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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 16:14:30 +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/t1292343176sk7z0v1sbxw2aup.htm/, Retrieved Tue, 14 Dec 2010 17:12:58 +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/t1292343176sk7z0v1sbxw2aup.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 «

-820.8 993.3 741.7 603.6 -145.8 -35.1 395.1 523.1 462.3 183.4 791.5 344.8 -217.0 406.7 228.6 -580.1 -1550.4 -1447.5 -40.1 -1033.5 -925.6 -347.8 -447.7 -102.6 -2062.2 -929.7 -720.7 -1541.8 -1432.3 -1216.2 -212.8 -378.2 76.9 -101.3 220.4 495.6 -1035.2 61.8 -734.8 -6.9 -1061.1 -854.6 -186.5 244.0 -992.6 -335.2 316.8 477.6 -572.1 1115.2

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	5 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.479176	-2.9147	0.003006
2	0.115827	0.7046	0.242751
3	0.118637	0.7216	0.237525
4	-0.027686	-0.1684	0.43359
5	-0.082838	-0.5039	0.308665
6	0.016921	0.1029	0.459289
7	-0.001462	-0.0089	0.496476
8	-0.032214	-0.1959	0.422861
9	0.023195	0.1411	0.444282
10	-0.116924	-0.7112	0.240704
11	0.287933	1.7514	0.044079
12	-0.269612	-1.64	0.054742
13	-0.072602	-0.4416	0.330667
14	0.197182	1.1994	0.118996
15	-0.255894	-1.5565	0.064046
16	0.043952	0.2674	0.395342
17	-0.061551	-0.3744	0.355122
18	0.124924	0.7599	0.22607
19	-0.110452	-0.6719	0.252926
20	0.103998	0.6326	0.265445
21	-0.020264	-0.1233	0.451283
22	0.05777	0.3514	0.363641
23	-0.03985	-0.2424	0.404905
24	-0.097794	-0.5949	0.277779
25	0.222623	1.3542	0.091949
26	-0.207879	-1.2645	0.106983
27	0.092627	0.5634	0.288271
28	0.04766	0.2899	0.386754
29	0.040809	0.2482	0.402664
30	-0.078382	-0.4768	0.318162
31	0.117364	0.7139	0.239885
32	-0.047948	-0.2917	0.38609
33	-0.040321	-0.2453	0.403804
34	-0.010198	-0.062	0.475436
35	-0.025209	-0.1533	0.439482
36	-0.033165	-0.2017	0.420614
37	NA	NA	NA
38	NA	NA	NA
39	NA	NA	NA
40	NA	NA	NA
41	NA	NA	NA
42	NA	NA	NA
43	NA	NA	NA
44	NA	NA	NA
45	NA	NA	NA
46	NA	NA	NA
47	NA	NA	NA
48	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.479176	-2.9147	0.003006
2	-0.147695	-0.8984	0.187393
3	0.148045	0.9005	0.186833
4	0.154098	0.9373	0.177331
5	-0.061387	-0.3734	0.355489
6	-0.138452	-0.8422	0.202552
7	-0.072908	-0.4435	0.330001
8	-0.006584	-0.04	0.484136
9	0.049853	0.3032	0.381702
10	-0.134534	-0.8183	0.209202
11	0.228339	1.3889	0.086579
12	-0.024252	-0.1475	0.441762
13	-0.338972	-2.0619	0.023147
14	-0.083234	-0.5063	0.307828
15	-0.143191	-0.871	0.194685
16	-0.018818	-0.1145	0.454743
17	-0.135908	-0.8267	0.206855
18	0.075814	0.4612	0.323693
19	0.066225	0.4028	0.344696
20	0.032885	0.2	0.421276
21	-0.023347	-0.142	0.443919
22	-0.077791	-0.4732	0.319431
23	0.047507	0.289	0.387107
24	-0.103043	-0.6268	0.267325
25	0.024162	0.147	0.441975
26	0.026691	0.1624	0.435955
27	0.02187	0.133	0.447444
28	0.026448	0.1609	0.436532
29	0.005055	0.0308	0.487817
30	-0.04666	-0.2838	0.389064
31	0.049833	0.3031	0.381748
32	-0.027652	-0.1682	0.433672
33	-0.008458	-0.0514	0.479623
34	-0.076124	-0.463	0.323021
35	0.048499	0.295	0.384818
36	-0.159333	-0.9692	0.169373
37	NA	NA	NA
38	NA	NA	NA
39	NA	NA	NA
40	NA	NA	NA
41	NA	NA	NA
42	NA	NA	NA
43	NA	NA	NA
44	NA	NA	NA
45	NA	NA	NA
46	NA	NA	NA
47	NA	NA	NA
48	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/14/t1292343176sk7z0v1sbxw2aup/17ygj1292343265.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/14/t1292343176sk7z0v1sbxw2aup/17ygj1292343265.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/14/t1292343176sk7z0v1sbxw2aup/27ygj1292343265.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/14/t1292343176sk7z0v1sbxw2aup/27ygj1292343265.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 1 ; 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 (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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