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W9 ACF

*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: Mon, 06 Dec 2010 17:45:00 +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/06/t1291657418y6bxafmihotyiic.htm/, Retrieved Mon, 06 Dec 2010 18:43:38 +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/06/t1291657418y6bxafmihotyiic.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 «

655362 873127 1107897 1555964 1671159 1493308 2957796 2638691 1305669 1280496 921900 867888 652586 913831 1108544 1555827 1699283 1509458 3268975 2425016 1312703 1365498 934453 775019 651142 843192 1146766 1652601 1465906 1652734 2922334 2702805 1458956 1410363 1019279 936574 708917 885295 1099663 1576220 1487870 1488635 2882530 2677026 1404398 1344370 936865 872705 628151 953712 1160384 1400618 1661511 1495347 2918786 2775677 1407026 1370199 964526 850851 683118 847224 1073256 1514326 1503734 1507712 2865698 2788128 1391596 1366378 946295 859626

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.580323	4.9242	3e-06
2	0.169292	1.4365	0.077597
3	-0.022645	-0.1921	0.424084
4	-0.334884	-2.8416	0.002917
5	-0.557729	-4.7325	5e-06
6	-0.653629	-5.5462	0
7	-0.526616	-4.4685	1.4e-05
8	-0.269955	-2.2906	0.012457
9	0.004388	0.0372	0.4852
10	0.170259	1.4447	0.076441
11	0.505958	4.2932	2.7e-05
12	0.823558	6.9881	0
13	0.491206	4.168	4.2e-05
14	0.149716	1.2704	0.104019
15	-0.009742	-0.0827	0.467173
16	-0.271984	-2.3079	0.011942
17	-0.452441	-3.8391	0.000131
18	-0.533287	-4.5251	1.2e-05
19	-0.427058	-3.6237	0.000269
20	-0.217796	-1.8481	0.03435
21	-0.009846	-0.0835	0.466824
22	0.130729	1.1093	0.135501
23	0.390947	3.3173	0.000714
24	0.649499	5.5112	0
25	0.407761	3.46	0.000456
26	0.11683	0.9913	0.162422
27	-0.003018	-0.0256	0.489821
28	-0.199177	-1.6901	0.04767
29	-0.35361	-3.0005	0.001851
30	-0.413491	-3.5086	0.00039
31	-0.333684	-2.8314	0.003002
32	-0.17491	-1.4842	0.071065
33	-0.009183	-0.0779	0.469055
34	0.101317	0.8597	0.196404
35	0.282385	2.3961	0.009585
36	0.493588	4.1882	3.9e-05
37	0.314247	2.6665	0.00473
38	0.090934	0.7716	0.221439
39	0.002029	0.0172	0.493156
40	-0.150154	-1.2741	0.103363
41	-0.258135	-2.1903	0.015869
42	-0.30089	-2.5531	0.006397
43	-0.239205	-2.0297	0.02304
44	-0.127352	-1.0806	0.141737
45	-0.0043	-0.0365	0.485499
46	0.073395	0.6228	0.267698
47	0.188674	1.601	0.056883
48	0.335012	2.8427	0.002909

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.580323	4.9242	3e-06
2	-0.252529	-2.1428	0.017756
3	0.00137	0.0116	0.49538
4	-0.444964	-3.7756	0.000163
5	-0.239114	-2.0289	0.023081
6	-0.455135	-3.8619	0.000122
7	-0.155908	-1.3229	0.095024
8	-0.296482	-2.5157	0.007055
9	-0.137955	-1.1706	0.122813
10	-0.570015	-4.8367	4e-06
11	0.242591	2.0585	0.021583
12	0.244486	2.0745	0.020803
13	-0.384684	-3.2642	0.000841
14	-0.140458	-1.1918	0.118622
15	-0.111465	-0.9458	0.173704
16	-0.001189	-0.0101	0.49599
17	0.001882	0.016	0.493652
18	0.013329	0.1131	0.455132
19	0.010644	0.0903	0.464142
20	-0.109556	-0.9296	0.177839
21	0.017348	0.1472	0.441691
22	-0.002071	-0.0176	0.493013
23	-0.029062	-0.2466	0.40296
24	0.029294	0.2486	0.402201
25	0.016375	0.1389	0.44494
26	-0.110983	-0.9417	0.174743
27	0.007431	0.0631	0.474948
28	0.007801	0.0662	0.473705
29	-0.017509	-0.1486	0.441153
30	0.021914	0.1859	0.426504
31	-0.026431	-0.2243	0.41159
32	-0.01444	-0.1225	0.451411
33	0.037832	0.321	0.374565
34	0.027565	0.2339	0.407864
35	-0.046318	-0.393	0.347731
36	0.001612	0.0137	0.494563
37	-0.064318	-0.5458	0.293459
38	0.107135	0.9091	0.183174
39	-0.118181	-1.0028	0.159658
40	0.035376	0.3002	0.382454
41	-0.025096	-0.2129	0.415986
42	0.023119	0.1962	0.422516
43	0.022696	0.1926	0.423916
44	0.015337	0.1301	0.448411
45	0.021696	0.1841	0.427226
46	0.030236	0.2566	0.399126
47	0.001842	0.0156	0.493785
48	-0.082264	-0.698	0.243703

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291657418y6bxafmihotyiic/1dk731291657496.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291657418y6bxafmihotyiic/1dk731291657496.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291657418y6bxafmihotyiic/26to61291657496.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291657418y6bxafmihotyiic/26to61291657496.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 0 ; 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 (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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