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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: Tue, 28 Dec 2010 16:41:00 +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/t1293554336szkmpl5spjboyb0.htm/, Retrieved Tue, 28 Dec 2010 17:38:59 +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/t1293554336szkmpl5spjboyb0.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 «

11100 8962 9173 8738 8459 8078 8411 8291 7810 8616 8312 9692 9911 8915 9452 9112 8472 8230 8384 8625 8221 8649 8625 10443 10357 8586 8892 8329 8101 7922 8120 7838 7735 8406 8209 9451 10041 9411 10405 8467 8464 8102 7627 7513 7510 8291 8064 9383 9706 8579 9474 8318 8213 8059 9111 7708 7680 8014 8007 8718 9486 9113 9025 8476 7952 7759 7835 7600 7651 8319 8812 8630

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	25 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.381295	2.9535	0.002241
2	0.085134	0.6594	0.256067
3	-0.081775	-0.6334	0.26443
4	-0.150806	-1.1681	0.123686
5	-0.230926	-1.7887	0.039352
6	-0.119331	-0.9243	0.179508
7	0.025941	0.2009	0.420714
8	-0.092074	-0.7132	0.239242
9	-0.004676	-0.0362	0.485615
10	-0.2112	-1.6359	0.053543
11	-0.436909	-3.3843	0.000631
12	-0.498287	-3.8597	0.00014
13	-0.093485	-0.7241	0.235901
14	0.183165	1.4188	0.080567
15	0.271458	2.1027	0.019848
16	0.401177	3.1075	0.001441
17	0.283474	2.1958	0.015993
18	0.136612	1.0582	0.147105
19	-0.037053	-0.287	0.387546
20	-0.072194	-0.5592	0.289048
21	-0.063084	-0.4887	0.313435
22	0.019797	0.1533	0.439319
23	0.176506	1.3672	0.08833
24	0.100335	0.7772	0.220051
25	-0.110827	-0.8585	0.197028
26	-0.256121	-1.9839	0.025924
27	-0.20267	-1.5699	0.060851
28	-0.260797	-2.0201	0.023921
29	-0.139845	-1.0832	0.141519
30	0.073911	0.5725	0.284558
31	0.204142	1.5813	0.059536
32	0.192215	1.4889	0.070877
33	0.075681	0.5862	0.279962
34	0.01282	0.0993	0.460614
35	-0.020964	-0.1624	0.435774
36	-0.030389	-0.2354	0.407354
37	0.068799	0.5329	0.29803
38	0.066544	0.5154	0.304068
39	0.054306	0.4207	0.337756
40	0.056277	0.4359	0.33223
41	0.010374	0.0804	0.468111
42	-0.185839	-1.4395	0.077603
43	-0.138655	-1.074	0.143558
44	-0.08311	-0.6438	0.261089
45	-0.021376	-0.1656	0.434522
46	0.019108	0.148	0.441416
47	0.061376	0.4754	0.318108
48	0.024814	0.1922	0.424115
49	-0.039487	-0.3059	0.380384
50	0.042724	0.3309	0.370923
51	-0.028979	-0.2245	0.411577
52	-0.006429	-0.0498	0.480225
53	0.026735	0.2071	0.41832
54	0.093302	0.7227	0.236332
55	0.033568	0.26	0.397872
56	0.015953	0.1236	0.451034
57	-0.02327	-0.1803	0.428781
58	-0.0573	-0.4438	0.329375
59	0.000318	0.0025	0.499021
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.381295	2.9535	0.002241
2	-0.070502	-0.5461	0.29351
3	-0.105417	-0.8166	0.208706
4	-0.089784	-0.6955	0.244725
5	-0.160911	-1.2464	0.108729
6	0.023452	0.1817	0.428232
7	0.067073	0.5195	0.302647
8	-0.202794	-1.5708	0.06074
9	0.065772	0.5095	0.306147
10	-0.320188	-2.4802	0.007978
11	-0.402841	-3.1204	0.001388
12	-0.371107	-2.8746	0.002795
13	0.034334	0.266	0.395595
14	0.107808	0.8351	0.203495
15	0.029499	0.2285	0.410017
16	0.100421	0.7779	0.219855
17	-0.017948	-0.139	0.444947
18	-0.015041	-0.1165	0.453819
19	-0.069788	-0.5406	0.295402
20	-0.115126	-0.8918	0.188042
21	0.007877	0.061	0.475774
22	-0.167385	-1.2966	0.099874
23	-0.090293	-0.6994	0.2435
24	-0.038784	-0.3004	0.382448
25	-0.074405	-0.5763	0.283272
26	0.02931	0.227	0.410584
27	0.169558	1.3134	0.097026
28	-0.015205	-0.1178	0.453318
29	-0.008422	-0.0652	0.4741
30	-0.026457	-0.2049	0.419157
31	6.1e-05	5e-04	0.499813
32	-0.060978	-0.4723	0.319202
33	-0.16765	-1.2986	0.099524
34	-0.082736	-0.6409	0.262025
35	0.152752	1.1832	0.120696
36	-0.075751	-0.5868	0.279781
37	0.030892	0.2393	0.405847
38	-0.017071	-0.1322	0.447623
39	-0.014248	-0.1104	0.456245
40	-0.013151	-0.1019	0.459602
41	0.038888	0.3012	0.382143
42	-0.099342	-0.7695	0.222308
43	0.144933	1.1226	0.13303
44	-0.096815	-0.7499	0.228115
45	-0.064607	-0.5004	0.309298
46	-0.022488	-0.1742	0.431151
47	0.017848	0.1383	0.445252
48	-0.113738	-0.881	0.190914
49	-0.000422	-0.0033	0.498702
50	-0.029049	-0.225	0.411367
51	-0.079895	-0.6189	0.269175
52	0.03762	0.2914	0.385873
53	-0.037539	-0.2908	0.386111
54	-0.053229	-0.4123	0.340791
55	0.069636	0.5394	0.295805
56	-0.035867	-0.2778	0.391052
57	-0.038741	-0.3001	0.382575
58	-0.055063	-0.4265	0.335629
59	-0.076478	-0.5924	0.277905
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293554336szkmpl5spjboyb0/114m51293554435.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293554336szkmpl5spjboyb0/114m51293554435.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293554336szkmpl5spjboyb0/2ce481293554435.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293554336szkmpl5spjboyb0/2ce481293554435.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293554336szkmpl5spjboyb0/3n5lt1293554435.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293554336szkmpl5spjboyb0/3n5lt1293554435.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; 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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