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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: Fri, 27 Nov 2009 05:10:08 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/27/t1259323851oc5xmbcxgje3del.htm/, Retrieved Fri, 27 Nov 2009 13:10:54 +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/2009/Nov/27/t1259323851oc5xmbcxgje3del.htm/},
    year = {2009},
}
@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 = {2009},
    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 «

19 18 19 19 22 23 20 14 14 14 15 11 17 16 20 24 23 20 21 19 23 23 23 23 27 26 17 24 26 24 27 27 26 24 23 23 24 17 21 19 22 22 18 16 14 12 14 16 8 3 0 5 1 1 3 6 7 8 14 14 13

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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.838306	5.8681	0
2	0.770642	5.3945	1e-06
3	0.67659	4.7361	9e-06
4	0.59063	4.1344	6.9e-05
5	0.520852	3.646	0.000322
6	0.447169	3.1302	0.001471
7	0.3921	2.7447	0.004221
8	0.35417	2.4792	0.008328
9	0.318234	2.2276	0.015264
10	0.225657	1.5796	0.060317
11	0.155601	1.0892	0.140696
12	0.014714	0.103	0.459193
13	0.018876	0.1321	0.447709
14	-0.068878	-0.4821	0.315926
15	-0.085562	-0.5989	0.275989
16	-0.09527	-0.6669	0.253985
17	-0.146593	-1.0261	0.154931
18	-0.198313	-1.3882	0.085679
19	-0.246646	-1.7265	0.045277
20	-0.289518	-2.0266	0.02408
21	-0.348015	-2.4361	0.009264
22	-0.331695	-2.3219	0.01222
23	-0.354916	-2.4844	0.008221
24	-0.3376	-2.3632	0.011065
25	-0.34404	-2.4083	0.009918
26	-0.308867	-2.1621	0.017762
27	-0.329019	-2.3031	0.012778
28	-0.352878	-2.4701	0.008517
29	-0.360594	-2.5242	0.007444
30	-0.348778	-2.4414	0.009143
31	-0.306151	-2.1431	0.01855
32	-0.268865	-1.8821	0.032887
33	-0.225879	-1.5812	0.060138
34	-0.187039	-1.3093	0.098274
35	-0.11081	-0.7757	0.220836
36	-0.073843	-0.5169	0.303775

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.838306	5.8681	0
2	0.22838	1.5987	0.058163
3	-0.047402	-0.3318	0.370722
4	-0.05066	-0.3546	0.362197
5	0.010713	0.075	0.470263
6	-0.029546	-0.2068	0.418503
7	0.011588	0.0811	0.467839
8	0.052134	0.3649	0.358364
9	0.01354	0.0948	0.462437
10	-0.225255	-1.5768	0.06064
11	-0.087208	-0.6105	0.272191
12	-0.28852	-2.0196	0.024454
13	0.326413	2.2849	0.013343
14	-0.161359	-1.1295	0.13209
15	0.119955	0.8397	0.202582
16	0.000652	0.0046	0.49819
17	-0.179796	-1.2586	0.107074
18	-0.209627	-1.4674	0.07433
19	0.017389	0.1217	0.451808
20	0.041667	0.2917	0.385884
21	-0.022697	-0.1589	0.437207
22	0.117775	0.8244	0.206846
23	-0.040181	-0.2813	0.389846
24	-0.22112	-1.5478	0.064048
25	0.078837	0.5519	0.291776
26	-0.005466	-0.0383	0.484818
27	0.021074	0.1475	0.441665
28	-0.07137	-0.4996	0.3098
29	-0.075235	-0.5266	0.300407
30	0.02788	0.1952	0.423039
31	0.063743	0.4462	0.328708
32	0.02494	0.1746	0.431063
33	-0.055059	-0.3854	0.350799
34	0.200354	1.4025	0.083538
35	-0.006046	-0.0423	0.483207
36	-0.038741	-0.2712	0.393693

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259323851oc5xmbcxgje3del/1bzkx1259323807.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259323851oc5xmbcxgje3del/1bzkx1259323807.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259323851oc5xmbcxgje3del/28gvv1259323807.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259323851oc5xmbcxgje3del/28gvv1259323807.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = MA ; 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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