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paperwerk_ACF3

*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 13:03:50 +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/t1292763725a0zzqx772fhm98z.htm/, Retrieved Sun, 19 Dec 2010 14:02:08 +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/t1292763725a0zzqx772fhm98z.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 «

6.7 6.7 6.5 6.3 6.3 6.3 6.5 6.6 6.5 6.3 6.3 6.5 7 7.1 7.3 7.3 7.4 7.4 7.3 7.4 7.5 7.7 7.7 7.7 7.7 7.7 7.8 8 8.1 8.1 8.2 8.2 8.2 8.1 8.1 8.2 8.3 8.3 8.4 8.5 8.5 8.4 8 7.9 8.1 8.5 8.8 8.8 8.6 8.3 8.3 8.3 8.4 8.4 8.5 8.6 8.6 8.6 8.6 8.6 8.5 8.4 8.4 8.4 8.5 8.5 8.6 8.6 8.4 8.2 8 8 8 8 7.9 7.9 7.8 7.8 8 7.8 7.4 7.2 7 7 7.2 7.2 7.2 7 6.9 6.8 6.8 6.8 6.9 7.2 7.2 7.2 7.1 7.2 7.3 7.5 7.6 7.7 7.7 7.7 7.8 8 8.1 8.1 8 8.1 8.2 8.3 8.4 8.4 8.4 8.5 8.5 8.6 8.6 8.5 8.5

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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.051402	-0.5317	0.298016
2	-0.044393	-0.4592	0.323511
3	-0.450935	-4.6645	4e-06
4	-0.205607	-2.1268	0.017867
5	0.023364	0.2417	0.404744
6	0.109813	1.1359	0.129265
7	0.11215	1.1601	0.124298
8	-0.023364	-0.2417	0.404744
9	0.259346	2.6827	0.004231
10	-0.100467	-1.0392	0.150518
11	0.149533	1.5468	0.062435
12	-0.42757	-4.4228	1.2e-05
13	0.009346	0.0967	0.461583
14	0.009346	0.0967	0.461583
15	0.119159	1.2326	0.110215
16	0.074766	0.7734	0.220499
17	-0.060748	-0.6284	0.265547
18	0.074766	0.7734	0.220499
19	-0.070093	-0.7251	0.235001
20	0.109813	1.1359	0.129265
21	-0.142523	-1.4743	0.071672
22	-0.060748	-0.6284	0.265547
23	-0.002336	-0.0242	0.490382
24	0.116822	1.2084	0.114775
25	0.014019	0.145	0.442488
26	-0.011682	-0.1208	0.452021
27	0.004673	0.0483	0.480769
28	-0.086449	-0.8942	0.186603
29	0.049065	0.5075	0.306411
30	-0.095794	-0.9909	0.161984
31	0.037383	0.3867	0.349875
32	0.102804	1.0634	0.144995
33	0.051402	0.5317	0.298016
34	0.11215	1.1601	0.124298
35	-0.198598	-2.0543	0.021191
36	-0.193925	-2.006	0.023691
37	-0.011682	-0.1208	0.452021
38	0.147196	1.5226	0.065403
39	0.121495	1.2568	0.105789
40	0.123832	1.2809	0.101495
41	-0.051402	-0.5317	0.298016
42	-0.168224	-1.7401	0.042356
43	0.014019	0.145	0.442488
44	-0.140187	-1.4501	0.074977
45	0.077103	0.7976	0.213447
46	0.004673	0.0483	0.480769
47	0.130841	1.3534	0.089385
48	0.098131	1.0151	0.15618
49	-0.063084	-0.6525	0.257724
50	-0.07243	-0.7492	0.227684
51	-0.095794	-0.9909	0.161984
52	0.051402	0.5317	0.298016
53	-0.067757	-0.7009	0.242448
54	0.133178	1.3776	0.085601
55	-0.077103	-0.7976	0.213447
56	0.100467	1.0392	0.150518
57	-0.014019	-0.145	0.442488
58	0.007009	0.0725	0.471168
59	-0.044393	-0.4592	0.323511
60	-0.133178	-1.3776	0.085601

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.051402	-0.5317	0.298016
2	-0.047159	-0.4878	0.313338
3	-0.457974	-4.7373	3e-06
4	-0.338684	-3.5034	0.000336
5	-0.152622	-1.5787	0.058675
6	-0.246508	-2.5499	0.006096
7	-0.288566	-2.9849	0.001758
8	-0.363594	-3.761	0.000138
9	0.097764	1.0113	0.157081
10	-0.131789	-1.3632	0.087835
11	0.182502	1.8878	0.03088
12	-0.217413	-2.2489	0.013282
13	0.102628	1.0616	0.145405
14	0.19926	2.0612	0.020856
15	-0.028755	-0.2974	0.383352
16	-0.070332	-0.7275	0.234249
17	-0.065472	-0.6772	0.249857
18	0.053178	0.5501	0.291706
19	-0.112645	-1.1652	0.123262
20	-0.149783	-1.5494	0.062124
21	0.054765	0.5665	0.286123
22	-0.232192	-2.4018	0.009019
23	0.1323	1.3685	0.087008
24	-0.048378	-0.5004	0.3089
25	-0.091961	-0.9512	0.171811
26	0.085113	0.8804	0.190305
27	0.050478	0.5222	0.301322
28	-0.044252	-0.4577	0.324032
29	-0.183484	-1.898	0.030197
30	-0.129832	-1.343	0.091057
31	-0.15932	-1.648	0.051141
32	-0.04498	-0.4653	0.321341
33	-0.018689	-0.1933	0.423538
34	0.078694	0.814	0.208723
35	0.073848	0.7639	0.223306
36	-0.096844	-1.0018	0.159359
37	0.071372	0.7383	0.230982
38	0.026249	0.2715	0.393258
39	-0.016515	-0.1708	0.432338
40	0.068455	0.7081	0.240211
41	0.025376	0.2625	0.396724
42	-0.115786	-1.1977	0.116839
43	-0.018688	-0.1933	0.423541
44	-0.075894	-0.785	0.21708
45	-0.064886	-0.6712	0.251776
46	0.033972	0.3514	0.362985
47	0.021257	0.2199	0.413192
48	0.078373	0.8107	0.209668
49	-0.007341	-0.0759	0.469806
50	0.072193	0.7468	0.228419
51	0.069307	0.7169	0.237492
52	0.054351	0.5622	0.287572
53	-0.012551	-0.1298	0.448472
54	-0.01531	-0.1584	0.437231
55	-0.004617	-0.0478	0.481001
56	0.056533	0.5848	0.279962
57	-0.045782	-0.4736	0.318386
58	-0.01142	-0.1181	0.453095
59	0.090675	0.9379	0.175192
60	-0.067161	-0.6947	0.244369

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292763725a0zzqx772fhm98z/1723g1292763827.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292763725a0zzqx772fhm98z/1723g1292763827.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292763725a0zzqx772fhm98z/2zt211292763827.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292763725a0zzqx772fhm98z/2zt211292763827.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292763725a0zzqx772fhm98z/3zt211292763827.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292763725a0zzqx772fhm98z/3zt211292763827.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 2 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 2 ; 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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