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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, 14 Dec 2010 12:02:33 +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/14/t12923281748ahdtlt7nqrguh1.htm/, Retrieved Tue, 14 Dec 2010 13:02:55 +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/14/t12923281748ahdtlt7nqrguh1.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 «

46 61 66 59 58 61 41 27 58 70 49 59 44 36 72 45 56 54 53 35 61 52 47 51 52 63 74 45 51 64 36 30 55 64 39 40 63 45 59 55 40 64 27 28 45 57 45 69 60 56 58 50 51 53 37 22 55 70 62 58 39 49 58 47 42 62 39 40 72 70 54 64

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	1 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.069616	0.5907	0.278281
2	-0.237467	-2.015	0.023821
3	0.065734	0.5578	0.289365
4	-0.143035	-1.2137	0.114415
5	-0.210745	-1.7882	0.038973
6	0.070471	0.598	0.275869
7	-0.100935	-0.8565	0.197293
8	-0.053624	-0.455	0.325234
9	0.118363	1.0043	0.159288
10	-0.113681	-0.9646	0.168983
11	0.116397	0.9877	0.163313
12	0.466638	3.9596	8.7e-05
13	-0.040597	-0.3445	0.365746
14	-0.27176	-2.306	0.011998
15	0.056152	0.4765	0.317594
16	-0.131249	-1.1137	0.134559
17	-0.17815	-1.5117	0.0675
18	0.047122	0.3998	0.345227
19	-0.101786	-0.8637	0.195316
20	0.027622	0.2344	0.407676
21	0.199569	1.6934	0.047351
22	-0.058949	-0.5002	0.309231
23	0.060153	0.5104	0.305661
24	0.374005	3.1735	0.001108
25	-0.007759	-0.0658	0.473844
26	-0.315766	-2.6794	0.004568
27	0.042892	0.3639	0.358482
28	-0.136677	-1.1597	0.124993
29	-0.147283	-1.2497	0.107722
30	0.06673	0.5662	0.286502
31	-0.009244	-0.0784	0.46885
32	0.051746	0.4391	0.330959
33	0.09451	0.8019	0.212613
34	-0.179335	-1.5217	0.066232
35	-0.03118	-0.2646	0.396047
36	0.23303	1.9773	0.025917
37	-0.032138	-0.2727	0.392931
38	-0.154691	-1.3126	0.096744
39	0.016205	0.1375	0.445509
40	-0.103999	-0.8825	0.190231
41	-0.171229	-1.4529	0.075294
42	0.082324	0.6985	0.243543
43	0.080567	0.6836	0.2482
44	0.005027	0.0427	0.483048
45	0.064717	0.5491	0.292304
46	-0.082903	-0.7035	0.242019
47	0.034321	0.2912	0.38586
48	0.191058	1.6212	0.054675
49	-0.003502	-0.0297	0.488187
50	-0.125989	-1.0691	0.144309
51	-0.025182	-0.2137	0.415702
52	-0.098123	-0.8326	0.203911
53	-0.020353	-0.1727	0.431687
54	0.094167	0.799	0.213449
55	0.016798	0.1425	0.443526
56	-0.012825	-0.1088	0.456823
57	0.037577	0.3189	0.375381
58	-0.076825	-0.6519	0.258276
59	0.009406	0.0798	0.468303
60	0.106579	0.9044	0.184413

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.069616	0.5907	0.278281
2	-0.243493	-2.0661	0.021208
3	0.110283	0.9358	0.176256
4	-0.236013	-2.0026	0.024491
5	-0.138865	-1.1783	0.121277
6	0.003509	0.0298	0.488165
7	-0.205533	-1.744	0.042713
8	-0.005323	-0.0452	0.482049
9	-0.038661	-0.3281	0.371912
10	-0.180454	-1.5312	0.065051
11	0.181644	1.5413	0.063814
12	0.350557	2.9746	0.001995
13	-0.014839	-0.1259	0.450077
14	-0.121724	-1.0329	0.152562
15	0.044451	0.3772	0.353576
16	-0.055449	-0.4705	0.31971
17	-0.033212	-0.2818	0.389447
18	-0.08339	-0.7076	0.240743
19	-0.159779	-1.3558	0.089704
20	0.055517	0.4711	0.319505
21	0.048407	0.4108	0.341238
22	-0.041739	-0.3542	0.362124
23	-0.005339	-0.0453	0.481995
24	0.187979	1.5951	0.05754
25	0.171947	1.459	0.074454
26	-0.128288	-1.0886	0.139989
27	0.065784	0.5582	0.289221
28	-0.111527	-0.9463	0.173571
29	0.068158	0.5783	0.28242
30	-0.039875	-0.3383	0.368043
31	-0.053553	-0.4544	0.325449
32	-0.012422	-0.1054	0.458173
33	-0.179208	-1.5206	0.066366
34	-0.16079	-1.3644	0.088353
35	-0.159244	-1.3512	0.090426
36	-0.127426	-1.0812	0.141599
37	0.022798	0.1934	0.423577
38	0.037687	0.3198	0.37503
39	-0.018236	-0.1547	0.438729
40	-0.046382	-0.3936	0.347533
41	-0.087741	-0.7445	0.229498
42	0.026211	0.2224	0.412315
43	0.08489	0.7203	0.23683
44	-0.113743	-0.9651	0.168851
45	-0.090887	-0.7712	0.221556
46	0.000141	0.0012	0.499525
47	0.068484	0.5811	0.281492
48	-0.032322	-0.2743	0.392333
49	-0.04829	-0.4098	0.3416
50	-0.004055	-0.0344	0.486323
51	0.00819	0.0695	0.472393
52	-0.049291	-0.4183	0.338504
53	0.137965	1.1707	0.122796
54	-0.04468	-0.3791	0.352855
55	0.051476	0.4368	0.331785
56	0.02007	0.1703	0.432627
57	0.036851	0.3127	0.377709
58	0.002577	0.0219	0.491309
59	-0.045214	-0.3837	0.351184
60	-0.092932	-0.7886	0.21648

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/14/t12923281748ahdtlt7nqrguh1/1iv5d1292328150.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/14/t12923281748ahdtlt7nqrguh1/1iv5d1292328150.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/14/t12923281748ahdtlt7nqrguh1/2iv5d1292328150.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/14/t12923281748ahdtlt7nqrguh1/2iv5d1292328150.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; 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 (par2 == 0) {

x <- log(x)

} else {

x <- (x ^ par2 - 1) / par2

}

if (par3 > 0) x <- diff(x,lag=1,difference=par3)

if (par4 > 0) x <- diff(x,lag=par5,difference=par4)

bitmap(file='pic1.png')

racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))

dev.off()

bitmap(file='pic2.png')

rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')

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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