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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: Mon, 13 Dec 2010 20:04:16 +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/13/t1292270548y0s5m82idse32l5.htm/, Retrieved Mon, 13 Dec 2010 21:02:28 +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/13/t1292270548y0s5m82idse32l5.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 «

113 95,4 86,2 111,7 97,5 99,7 111,5 91,8 86,3 88,7 95,1 105,1 104,5 89,1 82,6 102,7 91,8 94,1 103,1 93,2 91 94,3 99,4 115,7 116,8 99,8 96 115,9 109,1 117,3 109,8 112,8 110,7 100 113,3 122,4 112,5 104,2 92,5 117,2 109,3 106,1 118,8 105,3 106 102 112,9 116,5 114,8 100,5 85,4 114,6 109,9 100,7 115,5 100,7 99 102,3

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.628234	4.2609	5e-05
2	0.641434	4.3504	3.7e-05
3	0.710822	4.821	8e-06
4	0.41793	2.8345	0.003398
5	0.413604	2.8052	0.003672
6	0.316623	2.1474	0.018531
7	0.101731	0.69	0.246839
8	0.092651	0.6284	0.266428
9	-0.082631	-0.5604	0.288954
10	-0.129665	-0.8794	0.19187
11	-0.179913	-1.2202	0.114299
12	-0.315777	-2.1417	0.018773
13	-0.287235	-1.9481	0.028759
14	-0.339563	-2.303	0.012925
15	-0.366238	-2.4839	0.008349
16	-0.395919	-2.6853	0.005023
17	-0.348801	-2.3657	0.011134
18	-0.313667	-2.1274	0.01939
19	-0.325759	-2.2094	0.016082
20	-0.25548	-1.7328	0.04492
21	-0.245243	-1.6633	0.051524
22	-0.252368	-1.7116	0.046849
23	-0.148327	-1.006	0.159839
24	-0.187262	-1.2701	0.105223
25	-0.139025	-0.9429	0.175325
26	-0.087755	-0.5952	0.277318
27	-0.136391	-0.9251	0.179883
28	-0.055972	-0.3796	0.352987
29	-0.025869	-0.1755	0.430748
30	-0.064217	-0.4355	0.332604
31	0.016489	0.1118	0.45572
32	0.028896	0.196	0.422743
33	0.020544	0.1393	0.444896
34	0.057805	0.3921	0.348415
35	0.081529	0.553	0.291484
36	0.069081	0.4685	0.32081
37	0.098534	0.6683	0.253644
38	0.117462	0.7967	0.21487
39	0.085114	0.5773	0.283286
40	0.074823	0.5075	0.307123
41	0.077821	0.5278	0.300086
42	0.051532	0.3495	0.364153
43	0.044125	0.2993	0.38304
44	0.031217	0.2117	0.416628
45	0.005075	0.0344	0.486345
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	0.628234	4.2609	5e-05
2	0.407644	2.7648	0.004085
3	0.427997	2.9028	0.002831
4	-0.365705	-2.4803	0.008423
5	-0.186721	-1.2664	0.105872
6	-0.213543	-1.4483	0.077155
7	-0.159462	-1.0815	0.142551
8	-0.024899	-0.1689	0.433318
9	-0.148102	-1.0045	0.160201
10	0.149539	1.0142	0.157892
11	-0.003064	-0.0208	0.491755
12	-0.061166	-0.4148	0.340091
13	-0.065056	-0.4412	0.330557
14	-0.044098	-0.2991	0.383111
15	0.061443	0.4167	0.339409
16	-0.283845	-1.9251	0.030205
17	0.118324	0.8025	0.213193
18	0.091581	0.6211	0.26879
19	0.086524	0.5868	0.280092
20	-0.087012	-0.5901	0.278991
21	-0.234626	-1.5913	0.059194
22	-0.09694	-0.6575	0.257075
23	-0.037214	-0.2524	0.40093
24	-0.035079	-0.2379	0.406502
25	0.019324	0.1311	0.448148
26	0.066676	0.4522	0.326619
27	0.00197	0.0134	0.4947
28	-0.111693	-0.7575	0.226295
29	0.055522	0.3766	0.354112
30	-0.066075	-0.4481	0.328078
31	-0.02495	-0.1692	0.433184
32	-0.031568	-0.2141	0.415706
33	0.009951	0.0675	0.473243
34	0.009676	0.0656	0.473979
35	0.05449	0.3696	0.356699
36	-0.079343	-0.5381	0.296541
37	-0.054428	-0.3691	0.356855
38	-0.03603	-0.2444	0.404016
39	-0.068641	-0.4655	0.321869
40	-0.16016	-1.0863	0.141513
41	-0.021055	-0.1428	0.443535
42	0.061938	0.4201	0.338189
43	0.031334	0.2125	0.416321
44	0.038206	0.2591	0.398348
45	-0.001187	-0.0081	0.496805
46	NA	NA	NA
47	NA	NA	NA
48	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/13/t1292270548y0s5m82idse32l5/13qx71292270652.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/13/t1292270548y0s5m82idse32l5/13qx71292270652.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/13/t1292270548y0s5m82idse32l5/23qx71292270652.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/13/t1292270548y0s5m82idse32l5/23qx71292270652.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; 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 (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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