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ACF 2

*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, 15 Dec 2010 17:14:50 +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/15/t1292433166dbwwno3bvgwh4fb.htm/, Retrieved Wed, 15 Dec 2010 18:12:49 +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/15/t1292433166dbwwno3bvgwh4fb.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 «

12231 13604 15107 10853 13698 11536 8879 11005 13656 12631 10931 8064 12332 12452 14029 10003 12388 10492 9114 9304 9660 10569 8356 5998 10408 11420 11538 10860 10412 9521 7602 8197 10449 11561 8603 8080 10792 11943 11179 9939 10065 11021 9226 9554 11468 9937 8928 8395 11996 12385 15277 12657 11482 16797 11047 11794 13077 11725 10921 9334 11431 13085 16394 15701 14936 18282 12824 14784 16061 14814 14375 13644 16397 19254 21943 16731 22065 20937 18242 19017 20372 20561 18267 16170

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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.307151	-2.7983	0.003193
2	-0.167261	-1.5238	0.065677
3	0.017651	0.1608	0.436316
4	0.021634	0.1971	0.422117
5	0.081816	0.7454	0.229075
6	-0.154784	-1.4101	0.081117
7	0.007103	0.0647	0.474281
8	0.075622	0.6889	0.246388
9	0.030625	0.279	0.390466
10	-0.281994	-2.5691	0.005993
11	-0.050358	-0.4588	0.323794
12	0.543068	4.9476	2e-06
13	-0.168489	-1.535	0.064293
14	-0.087602	-0.7981	0.213547
15	-0.035608	-0.3244	0.373224
16	0.016524	0.1505	0.440353
17	0.136166	1.2405	0.109138
18	-0.174138	-1.5865	0.058218
19	9.1e-05	8e-04	0.49967
20	0.117989	1.0749	0.14276
21	-0.029819	-0.2717	0.393277
22	-0.302288	-2.754	0.003616
23	0.078125	0.7118	0.239306
24	0.308135	2.8072	0.003113
25	-0.041224	-0.3756	0.354099
26	-0.064032	-0.5834	0.280616
27	-0.098705	-0.8992	0.185562
28	0.094382	0.8599	0.19617
29	0.108275	0.9864	0.163395
30	-0.1612	-1.4686	0.07286
31	-0.007292	-0.0664	0.473597
32	0.13998	1.2753	0.102885
33	-0.122657	-1.1175	0.133511
34	-0.101619	-0.9258	0.178618
35	-0.061671	-0.5619	0.287865
36	0.218807	1.9934	0.02475
37	0.079535	0.7246	0.235369
38	-0.164481	-1.4985	0.068899
39	-0.023499	-0.2141	0.415503
40	0.059268	0.54	0.295338
41	0.123941	1.1292	0.131042
42	-0.168512	-1.5352	0.064267
43	0.023545	0.2145	0.41534
44	0.068296	0.6222	0.267757
45	-0.088558	-0.8068	0.211044
46	-0.019928	-0.1816	0.428189
47	-0.123274	-1.1231	0.132321
48	0.180565	1.645	0.051873
49	0.141591	1.29	0.100324
50	-0.21023	-1.9153	0.02945
51	0.015798	0.1439	0.442952
52	0.04717	0.4297	0.334251
53	0.021697	0.1977	0.421895
54	-0.068472	-0.6238	0.267232
55	0.049913	0.4547	0.325247
56	0.022731	0.2071	0.418224
57	-0.053915	-0.4912	0.312295
58	-0.038666	-0.3523	0.362765
59	-0.122857	-1.1193	0.133124
60	0.206499	1.8813	0.031719

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.307151	-2.7983	0.003193
2	-0.288854	-2.6316	0.005065
3	-0.165385	-1.5067	0.067839
4	-0.099825	-0.9095	0.182873
5	0.041182	0.3752	0.354241
6	-0.133697	-1.218	0.11333
7	-0.086601	-0.789	0.216188
8	-0.018513	-0.1687	0.433238
9	0.036025	0.3282	0.371792
10	-0.308696	-2.8124	0.003068
11	-0.349254	-3.1819	0.00103
12	0.367866	3.3514	0.000606
13	0.163948	1.4936	0.069531
14	0.079917	0.7281	0.234307
15	0.016212	0.1477	0.44147
16	-0.054683	-0.4982	0.309836
17	0.033484	0.3051	0.380546
18	-0.018857	-0.1718	0.432009
19	-0.012407	-0.113	0.455138
20	0.012187	0.111	0.455932
21	-0.028923	-0.2635	0.396408
22	-0.173321	-1.579	0.059066
23	-0.05637	-0.5136	0.304463
24	0.006759	0.0616	0.475523
25	0.07623	0.6945	0.244657
26	0.050493	0.46	0.323355
27	-0.009111	-0.083	0.467024
28	0.023155	0.211	0.416721
29	0.027598	0.2514	0.401053
30	0.018375	0.1674	0.433728
31	-0.033993	-0.3097	0.378785
32	-0.004685	-0.0427	0.483028
33	-0.111002	-1.0113	0.157412
34	0.140735	1.2822	0.101678
35	-0.094965	-0.8652	0.19472
36	-0.055691	-0.5074	0.30662
37	0.045343	0.4131	0.3403
38	-0.095401	-0.8691	0.193638
39	0.031778	0.2895	0.386455
40	-0.05476	-0.4989	0.309589
41	0.045015	0.4101	0.341393
42	-0.054562	-0.4971	0.310222
43	-0.034547	-0.3147	0.376874
44	-0.088513	-0.8064	0.211161
45	-0.061069	-0.5564	0.289729
46	0.020306	0.185	0.426841
47	0.014697	0.1339	0.446906
48	-0.032456	-0.2957	0.384102
49	0.071977	0.6557	0.256903
50	0.011832	0.1078	0.457209
51	-0.017679	-0.1611	0.436216
52	0.007954	0.0725	0.471205
53	-0.185152	-1.6868	0.047697
54	-0.086835	-0.7911	0.215568
55	0.0433	0.3945	0.347118
56	0.082698	0.7534	0.226666
57	-0.056027	-0.5104	0.305551
58	-0.08257	-0.7523	0.227014
59	-0.023223	-0.2116	0.41648
60	-0.017963	-0.1637	0.435202

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292433166dbwwno3bvgwh4fb/1b8bu1292433286.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292433166dbwwno3bvgwh4fb/1b8bu1292433286.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292433166dbwwno3bvgwh4fb/240tf1292433286.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292433166dbwwno3bvgwh4fb/240tf1292433286.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292433166dbwwno3bvgwh4fb/340tf1292433286.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292433166dbwwno3bvgwh4fb/340tf1292433286.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; 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 (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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