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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: Mon, 21 Dec 2009 05:12:24 -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/21/t12613976256ebaynlalgm8x2d.htm/, Retrieved Mon, 21 Dec 2009 13:13:47 +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/21/t12613976256ebaynlalgm8x2d.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 «

103.5 104.6 118.6 106.3 110.7 121.6 107 107.6 125.6 113.5 129.2 130.9 104.7 115.2 124.5 112.3 127.5 120.6 117.5 117.7 120.4 125 131.6 121.1 114.2 112.1 127 116.8 112 129.7 113.6 115.7 119.5 125.8 129.6 128 112.8 101.6 123.9 118.8 109.1 130.6 112.4 111 116.2 119.8 117.2 127.3 107.7 97.5 120.1 110.6 111.3 119.8 105.5 108.7 128.7 119.5 121.1 128.4

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	0.045508	0.3525	0.362849
2	-0.137553	-1.0655	0.145463
3	0.302322	2.3418	0.011265
4	-0.204869	-1.5869	0.058895
5	0.014118	0.1094	0.456641
6	0.417145	3.2312	0.001002
7	-0.138398	-1.072	0.144001
8	-0.165745	-1.2839	0.102064
9	0.101104	0.7831	0.21831
10	-0.286897	-2.2223	0.015022
11	-0.020425	-0.1582	0.437409
12	0.469796	3.639	0.000286
13	-0.010395	-0.0805	0.468047
14	-0.200811	-1.5555	0.062546
15	-0.006552	-0.0508	0.479845
16	-0.179444	-1.39	0.084837
17	-0.107684	-0.8341	0.203762
18	0.177775	1.377	0.086808
19	-0.085561	-0.6628	0.255013
20	-0.241312	-1.8692	0.03324
21	-0.014686	-0.1138	0.454906
22	-0.158771	-1.2298	0.111779
23	-0.088369	-0.6845	0.248145
24	0.276573	2.1423	0.018117
25	0.110886	0.8589	0.196902
26	-0.235807	-1.8266	0.036371
27	-0.00757	-0.0586	0.476719
28	-0.099537	-0.771	0.221862
29	-0.198184	-1.5351	0.065005
30	0.127476	0.9874	0.163701
31	0.007708	0.0597	0.476295
32	-0.246041	-1.9058	0.030733
33	-0.038615	-0.2991	0.382945
34	-0.046979	-0.3639	0.358606
35	-0.145449	-1.1266	0.13219
36	0.211684	1.6397	0.053151
37	0.143964	1.1151	0.134619
38	-0.192954	-1.4946	0.070128
39	0.059029	0.4572	0.324575
40	0.006231	0.0483	0.480834
41	-0.133269	-1.0323	0.153038
42	0.183465	1.4211	0.08023
43	0.048961	0.3792	0.352921
44	-0.141666	-1.0973	0.138439
45	0.122304	0.9474	0.173628
46	0.023981	0.1858	0.426633
47	-0.032762	-0.2538	0.400269
48	0.235477	1.824	0.036567
49	0.080987	0.6273	0.266415
50	-0.022294	-0.1727	0.431738
51	0.104033	0.8058	0.211759
52	-0.018746	-0.1452	0.442517
53	-0.031013	-0.2402	0.405486
54	0.067409	0.5222	0.301744
55	-0.032257	-0.2499	0.401775
56	-0.071004	-0.55	0.292183
57	-0.014999	-0.1162	0.453949
58	-0.045337	-0.3512	0.363343
59	-0.035978	-0.2787	0.390722
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.045508	0.3525	0.362849
2	-0.139914	-1.0838	0.141401
3	0.322799	2.5004	0.007578
4	-0.30857	-2.3902	0.009999
5	0.225656	1.7479	0.042797
6	0.233368	1.8077	0.037837
7	-0.089216	-0.6911	0.246095
8	-0.166142	-1.2869	0.101531
9	-0.047066	-0.3646	0.358357
10	-0.179867	-1.3932	0.084343
11	0.065463	0.5071	0.306981
12	0.356206	2.7592	0.003836
13	0.132589	1.027	0.154265
14	-0.245904	-1.9048	0.030804
15	-0.261882	-2.0285	0.023476
16	0.023085	0.1788	0.429344
17	-0.146801	-1.1371	0.130006
18	-0.111924	-0.867	0.19471
19	0.006706	0.0519	0.479372
20	0.006298	0.0488	0.480627
21	0.021588	0.1672	0.433879
22	0.043561	0.3374	0.368489
23	0.041187	0.319	0.375406
24	-0.070167	-0.5435	0.294395
25	0.048183	0.3732	0.355148
26	-0.168351	-1.304	0.0986
27	0.013381	0.1037	0.458896
28	-0.18487	-1.432	0.078667
29	-0.103183	-0.7993	0.213649
30	-0.139229	-1.0785	0.142572
31	0.105212	0.815	0.209157
32	-0.011469	-0.0888	0.464752
33	-0.047208	-0.3657	0.357948
34	0.037332	0.2892	0.386722
35	-0.05078	-0.3933	0.347731
36	-0.072461	-0.5613	0.288349
37	-0.126553	-0.9803	0.165443
38	-0.043518	-0.3371	0.368614
39	0.013301	0.103	0.45914
40	0.008523	0.066	0.47379
41	0.080292	0.6219	0.268168
42	0.082831	0.6416	0.261786
43	-0.139774	-1.0827	0.141641
44	-0.023069	-0.1787	0.429391
45	0.135175	1.0471	0.149635
46	-0.026804	-0.2076	0.418112
47	-0.005416	-0.042	0.483338
48	-0.088557	-0.686	0.247691
49	-0.016363	-0.1267	0.449782
50	0.012889	0.0998	0.460402
51	0.065398	0.5066	0.307156
52	-0.04756	-0.3684	0.356938
53	0.013615	0.1055	0.458181
54	-0.10166	-0.7875	0.217057
55	-0.021745	-0.1684	0.433404
56	-0.065494	-0.5073	0.306898
57	-0.12178	-0.9433	0.174654
58	-0.131907	-1.0217	0.155501
59	-0.047203	-0.3656	0.357963
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/21/t12613976256ebaynlalgm8x2d/14xx11261397542.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t12613976256ebaynlalgm8x2d/14xx11261397542.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t12613976256ebaynlalgm8x2d/2suhp1261397542.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t12613976256ebaynlalgm8x2d/2suhp1261397542.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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