0.102515	-0.774	0.221074
8	0.093289	0.7043	0.242053
9	-0.18735	-1.4145	0.081333
10	-0.167435	-1.2641	0.105669
11	0.014076	0.1063	0.457869
12	-0.112279	-0.8477	0.20008
13	-0.15928	-1.2025	0.117063
14	-0.048027	-0.3626	0.359124
15	0.031031	0.2343	0.407804
16	-0.101991	-0.77	0.222236
17	-0.121214	-0.9151	0.181986
18	-0.201057	-1.518	0.067277
19	0.088224	0.6661	0.254025
20	-0.177531	-1.3403	0.092729
21	-4.3e-05	-3e-04	0.499871
22	-0.135422	-1.0224	0.155453
23	-0.024653	-0.1861	0.426502
24	-0.123276	-0.9307	0.177964
25	0.096133	0.7258	0.235469
26	0.011093	0.0838	0.466773
27	-0.102895	-0.7768	0.220232
28	0.030557	0.2307	0.409186
29	-0.037792	-0.2853	0.388217
30	-0.023548	-0.1778	0.42976
31	-0.020389	-0.1539	0.439102
32	-0.020924	-0.158	0.43752
33	-0.046584	-0.3517	0.36318
34	-0.092263	-0.6966	0.244452
35	0.073112	0.552	0.291558
36	-0.012772	-0.0964	0.461759
37	-0.038521	-0.2908	0.386118
38	-0.104222	-0.7869	0.217312
39	0.016874	0.1274	0.449536
40	-0.026933	-0.2033	0.419798
41	0.015452	0.1167	0.453769
42	-0.081352	-0.6142	0.270767
43	0.0057	0.043	0.482912
44	-0.090372	-0.6823	0.248907
45	0.068628	0.5181	0.303186
46	-0.049835	-0.3762	0.354067
47	-0.061949	-0.4677	0.32089
48	0.012545	0.0947	0.462437

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292430082jj2j5jlbf152z88/1pii51292429945.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292430082jj2j5jlbf152z88/1pii51292429945.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292430082jj2j5jlbf152z88/209h81292429945.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292430082jj2j5jlbf152z88/209h81292429945.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292430082jj2j5jlbf152z88/309h81292429945.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292430082jj2j5jlbf152z88/309h81292429945.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 2 ; 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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