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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: Wed, 15 Dec 2010 15:04:15 +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/t1292425601ngge702jsicwme9.htm/, Retrieved Wed, 15 Dec 2010 16:06:44 +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/t1292425601ngge702jsicwme9.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 «

186448 190530 194207 190855 200779 204428 207617 212071 214239 215883 223484 221529 225247 226699 231406 232324 237192 236727 240698 240688 245283 243556 247826 245798 250479 249216 251896 247616 249994 246552 248771 247551 249745 245742 249019 245841 248771 244723 246878 246014 248496 244351 248016 246509 249426 247840 251035 250161 254278 250801 253985 249174 251287 247947 249992 243805 255812 250417 253033 248705 253950 251484 251093 245996 252721 248019 250464 245571 252690 250183 253639 254436 265280 268705 270643 271480

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	0.895483	7.8066	0
2	0.821927	7.1654	0
3	0.72617	6.3306	0
4	0.643992	5.6142	0
5	0.563035	4.9084	3e-06
6	0.51117	4.4563	1.4e-05
7	0.441458	3.8485	0.000123
8	0.402166	3.506	0.000383
9	0.343752	2.9968	0.001842
10	0.303571	2.6465	0.004941
11	0.258361	2.2523	0.013594
12	0.223326	1.9469	0.02762
13	0.17701	1.5431	0.063476
14	0.148196	1.2919	0.100146
15	0.105132	0.9165	0.181147
16	0.080721	0.7037	0.241881
17	0.049276	0.4296	0.33436
18	0.029727	0.2592	0.398109
19	0.00234	0.0204	0.49189
20	-0.01254	-0.1093	0.456618
21	-0.02051	-0.1788	0.429286
22	-0.022302	-0.1944	0.423183
23	-0.029813	-0.2599	0.39782
24	-0.027601	-0.2406	0.40525
25	-0.030097	-0.2624	0.396869
26	-0.026936	-0.2348	0.407491
27	-0.030708	-0.2677	0.394825
28	-0.032994	-0.2876	0.387204
29	-0.040117	-0.3497	0.363754
30	-0.041917	-0.3654	0.357905
31	-0.051337	-0.4475	0.327876
32	-0.049517	-0.4317	0.333598
33	-0.054416	-0.4744	0.318292
34	-0.056664	-0.494	0.31137
35	-0.061297	-0.5344	0.297321
36	-0.06501	-0.5667	0.28628
37	-0.07177	-0.6257	0.266701
38	-0.076317	-0.6653	0.253932
39	-0.086802	-0.7567	0.225778
40	-0.091987	-0.8019	0.212549
41	-0.099977	-0.8716	0.193092
42	-0.111098	-0.9685	0.167926
43	-0.120704	-1.0523	0.148005
44	-0.128997	-1.1246	0.132155
45	-0.137881	-1.202	0.116543
46	-0.140118	-1.2215	0.112833
47	-0.143246	-1.2488	0.107788
48	-0.143811	-1.2537	0.106895
49	-0.140396	-1.2239	0.112378
50	-0.143976	-1.2552	0.106635
51	-0.144407	-1.2589	0.105958
52	-0.152244	-1.3272	0.094202
53	-0.159536	-1.3908	0.084172
54	-0.16975	-1.4798	0.071524
55	-0.178511	-1.5562	0.061905
56	-0.200912	-1.7515	0.041946
57	-0.197385	-1.7208	0.044681
58	-0.203279	-1.7721	0.040189
59	-0.203487	-1.774	0.040038
60	-0.213835	-1.8642	0.03308

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.895483	7.8066	0
2	0.101145	0.8818	0.190343
3	-0.132493	-1.155	0.125845
4	-0.012371	-0.1078	0.457201
5	-0.020743	-0.1808	0.428489
6	0.094407	0.823	0.206534
7	-0.094477	-0.8236	0.206364
8	0.069213	0.6034	0.274025
9	-0.077072	-0.6719	0.251843
10	0.015755	0.1373	0.44556
11	-0.011704	-0.102	0.459501
12	-0.00951	-0.0829	0.467072
13	-0.049997	-0.4359	0.332086
14	0.012413	0.1082	0.457057
15	-0.046668	-0.4068	0.342634
16	0.018163	0.1583	0.437304
17	-0.018685	-0.1629	0.435519
18	-0.000155	-0.0013	0.499464
19	-0.030856	-0.269	0.394332
20	0.002064	0.018	0.492847
21	0.064669	0.5638	0.287283
22	-0.007458	-0.065	0.474165
23	-0.017676	-0.1541	0.438971
24	0.009847	0.0858	0.465907
25	0.007735	0.0674	0.473209
26	0.006808	0.0594	0.476413
27	-0.022875	-0.1994	0.421233
28	-0.016977	-0.148	0.441367
29	-0.015744	-0.1372	0.445598
30	0.003761	0.0328	0.486966
31	-0.022808	-0.1988	0.42146
32	0.020158	0.1757	0.430486
33	-0.018188	-0.1586	0.437218
34	-0.016715	-0.1457	0.442264
35	-0.007767	-0.0677	0.473096
36	-0.013495	-0.1176	0.453329
37	-0.005992	-0.0522	0.47924
38	-0.02067	-0.1802	0.428739
39	-0.024105	-0.2101	0.41706
40	-0.001303	-0.0114	0.495483
41	-0.004258	-0.0371	0.485244
42	-0.043121	-0.3759	0.354011
43	-0.008225	-0.0717	0.471514
44	-0.012498	-0.109	0.456762
45	-0.004416	-0.0385	0.484695
46	0.004205	0.0367	0.485428
47	-0.007467	-0.0651	0.474134
48	-0.00895	-0.078	0.469007
49	0.01174	0.1023	0.459377
50	-0.041041	-0.3578	0.360747
51	-0.00314	-0.0274	0.489117
52	-0.04517	-0.3938	0.347423
53	-0.01622	-0.1414	0.443964
54	-0.031507	-0.2747	0.392156
55	-0.020049	-0.1748	0.430856
56	-0.084154	-0.7336	0.232712
57	0.079876	0.6963	0.244169
58	-0.025725	-0.2243	0.411578
59	-0.029087	-0.2536	0.400256
60	-0.061325	-0.5346	0.297236

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292425601ngge702jsicwme9/14j5z1292425452.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292425601ngge702jsicwme9/14j5z1292425452.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292425601ngge702jsicwme9/2xamk1292425452.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292425601ngge702jsicwme9/2xamk1292425452.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292425601ngge702jsicwme9/3xamk1292425452.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292425601ngge702jsicwme9/3xamk1292425452.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 4 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 4 ; 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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