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R Software Module: /rwasp_autocorrelation.wasp (opens new window with default values)

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Sat, 19 Dec 2009 09:19:51 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/19/t1261239608iku5q72kryixjjb.htm/, Retrieved Sat, 19 Dec 2009 17:20:10 +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/2009/Dec/19/t1261239608iku5q72kryixjjb.htm/},
    year = {2009},
}
@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 = {2009},
    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 «

104.7 86 92.1 106.9 112.6 101.7 92 97.4 97 105.4 102.7 98.1 104.5 87.4 89.9 109.8 111.7 98.6 96.9 95.1 97 112.7 102.9 97.4 111.4 87.4 96.8 114.1 110.3 103.9 101.6 94.6 95.9 104.7 102.8 98.1 113.9 80.9 95.7 113.2 105.9 108.8 102.3 99 100.7 115.5 100.7 109.9 114.6 85.4 100.5 114.8 116.5 112.9 102 106 105.3 118.8 106.1 109.3 117.2 92.5 104.2 112.5 122.4 113.3 100 110.7 112.8 109.8 117.3 109.1 115.9 96 99.8 116.8 115.7 99.4 94.3 91 93.2 103.1 94.1 91.8 102.7 82.6 89.1

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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.48974	4.2413	3.1e-05
2	0.575582	4.9847	2e-06
3	0.654519	5.6683	0
4	0.351601	3.045	0.001605
5	0.391297	3.3887	0.000561
6	0.361031	3.1266	0.001258
7	0.117246	1.0154	0.156594
8	0.16963	1.469	0.073002
9	0.079515	0.6886	0.246593
10	-0.013654	-0.1182	0.453095
11	0.050733	0.4394	0.330832
12	-0.077882	-0.6745	0.25104
13	-0.020819	-0.1803	0.428701
14	-0.003807	-0.033	0.486892
15	-0.039092	-0.3385	0.367949
16	-0.073468	-0.6363	0.263274
17	0.023303	0.2018	0.420307
18	-0.059942	-0.5191	0.302605
19	-0.094752	-0.8206	0.207245
20	-0.006281	-0.0544	0.478383
21	-0.050453	-0.4369	0.331707
22	-0.172532	-1.4942	0.069663
23	0.046306	0.401	0.344771
24	-0.184639	-1.599	0.05701
25	-0.121133	-1.049	0.148763
26	-0.017696	-0.1532	0.439307
27	-0.182558	-1.581	0.059044
28	-0.138038	-1.1954	0.11784
29	-0.090841	-0.7867	0.216966
30	-0.201865	-1.7482	0.042261
31	-0.120627	-1.0447	0.149768
32	-0.12037	-1.0424	0.150279
33	-0.229394	-1.9866	0.025309
34	-0.102736	-0.8897	0.188231
35	-0.189587	-1.6419	0.052402
36	-0.138053	-1.1956	0.117815
37	-0.107017	-0.9268	0.178502
38	-0.122436	-1.0603	0.1462
39	-0.102376	-0.8866	0.189064
40	-0.006991	-0.0605	0.475942
41	-0.03892	-0.3371	0.368507
42	-0.014528	-0.1258	0.450108
43	0.050583	0.4381	0.331301
44	0.056155	0.4863	0.314079
45	0.019735	0.1709	0.432378
46	0.113007	0.9787	0.165445
47	0.035257	0.3053	0.38048
48	-0.024377	-0.2111	0.416686
49	0.063478	0.5497	0.292068
50	-0.050746	-0.4395	0.33079
51	-0.051711	-0.4478	0.327782
52	-0.018185	-0.1575	0.437641
53	-0.123876	-1.0728	0.143402
54	-0.092013	-0.7969	0.214024
55	-0.095364	-0.8259	0.205747
56	-0.173949	-1.5064	0.068078
57	-0.068571	-0.5938	0.277203
58	-0.121527	-1.0525	0.147985
59	-0.124855	-1.0813	0.14152
60	-0.038769	-0.3357	0.369

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.48974	4.2413	3.1e-05
2	0.441668	3.825	0.000134
3	0.45897	3.9748	8e-05
4	-0.210045	-1.819	0.036448
5	-0.190024	-1.6457	0.05201
6	-0.038091	-0.3299	0.371207
7	-0.174805	-1.5139	0.067133
8	-0.06112	-0.5293	0.299075
9	-0.024068	-0.2084	0.417726
10	0.084546	0.7322	0.233168
11	0.133155	1.1532	0.126255
12	-0.074695	-0.6469	0.259842
13	0.072181	0.6251	0.266901
14	0.047722	0.4133	0.340288
15	0.065165	0.5643	0.287103
16	-0.247466	-2.1431	0.017673
17	0.014825	0.1284	0.449092
18	0.015534	0.1345	0.446674
19	-0.155171	-1.3438	0.091528
20	-0.010702	-0.0927	0.463203
21	0.170901	1.48	0.071525
22	-0.141934	-1.2292	0.111422
23	0.176737	1.5306	0.065039
24	-0.225168	-1.95	0.027456
25	0.082258	0.7124	0.239221
26	0.001166	0.0101	0.495984
27	0.003354	0.029	0.488451
28	-0.234063	-2.027	0.023106
29	-0.009967	-0.0863	0.465721
30	0.044371	0.3843	0.350936
31	0.007246	0.0628	0.475064
32	-0.013104	-0.1135	0.454974
33	-0.003237	-0.028	0.488854
34	-0.055093	-0.4771	0.317333
35	0.032416	0.2807	0.389845
36	0.010646	0.0922	0.463395
37	0.050793	0.4399	0.330644
38	-0.012406	-0.1074	0.457364
39	0.049205	0.4261	0.335616
40	-0.017841	-0.1545	0.438813
41	0.079039	0.6845	0.247886
42	-0.046353	-0.4014	0.344624
43	-0.023327	-0.202	0.420224
44	0.005054	0.0438	0.482602
45	0.04278	0.3705	0.356032
46	-0.118647	-1.0275	0.153741
47	-0.019987	-0.1731	0.431523
48	-0.191507	-1.6585	0.050697
49	0.060109	0.5206	0.302102
50	-0.02805	-0.2429	0.404364
51	0.119833	1.0378	0.151352
52	-0.071068	-0.6155	0.270055
53	0.002303	0.0199	0.492071
54	-0.041049	-0.3555	0.361607
55	-0.07573	-0.6558	0.256966
56	-0.050403	-0.4365	0.331863
57	0.020932	0.1813	0.42832
58	0.006963	0.0603	0.476037
59	0.034935	0.3025	0.381538
60	0.019963	0.1729	0.431603

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261239608iku5q72kryixjjb/164it1261239590.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261239608iku5q72kryixjjb/164it1261239590.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261239608iku5q72kryixjjb/2gyb61261239590.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261239608iku5q72kryixjjb/2gyb61261239590.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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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