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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, 07 Dec 2010 17:58:45 +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/07/t1291744665eahwanpq4h52beg.htm/, Retrieved Tue, 07 Dec 2010 18:57:46 +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/07/t1291744665eahwanpq4h52beg.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	-0.317498	-2.1997	0.016339
2	0.23709	1.6426	0.0535
3	0.073833	0.5115	0.305662
4	-0.0085	-0.0589	0.476642
5	0.087561	0.6066	0.273473
6	-0.094228	-0.6528	0.258489
7	-0.167911	-1.1633	0.125224
8	-0.021706	-0.1504	0.440547
9	-0.105651	-0.732	0.233873
10	-0.199022	-1.3789	0.087165
11	0.074402	0.5155	0.304295
12	-0.439446	-3.0446	0.001888
13	0.1164	0.8064	0.211982
14	-0.10566	-0.732	0.233854
15	0.001204	0.0083	0.49669
16	0.004919	0.0341	0.486477
17	0.034048	0.2359	0.40726
18	0.203636	1.4108	0.082372
19	0.023393	0.1621	0.435966
20	-0.004005	-0.0277	0.48899
21	0.216836	1.5023	0.069788
22	-0.089567	-0.6205	0.268921
23	0.183417	1.2708	0.10497
24	-0.067755	-0.4694	0.320447
25	-0.012621	-0.0874	0.465342
26	0.04516	0.3129	0.377865
27	-0.057715	-0.3999	0.345517
28	0.010733	0.0744	0.470516
29	-0.015257	-0.1057	0.458128
30	-0.15548	-1.0772	0.143388
31	0.056401	0.3908	0.348852
32	0.05461	0.3784	0.353419
33	-0.185412	-1.2846	0.102554
34	0.1447	1.0025	0.160562
35	-0.123601	-0.8563	0.198035
36	0.080706	0.5591	0.289331
37	0.013414	0.0929	0.46317
38	-0.025656	-0.1777	0.429834
39	0.025939	0.1797	0.429069
40	0.014526	0.1006	0.460129
41	-0.011891	-0.0824	0.467343
42	0.010509	0.0728	0.47113
43	-0.008081	-0.056	0.477792
44	0.002466	0.0171	0.493221
45	0.002964	0.0205	0.491849
46	-0.002432	-0.0168	0.493314
47	0.000224	0.0016	0.499384
48	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.317498	-2.1997	0.016339
2	0.151564	1.0501	0.149473
3	0.211511	1.4654	0.074667
4	0.037495	0.2598	0.398075
5	0.03483	0.2413	0.405171
6	-0.097613	-0.6763	0.251053
7	-0.300549	-2.0823	0.021336
8	-0.180209	-1.2485	0.108947
9	-0.047568	-0.3296	0.371584
10	-0.180872	-1.2531	0.108116
11	0.052832	0.366	0.357975
12	-0.367502	-2.5461	0.007078
13	-0.229612	-1.5908	0.05911
14	-0.090358	-0.626	0.267135
15	0.030986	0.2147	0.415465
16	-0.035251	-0.2442	0.404048
17	-0.017644	-0.1222	0.451608
18	0.152573	1.0571	0.147889
19	-0.086426	-0.5988	0.27607
20	-0.308332	-2.1362	0.018896
21	0.026608	0.1843	0.427259
22	-0.208952	-1.4477	0.077106
23	0.057579	0.3989	0.34586
24	-0.164161	-1.1373	0.130521
25	-0.1566	-1.085	0.14168
26	-0.145022	-1.0047	0.16003
27	-0.080718	-0.5592	0.289302
28	0.028924	0.2004	0.42101
29	0.054955	0.3807	0.352539
30	-0.008544	-0.0592	0.476521
31	-0.050272	-0.3483	0.364571
32	-0.079047	-0.5477	0.293234
33	-0.069694	-0.4829	0.315697
34	-0.113372	-0.7855	0.218021
35	0.00982	0.068	0.473021
36	-0.130569	-0.9046	0.185095
37	-0.07486	-0.5186	0.303195
38	-0.033763	-0.2339	0.408022
39	-0.094531	-0.6549	0.25782
40	0.002122	0.0147	0.494165
41	0.03636	0.2519	0.401094
42	-0.068021	-0.4713	0.319795
43	-0.010315	-0.0715	0.471664
44	0.02142	0.1484	0.441324
45	-0.045552	-0.3156	0.376841
46	-0.095524	-0.6618	0.255628
47	-0.000613	-0.0042	0.498316
48	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291744665eahwanpq4h52beg/1ar5w1291744721.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291744665eahwanpq4h52beg/1ar5w1291744721.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291744665eahwanpq4h52beg/2ar5w1291744721.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291744665eahwanpq4h52beg/2ar5w1291744721.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 2 ; 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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