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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, 28 Dec 2010 12:28:43 +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/28/t1293539194tub9haticxaqrz4.htm/, Retrieved Tue, 28 Dec 2010 13:26:34 +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/28/t1293539194tub9haticxaqrz4.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 «

6 6 8 4 8 10 9 12 9 11 11 11 11 11 9 8 6 7 8 6 5 2 3 3 7 8 7 7 6 6 7 5 5 5 4 4 4 1 -1 3 4 3 2 1 4 3 5 6 6 6 6 6 5 6 5 6 5 7 4 5 6 6 5 3 2 3 3 2 0 4 4 5 6 6 5 5 3 5 5 5 3 6 6 4 6 5 4 5 5 4 3 2 3 2 -1 0 -2 1 -2 -2 -2 -6 -4 -2 0 -5 -4 -5 -1 -2 -4 -1 1 1 -2 1 1 3 3 1 1 0 2 2 -1 1 0 1 1 3 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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.303627	-3.4619	0.000363
2	-0.024219	-0.2761	0.391442
3	-0.09504	-1.0836	0.140269
4	0.027852	0.3176	0.375664
5	0.162887	1.8572	0.032773
6	-0.078965	-0.9003	0.184803
7	0.039551	0.451	0.326388
8	-0.095343	-1.0871	0.139507
9	0.056066	0.6393	0.261892
10	-0.12401	-1.4139	0.079885
11	0.039542	0.4508	0.326425
12	-0.024314	-0.2772	0.391025
13	-0.019576	-0.2232	0.411867
14	-0.045652	-0.5205	0.301797
15	0.035011	0.3992	0.345204
16	0.072862	0.8308	0.203818
17	-0.145068	-1.654	0.050267
18	0.084782	0.9667	0.167754
19	-0.102479	-1.1684	0.122385
20	0.096483	1.1001	0.136665
21	-0.031154	-0.3552	0.361506
22	0.042325	0.4826	0.315102
23	0.025439	0.29	0.386121
24	-0.152559	-1.7394	0.042162
25	0.108032	1.2318	0.110132
26	0.004172	0.0476	0.481067
27	0.001653	0.0189	0.492494
28	-0.05057	-0.5766	0.282609
29	-0.086273	-0.9837	0.163553
30	0.079868	0.9106	0.182085
31	0.061049	0.6961	0.243814
32	-0.100137	-1.1417	0.12783
33	0.004375	0.0499	0.480147
34	0.001856	0.0212	0.491573
35	0.080222	0.9147	0.181029
36	-0.137926	-1.5726	0.059121
37	0.073471	0.8377	0.201869
38	0.033391	0.3807	0.352016
39	-0.030975	-0.3532	0.362266
40	0.006948	0.0792	0.468488
41	-0.099574	-1.1353	0.129165
42	0.158939	1.8122	0.036133
43	-0.004545	-0.0518	0.479373
44	-0.038024	-0.4335	0.332668
45	-0.014177	-0.1616	0.435918
46	0.016562	0.1888	0.425257
47	0.028193	0.3214	0.374193
48	0.04967	0.5663	0.286075

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.303627	-3.4619	0.000363
2	-0.128229	-1.462	0.073072
3	-0.159338	-1.8167	0.035781
4	-0.068321	-0.779	0.218705
5	0.149553	1.7052	0.045276
6	0.0181	0.2064	0.418411
7	0.059698	0.6807	0.248648
8	-0.041727	-0.4758	0.317523
9	0.004606	0.0525	0.479098
10	-0.162558	-1.8534	0.033043
11	-0.069773	-0.7955	0.213876
12	-0.075157	-0.8569	0.196533
13	-0.061347	-0.6995	0.242755
14	-0.096001	-1.0946	0.137862
15	0.032677	0.3726	0.355037
16	0.088878	1.0134	0.156384
17	-0.089839	-1.0243	0.153794
18	0.024566	0.2801	0.389926
19	-0.081005	-0.9236	0.178703
20	-0.029218	-0.3331	0.369785
21	-0.052959	-0.6038	0.273506
22	0.040415	0.4608	0.322855
23	0.04422	0.5042	0.307494
24	-0.127576	-1.4546	0.074096
25	0.008146	0.0929	0.463072
26	0.054452	0.6208	0.267893
27	-0.070652	-0.8056	0.210985
28	-0.0569	-0.6488	0.25882
29	-0.124255	-1.4167	0.079477
30	-0.027308	-0.3114	0.378012
31	0.034732	0.396	0.346376
32	-0.074478	-0.8492	0.198671
33	0.007274	0.0829	0.467014
34	-0.015305	-0.1745	0.43087
35	0.076745	0.875	0.191586
36	-0.159699	-1.8208	0.035465
37	0.000552	0.0063	0.497496
38	-0.002698	-0.0308	0.487754
39	-0.04087	-0.466	0.321
40	-0.024788	-0.2826	0.388954
41	-0.119392	-1.3613	0.087891
42	0.081795	0.9326	0.176377
43	0.044908	0.512	0.304749
44	-0.012365	-0.141	0.44405
45	0.016593	0.1892	0.425118
46	-0.037743	-0.4303	0.333833
47	-0.004851	-0.0553	0.477989
48	0.050131	0.5716	0.284296

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293539194tub9haticxaqrz4/19b5v1293539319.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293539194tub9haticxaqrz4/19b5v1293539319.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293539194tub9haticxaqrz4/29b5v1293539319.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293539194tub9haticxaqrz4/29b5v1293539319.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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

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 (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='lags',ylab='ACF')

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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