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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, 21 Dec 2010 16:01:31 +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/21/t1292947156k50tdzknyt6lduv.htm/, Retrieved Tue, 21 Dec 2010 16:59:17 +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/21/t1292947156k50tdzknyt6lduv.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 «

77.33 75.28 77.43 73.25 68.41 72.87 65.61 69.04 57.84 51.07 47.48 44.01 45.29 43.8 55.48 75.73 101.42 116.07 135.81 132.69 124.05 109.65 102.79 94.09 92.23 90.6 92.6 81.71 76.36 71.44 75.26 70.3 67.68 67.65 61.92 58.34 55.04 62.5 59.44 60.03 64.24 74.33 74.41 69.75 72.03 68.18 63.01 61.71 63.52

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	-0.336627	-2.3078	0.01273
2	0.229007	1.57	0.061563
3	-0.228347	-1.5655	0.062091
4	0.108436	0.7434	0.23047
5	-0.236136	-1.6189	0.056084
6	-0.160876	-1.1029	0.13784
7	0.067126	0.4602	0.323751
8	0.062888	0.4311	0.334169
9	-0.053291	-0.3653	0.358247
10	-0.099721	-0.6837	0.248776
11	0.217535	1.4913	0.071277
12	-0.092624	-0.635	0.264254
13	0.007379	0.0506	0.479934
14	-0.027236	-0.1867	0.426341
15	0.140506	0.9633	0.170173
16	-0.077043	-0.5282	0.299931
17	-0.010665	-0.0731	0.471012
18	-0.091995	-0.6307	0.265651
19	0.181252	1.2426	0.110089
20	-0.224627	-1.54	0.065137
21	0.101209	0.6939	0.245595
22	-0.116311	-0.7974	0.214617
23	0.198992	1.3642	0.089498
24	-0.096311	-0.6603	0.25615
25	0.091122	0.6247	0.267595
26	0.090985	0.6238	0.2679
27	-0.094639	-0.6488	0.259808
28	0.013521	0.0927	0.46327
29	-0.124017	-0.8502	0.199757
30	0.102601	0.7034	0.242639
31	-0.131839	-0.9038	0.185344
32	0.090218	0.6185	0.269615
33	-0.072191	-0.4949	0.311482
34	0.060103	0.412	0.34109
35	0.020912	0.1434	0.443306
36	-0.02414	-0.1655	0.434631
37	0.044615	0.3059	0.380528
38	-0.058734	-0.4027	0.344511
39	0.062897	0.4312	0.334147
40	-0.022332	-0.1531	0.439487
41	-0.031118	-0.2133	0.415994
42	0.025082	0.172	0.432107
43	0.003125	0.0214	0.491499
44	-0.011866	-0.0813	0.467755
45	-0.001402	-0.0096	0.496186
46	0.004579	0.0314	0.487545
47	NA	NA	NA
48	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.336627	-2.3078	0.01273
2	0.130474	0.8945	0.18781
3	-0.13469	-0.9234	0.180261
4	-0.024049	-0.1649	0.434876
5	-0.187535	-1.2857	0.102428
6	-0.374275	-2.5659	0.00677
7	-0.046095	-0.316	0.376696
8	0.091387	0.6265	0.267003
9	-0.137687	-0.9439	0.175014
10	-0.293719	-2.0136	0.024897
11	0.036015	0.2469	0.403027
12	-0.069453	-0.4761	0.318089
13	-0.130828	-0.8969	0.187168
14	-0.021713	-0.1489	0.441151
15	-0.024344	-0.1669	0.434086
16	-0.105835	-0.7256	0.235851
17	0.000897	0.0061	0.497561
18	-0.182908	-1.254	0.10803
19	0.013384	0.0918	0.463641
20	-0.112399	-0.7706	0.222409
21	-0.067654	-0.4638	0.322462
22	-0.206932	-1.4187	0.081299
23	-0.013796	-0.0946	0.462526
24	0.016654	0.1142	0.454794
25	-0.022362	-0.1533	0.439407
26	0.086321	0.5918	0.278415
27	-0.165867	-1.1371	0.130625
28	-0.069591	-0.4771	0.317755
29	0.029111	0.1996	0.421337
30	-0.035658	-0.2445	0.403969
31	-0.054387	-0.3729	0.355466
32	0.01812	0.1242	0.450833
33	-0.082104	-0.5629	0.288097
34	-0.171075	-1.1728	0.123387
35	0.153039	1.0492	0.14973
36	-0.028283	-0.1939	0.423545
37	-0.115271	-0.7903	0.216673
38	-0.050194	-0.3441	0.366149
39	-0.027078	-0.1856	0.426765
40	-0.037442	-0.2567	0.39927
41	0.005915	0.0406	0.483912
42	-0.046494	-0.3187	0.375664
43	-0.067065	-0.4598	0.323898
44	-0.015988	-0.1096	0.456592
45	0.020092	0.1377	0.445516
46	-0.051119	-0.3505	0.363781
47	NA	NA	NA
48	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292947156k50tdzknyt6lduv/1e0uk1292947287.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292947156k50tdzknyt6lduv/1e0uk1292947287.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292947156k50tdzknyt6lduv/2e0uk1292947287.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292947156k50tdzknyt6lduv/2e0uk1292947287.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 = 2 ; 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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