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ACF 3

*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 17:17:28 +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/t1292433421vnc13pndbisr8x7.htm/, Retrieved Wed, 15 Dec 2010 18:17:04 +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/t1292433421vnc13pndbisr8x7.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	2 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.54952	-4.6303	8e-06
2	0.150521	1.2683	0.104415
3	0.006681	0.0563	0.477631
4	-0.127243	-1.0722	0.143637
5	0.061836	0.521	0.301981
6	0.024828	0.2092	0.417444
7	-0.071622	-0.6035	0.27405
8	0.002972	0.025	0.490046
9	0.096855	0.8161	0.208583
10	-0.009269	-0.0781	0.468983
11	-0.009418	-0.0794	0.468486
12	-0.074181	-0.6251	0.266967
13	-0.047145	-0.3973	0.346186
14	0.002671	0.0225	0.491053
15	0.08595	0.7242	0.235653
16	-0.085343	-0.7191	0.237215
17	0.058744	0.495	0.311069
18	0.024442	0.206	0.418709
19	-0.064529	-0.5437	0.294165
20	0.010729	0.0904	0.464109
21	0.139642	1.1766	0.121634
22	-0.311082	-2.6212	0.005355
23	0.36221	3.052	0.001598
24	-0.190444	-1.6047	0.056499
25	-0.055241	-0.4655	0.32151
26	0.246219	2.0747	0.020821
27	-0.268748	-2.2645	0.013299
28	0.14377	1.2114	0.114873
29	-0.066104	-0.557	0.289638
30	0.063497	0.535	0.297149
31	-0.083475	-0.7034	0.242061
32	0.175286	1.477	0.072051
33	-0.193172	-1.6277	0.05401
34	-0.010852	-0.0914	0.463699
35	0.065232	0.5497	0.292141
36	-0.026677	-0.2248	0.411397
37	0.004997	0.0421	0.483267
38	0.003846	0.0324	0.487121
39	0.05166	0.4353	0.332334
40	-0.045049	-0.3796	0.352691
41	0.105989	0.8931	0.187417
42	-0.114179	-0.9621	0.169635
43	-0.000131	-0.0011	0.499561
44	0.009963	0.0839	0.466667
45	-0.005236	-0.0441	0.482467
46	0.062119	0.5234	0.301155
47	0.04516	0.3805	0.352345
48	-0.176668	-1.4886	0.070507
49	0.209951	1.7691	0.040588
50	-0.18145	-1.5289	0.065363
51	0.07139	0.6015	0.274698
52	-0.038419	-0.3237	0.373548
53	-0.001185	-0.01	0.496032
54	-0.033228	-0.28	0.390152
55	0.103721	0.874	0.192542
56	-0.074042	-0.6239	0.26735
57	-0.007005	-0.059	0.476549
58	0.023529	0.1983	0.421704
59	-0.030632	-0.2581	0.398533
60	0.009802	0.0826	0.467203

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.54952	-4.6303	8e-06
2	-0.21697	-1.8282	0.035858
3	-0.017872	-0.1506	0.440364
4	-0.147548	-1.2433	0.108931
5	-0.131878	-1.1112	0.13511
6	-0.005395	-0.0455	0.481936
7	-0.058596	-0.4937	0.311506
8	-0.133605	-1.1258	0.132026
9	0.044221	0.3726	0.355274
10	0.15017	1.2654	0.10494
11	0.072266	0.6089	0.272259
12	-0.112934	-0.9516	0.172265
13	-0.192293	-1.6203	0.054802
14	-0.173205	-1.4595	0.074425
15	-0.004755	-0.0401	0.484076
16	-0.057701	-0.4862	0.314161
17	-0.048516	-0.4088	0.341957
18	0.034922	0.2943	0.384709
19	-0.048831	-0.4115	0.34099
20	-0.153187	-1.2908	0.100485
21	0.181652	1.5306	0.065153
22	-0.10193	-0.8589	0.196648
23	0.168404	1.419	0.080137
24	0.085102	0.7171	0.237837
25	-0.199438	-1.6805	0.048628
26	0.075105	0.6328	0.264433
27	-0.063013	-0.531	0.298554
28	-0.020535	-0.173	0.431558
29	-0.069186	-0.583	0.280879
30	0.069383	0.5846	0.280324
31	-0.037542	-0.3163	0.376337
32	0.126859	1.0689	0.144361
33	-0.047324	-0.3988	0.345634
34	-0.214343	-1.8061	0.037571
35	-0.078541	-0.6618	0.255122
36	0.017753	0.1496	0.440756
37	0.018483	0.1557	0.438341
38	-0.10055	-0.8473	0.199851
39	0.110776	0.9334	0.176885
40	0.037258	0.3139	0.377244
41	0.015704	0.1323	0.447552
42	0.020205	0.1703	0.432649
43	0.070916	0.5976	0.27602
44	-0.063449	-0.5346	0.297289
45	0.059096	0.498	0.310029
46	-0.040531	-0.3415	0.36686
47	-0.010943	-0.0922	0.463395
48	-0.011144	-0.0939	0.462727
49	-0.057751	-0.4866	0.314013
50	-0.056702	-0.4778	0.317137
51	-0.00159	-0.0134	0.494676
52	-0.010323	-0.087	0.465466
53	-0.044074	-0.3714	0.355733
54	-0.015544	-0.131	0.448084
55	-0.011213	-0.0945	0.462497
56	-0.105016	-0.8849	0.189603
57	0.023741	0.2	0.42101
58	-0.087188	-0.7347	0.232483
59	0.015831	0.1334	0.447128
60	-0.044485	-0.3748	0.354448

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292433421vnc13pndbisr8x7/1slak1292433445.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292433421vnc13pndbisr8x7/1slak1292433445.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292433421vnc13pndbisr8x7/2kurn1292433445.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292433421vnc13pndbisr8x7/2kurn1292433445.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292433421vnc13pndbisr8x7/3kurn1292433445.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292433421vnc13pndbisr8x7/3kurn1292433445.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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