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Identifying Integration Processes 1

*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: Sat, 19 Dec 2009 09:25:55 -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/t1261239993fpzdikfz324q4ou.htm/, Retrieved Sat, 19 Dec 2009 17:26:36 +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/t1261239993fpzdikfz324q4ou.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 «

103.34 102.60 100.69 105.67 123.61 113.08 106.46 123.38 109.87 95.74 123.06 123.39 120.28 115.33 110.40 114.49 132.03 123.16 118.82 128.32 112.24 104.53 132.57 122.52 131.80 124.55 120.96 122.60 145.52 118.57 134.25 136.70 121.37 111.63 134.42 137.65 137.86 119.77 130.69 128.28 147.45 128.42 136.90 143.95 135.64 122.48 136.83 153.04 142.71 123.46 144.37 146.15 147.61 158.51 147.40 165.05 154.64 126.20 157.36 154.15 123.21 113.07 110.45 113.57 122.44 114.93 111.85 126.04 121.34 124.36

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	0.582682	4.8751	3e-06
2	0.412995	3.4554	0.000469
3	0.496759	4.1562	4.5e-05
4	0.442935	3.7059	0.000209
5	0.364481	3.0495	0.001618
6	0.385075	3.2218	0.000967
7	0.215965	1.8069	0.037538
8	0.283614	2.3729	0.0102
9	0.162816	1.3622	0.088748
10	-0.000477	-0.004	0.498413
11	0.136967	1.146	0.127859
12	0.340747	2.8509	0.002862
13	0.094381	0.7896	0.216201
14	0.007214	0.0604	0.476022
15	0.058257	0.4874	0.313743
16	0.088321	0.7389	0.231206
17	0.044044	0.3685	0.356806
18	0.069407	0.5807	0.281653
19	0.021307	0.1783	0.429515
20	0.055909	0.4678	0.320701
21	-0.055762	-0.4665	0.321141
22	-0.146939	-1.2294	0.111524
23	-0.041818	-0.3499	0.363741
24	0.067671	0.5662	0.286542
25	-0.064514	-0.5398	0.295537
26	-0.176651	-1.478	0.071951
27	-0.106618	-0.892	0.187717
28	-0.041976	-0.3512	0.363247
29	-0.110136	-0.9215	0.179987
30	-0.110552	-0.9249	0.179087
31	-0.081405	-0.6811	0.249034
32	-0.138838	-1.1616	0.124671
33	-0.178258	-1.4914	0.070173
34	-0.225487	-1.8866	0.031684
35	-0.213252	-1.7842	0.039363
36	-0.100021	-0.8368	0.202766
37	-0.176526	-1.4769	0.072091
38	-0.299958	-2.5096	0.007201
39	-0.196055	-1.6403	0.052713
40	-0.165978	-1.3887	0.084668
41	-0.21649	-1.8113	0.037193
42	-0.187297	-1.567	0.060807
43	-0.160095	-1.3395	0.092378
44	-0.219902	-1.8398	0.035017
45	-0.21201	-1.7738	0.040222
46	-0.237641	-1.9883	0.025348
47	-0.218489	-1.828	0.035905
48	-0.123066	-1.0296	0.15336
49	-0.189643	-1.5867	0.058548
50	-0.258755	-2.1649	0.016903
51	-0.157255	-1.3157	0.096286
52	-0.145708	-1.2191	0.113453
53	-0.160653	-1.3441	0.091625
54	-0.092936	-0.7776	0.219725
55	-0.084813	-0.7096	0.240155
56	-0.056187	-0.4701	0.319875
57	-0.007737	-0.0647	0.474285
58	-0.025023	-0.2094	0.417387
59	0.043856	0.3669	0.35739
60	0.111511	0.933	0.177021

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.582682	4.8751	3e-06
2	0.111247	0.9308	0.177588
3	0.334296	2.7969	0.003328
4	0.060272	0.5043	0.307828
5	0.048788	0.4082	0.342191
6	0.092934	0.7775	0.21973
7	-0.233449	-1.9532	0.027398
8	0.213774	1.7886	0.039007
9	-0.320262	-2.6795	0.004592
10	-0.08935	-0.7476	0.228616
11	0.205157	1.7165	0.045249
12	0.347951	2.9112	0.002413
13	-0.202539	-1.6946	0.047302
14	-0.171378	-1.4339	0.078034
15	0.027631	0.2312	0.408926
16	0.047833	0.4002	0.345115
17	-0.088355	-0.7392	0.23112
18	0.063577	0.5319	0.298232
19	0.027068	0.2265	0.41075
20	-0.115445	-0.9659	0.168713
21	-0.065993	-0.5521	0.291307
22	0.034789	0.2911	0.385932
23	0.03333	0.2789	0.390586
24	-0.108773	-0.9101	0.182957
25	0.088754	0.7426	0.230115
26	-0.15732	-1.3162	0.096194
27	0.108984	0.9118	0.182494
28	0.021499	0.1799	0.428885
29	-0.031803	-0.2661	0.39548
30	-0.087598	-0.7329	0.233034
31	-0.032743	-0.2739	0.392467
32	-0.132647	-1.1098	0.135441
33	0.039863	0.3335	0.369869
34	-0.004979	-0.0417	0.483446
35	-0.117934	-0.9867	0.163592
36	0.022453	0.1879	0.425767
37	-0.000157	-0.0013	0.499476
38	0.062729	0.5248	0.300681
39	-0.087458	-0.7317	0.233388
40	0.019388	0.1622	0.435804
41	-0.027109	-0.2268	0.410616
42	-0.073585	-0.6157	0.270059
43	-0.010461	-0.0875	0.465253
44	-0.050089	-0.4191	0.338223
45	-0.042941	-0.3593	0.360238
46	-0.005464	-0.0457	0.481833
47	-0.017519	-0.1466	0.441945
48	0.031045	0.2597	0.397914
49	-0.094328	-0.7892	0.216329
50	0.100002	0.8367	0.202811
51	-0.033217	-0.2779	0.390948
52	-0.036188	-0.3028	0.381482
53	0.055178	0.4617	0.32288
54	0.021139	0.1769	0.430065
55	-0.013422	-0.1123	0.455455
56	0.090553	0.7576	0.225611
57	0.095817	0.8017	0.21273
58	-0.049772	-0.4164	0.339189
59	0.035589	0.2978	0.383384
60	0.024072	0.2014	0.420486

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261239993fpzdikfz324q4ou/12d9o1261239954.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261239993fpzdikfz324q4ou/12d9o1261239954.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261239993fpzdikfz324q4ou/2nq321261239954.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261239993fpzdikfz324q4ou/2nq321261239954.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 0.0 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 0.0 ; 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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