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Paper: ACF (18t/m24)

*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 15:07:58 +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/t129363514326r98529xh8o6pu.htm/, Retrieved Wed, 29 Dec 2010 16:05:44 +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/t129363514326r98529xh8o6pu.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 «

49915 47469 45652 43492 41087 42931 67256 72316 65624 59450 52851 51214 44092 43752 40320 40551 38329 39530 59648 61031 55560 43877 38510 36085 35994 32617 30001 27894 26083 28817 48742 49915 40264 34276 30426 30793 29855 28081 26820 25782 22654 27373 43675 45096 38145 34017 31537 33814 36531 36935 36497 35110 33137 37407 53963 56602 49694 43957 41723 45599 42503 42153 39098 37449 34748 36548 53639 55289 47774 42156 38019

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.068946	-0.5251	0.300766
2	0.190465	1.4505	0.076148
3	-0.086052	-0.6554	0.257416
4	0.197709	1.5057	0.068784
5	0.032458	0.2472	0.402816
6	0.038933	0.2965	0.383951
7	0.103479	0.7881	0.216931
8	-0.097331	-0.7412	0.230767
9	0.086929	0.662	0.255285
10	-0.052799	-0.4021	0.344542
11	0.263755	2.0087	0.024616
12	-0.271785	-2.0699	0.021465
13	-0.005818	-0.0443	0.482405
14	-0.044745	-0.3408	0.367254
15	0.071115	0.5416	0.295086
16	-0.269555	-2.0529	0.022303
17	0.002728	0.0208	0.491747
18	-0.023328	-0.1777	0.429805
19	-0.076939	-0.586	0.280091
20	-0.050058	-0.3812	0.352212
21	-0.045582	-0.3471	0.364872
22	0.020303	0.1546	0.438829
23	-0.099959	-0.7613	0.224792
24	-0.059889	-0.4561	0.32501
25	-0.089828	-0.6841	0.248316
26	-0.023044	-0.1755	0.430651
27	-0.277741	-2.1152	0.019359
28	0.098473	0.75	0.228158
29	-0.116147	-0.8846	0.190026
30	-0.132195	-1.0068	0.159115
31	-0.118439	-0.902	0.185392
32	-0.003406	-0.0259	0.489696
33	0.092266	0.7027	0.242534
34	-0.020228	-0.1541	0.439052
35	0.08592	0.6543	0.257738
36	-0.079883	-0.6084	0.272659
37	0.01759	0.134	0.446949
38	-0.047787	-0.3639	0.358615
39	0.107624	0.8196	0.207888
40	0.010491	0.0799	0.468297
41	0.002476	0.0189	0.492512
42	0.072536	0.5524	0.291393
43	0.071775	0.5466	0.293368
44	0.056258	0.4285	0.334955
45	-0.020818	-0.1585	0.437289
46	0.033354	0.254	0.400191
47	-0.012768	-0.0972	0.461437
48	0.01551	0.1181	0.45319
49	0.02623	0.1998	0.421181
50	-0.011982	-0.0913	0.463803
51	0.031942	0.2433	0.404331
52	-0.010183	-0.0776	0.469226
53	0.006921	0.0527	0.479071
54	-0.001681	-0.0128	0.494915
55	-0.017457	-0.1329	0.447347
56	0.010545	0.0803	0.468133
57	-0.011416	-0.0869	0.465507
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.068946	-0.5251	0.300766
2	0.186599	1.4211	0.080322
3	-0.06507	-0.4956	0.311041
4	0.161623	1.2309	0.111667
5	0.07992	0.6087	0.272566
6	-0.024448	-0.1862	0.426474
7	0.121023	0.9217	0.180256
8	-0.124942	-0.9515	0.172641
9	0.028511	0.2171	0.414432
10	-0.002294	-0.0175	0.49306
11	0.202055	1.5388	0.064645
12	-0.242065	-1.8435	0.035182
13	-0.116798	-0.8895	0.188703
14	0.077616	0.5911	0.278372
15	-0.009672	-0.0737	0.470768
16	-0.290582	-2.213	0.015423
17	0.055833	0.4252	0.336128
18	0.05559	0.4234	0.336799
19	-0.077193	-0.5879	0.279445
20	-0.045256	-0.3447	0.3658
21	0.03936	0.2998	0.382717
22	-0.028125	-0.2142	0.415572
23	0.079671	0.6068	0.273189
24	-0.14992	-1.1418	0.129123
25	-0.138294	-1.0532	0.148305
26	0.046854	0.3568	0.361258
27	-0.169503	-1.2909	0.100931
28	-0.047585	-0.3624	0.359187
29	-0.054653	-0.4162	0.339391
30	-0.157407	-1.1988	0.117745
31	-0.02299	-0.1751	0.43081
32	-0.071457	-0.5442	0.294194
33	0.141679	1.079	0.142528
34	0.096661	0.7362	0.232303
35	0.074951	0.5708	0.285166
36	-0.054254	-0.4132	0.340497
37	-0.088702	-0.6755	0.25101
38	0.073712	0.5614	0.288353
39	-0.053357	-0.4064	0.342989
40	-0.080958	-0.6166	0.26997
41	0.066026	0.5028	0.308492
42	0.033216	0.253	0.400596
43	-0.131422	-1.0009	0.16052
44	-0.02244	-0.1709	0.432449
45	-0.005083	-0.0387	0.484627
46	-0.127319	-0.9696	0.168127
47	0.049047	0.3735	0.355058
48	-0.04038	-0.3075	0.379773
49	-0.001735	-0.0132	0.49475
50	0.035552	0.2708	0.39377
51	-0.002109	-0.0161	0.49362
52	-0.042824	-0.3261	0.372747
53	-0.064422	-0.4906	0.312772
54	-0.045807	-0.3489	0.364232
55	-0.056106	-0.4273	0.335376
56	-0.092469	-0.7042	0.242057
57	-0.012359	-0.0941	0.462669
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/29/t129363514326r98529xh8o6pu/16lsf1293635274.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t129363514326r98529xh8o6pu/16lsf1293635274.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t129363514326r98529xh8o6pu/2ycsi1293635274.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t129363514326r98529xh8o6pu/2ycsi1293635274.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t129363514326r98529xh8o6pu/3ycsi1293635274.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t129363514326r98529xh8o6pu/3ycsi1293635274.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = 0.5 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 2 ; par7 = 1 ; par8 = 0 ; par9 = 1 ; par10 = FALSE ;

Parameters (R input):

par1 = 60 ; par2 = 0.3 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par9 = 1 ; par10 = FALSE ;

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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