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stationarity in the mean

*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 13:25:21 +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/t12917282322zpgzymas5ao72b.htm/, Retrieved Tue, 07 Dec 2010 14:23:53 +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/t12917282322zpgzymas5ao72b.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 «

31806 34571 37121 40438 43635 48064 50846 53668 58465 58618 55826 60412 62714 63332 66050 62948 59535 57298 56599 57686 57472 60463 60784 63154 64042 65460 65268 65774 66028 67104 68102 69897 72185 73538 72325 74820 74813 74533 76916 80371 81261 81557 81446 81995 79948

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	0.302191	2.0045	0.025597
2	0.153111	1.0156	0.15768
3	0.208248	1.3814	0.087072
4	-0.039812	-0.2641	0.396475
5	-0.121433	-0.8055	0.212433
6	0.083816	0.556	0.290523
7	0.083094	0.5512	0.292149
8	-0.029352	-0.1947	0.423262
9	-0.114348	-0.7585	0.226099
10	0.009956	0.066	0.473823
11	-0.169247	-1.1227	0.133836
12	-0.181174	-1.2018	0.11794
13	-0.202138	-1.3408	0.093428
14	-0.146016	-0.9686	0.16903
15	-0.155523	-1.0316	0.153943
16	-0.016968	-0.1126	0.455448
17	0.021523	0.1428	0.443562
18	0.106387	0.7057	0.242049
19	0.014027	0.093	0.463144
20	0.003546	0.0235	0.49067
21	-0.019363	-0.1284	0.449194
22	-0.105372	-0.699	0.244129
23	-0.196232	-1.3017	0.099904
24	0.092925	0.6164	0.270405
25	0.016769	0.1112	0.45597
26	0.04827	0.3202	0.375172
27	0.209077	1.3869	0.086235
28	0.106761	0.7082	0.241286
29	-0.043365	-0.2877	0.387482
30	-0.038774	-0.2572	0.399113
31	0.029593	0.1963	0.422641
32	-0.008576	-0.0569	0.477447
33	-0.057529	-0.3816	0.352296
34	0.086061	0.5709	0.285499
35	0.004748	0.0315	0.487508
36	-0.074835	-0.4964	0.311041
37	-0.040169	-0.2665	0.395569
38	-0.045243	-0.3001	0.382754
39	-0.091894	-0.6096	0.272646
40	-0.063412	-0.4206	0.338038
41	-0.056924	-0.3776	0.353774
42	-0.031888	-0.2115	0.416729
43	-0.030518	-0.2024	0.420255
44	NA	NA	NA
45	NA	NA	NA
46	NA	NA	NA
47	NA	NA	NA
48	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.302191	2.0045	0.025597
2	0.068002	0.4511	0.327076
3	0.159844	1.0603	0.1474
4	-0.167945	-1.114	0.135659
5	-0.111919	-0.7424	0.2309
6	0.154544	1.0251	0.155453
7	0.097551	0.6471	0.260471
8	-0.071139	-0.4719	0.31967
9	-0.220404	-1.462	0.075424
10	0.087362	0.5795	0.282605
11	-0.10109	-0.6706	0.253004
12	-0.058057	-0.3851	0.351008
13	-0.249046	-1.652	0.052829
14	0.005933	0.0394	0.484394
15	0.004486	0.0298	0.488197
16	0.103212	0.6846	0.248583
17	-0.04172	-0.2767	0.391639
18	0.099426	0.6595	0.2565
19	-0.022674	-0.1504	0.440569
20	-0.021462	-0.1424	0.443721
21	-0.045459	-0.3015	0.382211
22	-0.155471	-1.0313	0.154023
23	-0.178682	-1.1852	0.121142
24	0.179002	1.1874	0.120728
25	-0.006692	-0.0444	0.482398
26	0.008889	0.059	0.476625
27	0.104302	0.6919	0.246329
28	0.008141	0.054	0.478589
29	0.030364	0.2014	0.420652
30	-0.127404	-0.8451	0.201312
31	0.099066	0.6571	0.257261
32	-0.019876	-0.1318	0.447854
33	-0.034868	-0.2313	0.409083
34	-0.123709	-0.8206	0.208151
35	-0.011593	-0.0769	0.469527
36	-0.057051	-0.3784	0.353463
37	-0.019133	-0.1269	0.449794
38	-0.042943	-0.2849	0.388547
39	0.062051	0.4116	0.341315
40	0.07683	0.5096	0.306429
41	-0.007737	-0.0513	0.479651
42	-0.04204	-0.2789	0.390828
43	-0.042194	-0.2799	0.390439
44	NA	NA	NA
45	NA	NA	NA
46	NA	NA	NA
47	NA	NA	NA
48	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/07/t12917282322zpgzymas5ao72b/1n64x1291728318.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t12917282322zpgzymas5ao72b/1n64x1291728318.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t12917282322zpgzymas5ao72b/2n64x1291728318.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t12917282322zpgzymas5ao72b/2n64x1291728318.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 1 ; 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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