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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: Mon, 13 Dec 2010 09:24:16 +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/13/t1292232266ipq6juirh74njp7.htm/, Retrieved Mon, 13 Dec 2010 10:24:27 +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/13/t1292232266ipq6juirh74njp7.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 «

113 95.4 86.2 111.7 97.5 99.7 111.5 91.8 86.3 88.7 95.1 105.1 104.5 89.1 82.6 102.7 91.8 94.1 103.1 93.2 91 94.3 99.4 115.7 116.8 99.8 96 115.9 109.1 117.3 109.8 112.8 110.7 100 113.3 122.4 112.5 104.2 92.5 117.2 109.3 106.1 118.8 105.3 106 102 112.9 116.5 114.8 100.5 85.4 114.6 109.9 100.7 115.5 100.7 99 102.3

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	-0.287273	-2.1689	0.01714
2	-0.320895	-2.4227	0.009303
3	0.15503	1.1704	0.123346
4	-0.1958	-1.4783	0.072422
5	0.138974	1.0492	0.149251
6	0.093186	0.7035	0.242292
7	0.058779	0.4438	0.329443
8	-0.022485	-0.1698	0.432899
9	-0.030256	-0.2284	0.410065
10	-0.208299	-1.5726	0.06067
11	-0.14468	-1.0923	0.139646
12	0.592116	4.4704	1.9e-05
13	-0.110137	-0.8315	0.204577
14	-0.253324	-1.9126	0.030417
15	0.030343	0.2291	0.409813
16	-0.087775	-0.6627	0.255101
17	0.134251	1.0136	0.157536
18	0.009837	0.0743	0.470528
19	0.048988	0.3699	0.356432
20	0.008772	0.0662	0.473713
21	-0.08351	-0.6305	0.265447
22	-0.130977	-0.9889	0.163457
23	-0.06409	-0.4839	0.315165
24	0.35095	2.6496	0.005205
25	-0.017664	-0.1334	0.447188
26	-0.2064	-1.5583	0.062351
27	-0.034468	-0.2602	0.397813
28	0.016943	0.1279	0.449334
29	0.057057	0.4308	0.334129
30	0.005033	0.038	0.484912
31	0.094278	0.7118	0.23975
32	-0.108017	-0.8155	0.209088
33	0.014889	0.1124	0.455447
34	-0.041255	-0.3115	0.378289
35	-0.159783	-1.2063	0.116336
36	0.347719	2.6252	0.005549
37	-0.038888	-0.2936	0.385065
38	-0.205772	-1.5535	0.062914
39	0.096092	0.7255	0.235562
40	-0.053985	-0.4076	0.342554
41	0.007292	0.0551	0.478144
42	0.072397	0.5466	0.293399
43	0.038486	0.2906	0.386219
44	-0.102527	-0.7741	0.221047
45	0.039586	0.2989	0.383065
46	-0.013513	-0.102	0.459549
47	-0.122072	-0.9216	0.180306
48	0.211805	1.5991	0.057664

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.287273	-2.1689	0.01714
2	-0.439708	-3.3197	0.000788
3	-0.140531	-1.061	0.146586
4	-0.444158	-3.3533	0.000712
5	-0.163672	-1.2357	0.11082
6	-0.210041	-1.5858	0.059162
7	0.156715	1.1832	0.120826
8	0.133967	1.0114	0.158043
9	0.413575	3.1224	0.001408
10	-0.009764	-0.0737	0.470748
11	-0.354671	-2.6777	0.004833
12	0.204628	1.5449	0.063951
13	0.06468	0.4883	0.313597
14	0.083619	0.6313	0.265181
15	-0.267092	-2.0165	0.024234
16	-0.033948	-0.2563	0.39932
17	-0.033929	-0.2562	0.399376
18	0.005696	0.043	0.482924
19	-0.049641	-0.3748	0.354606
20	-0.065248	-0.4926	0.312091
21	-0.002843	-0.0215	0.491474
22	-0.035715	-0.2696	0.394204
23	0.012885	0.0973	0.461422
24	-0.102919	-0.777	0.22018
25	-0.041635	-0.3143	0.377206
26	-0.113998	-0.8607	0.196514
27	-0.087513	-0.6607	0.25573
28	-0.007819	-0.059	0.476565
29	-0.109957	-0.8302	0.204958
30	-0.0092	-0.0695	0.472435
31	0.072691	0.5488	0.292642
32	-0.090571	-0.6838	0.248436
33	0.07513	0.5672	0.286396
34	0.094081	0.7103	0.240207
35	-0.018784	-0.1418	0.443864
36	0.055562	0.4195	0.338219
37	-0.09201	-0.6947	0.245044
38	-0.080372	-0.6068	0.273197
39	0.047333	0.3574	0.361073
40	-0.011894	-0.0898	0.46438
41	-0.107564	-0.8121	0.210059
42	-0.073611	-0.5557	0.290278
43	-0.006926	-0.0523	0.479242
44	0.001063	0.008	0.496813
45	-0.029535	-0.223	0.412173
46	-0.051802	-0.3911	0.348591
47	0.033701	0.2544	0.400036
48	-0.097107	-0.7331	0.233238

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/13/t1292232266ipq6juirh74njp7/1y8em1292232252.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/13/t1292232266ipq6juirh74njp7/1y8em1292232252.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/13/t1292232266ipq6juirh74njp7/2y8em1292232252.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/13/t1292232266ipq6juirh74njp7/2y8em1292232252.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 = 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 (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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