Home » date » 2009 » May » 14 »

Autocorrelation 6b bis - Kelly Michielsen - MAR 201b

*Unverified author*

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

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Thu, 14 May 2009 05:47:59 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/May/14/t1242301709n2x4lhsxs2uh2f7.htm/, Retrieved Thu, 14 May 2009 13:48:29 +0200

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/May/14/t1242301709n2x4lhsxs2uh2f7.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 «

104.9 110.9 104.8 94.1 95.8 99.3 101.1 104.0 99.0 105.4 107.1 110.7 117.1 118.7 126.5 127.5 134.6 131.8 135.9 142.7 141.7 153.4 145.0 137.7 148.3 152.2 169.4 168.6 161.1 174.1 179.0 190.6 190.0 181.6 174.8 180.5 196.8 193.8 197.0 216.3 221.4 217.9 229.7 227.4 204.2 196.6 198.8 207.5 190.7 201.6 210.5 223.5 223.8 231.2 244.0 234.7 250.2 265.7 287.6 283.3 295.4 312.3 333.8 347.7 383.2 407.1 413.6 362.7 321.9 239.4 191.0 159.7 166.7

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.963786	8.2346	0
2	0.897651	7.6695	0
3	0.811946	6.9373	0
4	0.722154	6.1701	0
5	0.638996	5.4596	0
6	0.570121	4.8711	3e-06
7	0.515208	4.4019	1.8e-05
8	0.465837	3.9801	8e-05
9	0.418277	3.5738	0.000314
10	0.37729	3.2236	0.000947
11	0.33765	2.8849	0.002572
12	0.299143	2.5559	0.006337
13	0.264525	2.2601	0.013399
14	0.236262	2.0186	0.0236
15	0.21121	1.8046	0.037632
16	0.184171	1.5736	0.059957
17	0.161756	1.382	0.085586
18	0.142766	1.2198	0.113234
19	0.12958	1.1071	0.135936
20	0.120012	1.0254	0.154285
21	0.11332	0.9682	0.168068
22	0.107532	0.9188	0.180626
23	0.096145	0.8215	0.207028
24	0.077986	0.6663	0.253657
25	0.057559	0.4918	0.312174
26	0.030622	0.2616	0.397171
27	0.000679	0.0058	0.497694
28	-0.030625	-0.2617	0.397161
29	-0.060775	-0.5193	0.302575
30	-0.084006	-0.7177	0.237601
31	-0.103534	-0.8846	0.18964
32	-0.117538	-1.0042	0.159289
33	-0.129511	-1.1065	0.136063
34	-0.142884	-1.2208	0.113045
35	-0.158811	-1.3569	0.0895
36	-0.176537	-1.5083	0.067892
37	-0.192696	-1.6464	0.05199
38	-0.212002	-1.8113	0.037101
39	-0.22975	-1.963	0.026729
40	-0.241626	-2.0645	0.021264
41	-0.250746	-2.1424	0.017749
42	-0.259759	-2.2194	0.014784
43	-0.266478	-2.2768	0.012866
44	-0.270622	-2.3122	0.011795
45	-0.279029	-2.384	0.009863
46	-0.288387	-2.464	0.008048
47	-0.298561	-2.5509	0.00642
48	-0.309573	-2.645	0.004998

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.963786	8.2346	0
2	-0.439166	-3.7522	0.000174
3	-0.172076	-1.4702	0.0729
4	0.055974	0.4782	0.316954
5	0.09072	0.7751	0.220389
6	0.09194	0.7855	0.217341
7	0.005629	0.0481	0.480886
8	-0.125738	-1.0743	0.143112
9	-0.055142	-0.4711	0.319474
10	0.128168	1.0951	0.138543
11	-0.034504	-0.2948	0.38449
12	-0.043392	-0.3707	0.355952
13	0.021935	0.1874	0.425928
14	0.040427	0.3454	0.365391
15	-0.027746	-0.2371	0.406635
16	-0.093152	-0.7959	0.214338
17	0.084138	0.7189	0.237256
18	0.023931	0.2045	0.419277
19	0.064885	0.5544	0.290507
20	-0.035938	-0.3071	0.379839
21	-0.05075	-0.4336	0.332927
22	-0.003233	-0.0276	0.48902
23	-0.055255	-0.4721	0.319132
24	-0.048589	-0.4151	0.339626
25	0.027969	0.239	0.405901
26	-0.087002	-0.7433	0.229828
27	-0.027496	-0.2349	0.407462
28	-0.019863	-0.1697	0.432852
29	-0.031455	-0.2688	0.39444
30	0.095321	0.8144	0.209027
31	-0.029043	-0.2481	0.402359
32	-0.034545	-0.2952	0.384359
33	-0.050019	-0.4274	0.335186
34	-0.046652	-0.3986	0.345677
35	-0.019389	-0.1657	0.434442
36	-0.00238	-0.0203	0.491915
37	0.025318	0.2163	0.414671
38	-0.116578	-0.996	0.161259
39	0.016093	0.1375	0.445509
40	0.054352	0.4644	0.321876
41	-0.04859	-0.4152	0.339623
42	-0.087498	-0.7476	0.228556
43	0.042426	0.3625	0.359019
44	0.006043	0.0516	0.479483
45	-0.141289	-1.2072	0.11563
46	0.044023	0.3761	0.353956
47	-0.061681	-0.527	0.299894
48	-0.015546	-0.1328	0.44735

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/14/t1242301709n2x4lhsxs2uh2f7/1qbnl1242301674.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/14/t1242301709n2x4lhsxs2uh2f7/1qbnl1242301674.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/14/t1242301709n2x4lhsxs2uh2f7/2t8yk1242301674.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/14/t1242301709n2x4lhsxs2uh2f7/2t8yk1242301674.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

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 (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='lags',ylab='ACF')

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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