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 05:45:44 -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/t1242301590prpfa4aihh5gv1t.htm/, Retrieved Thu, 14 May 2009 13:46:32 +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/t1242301590prpfa4aihh5gv1t.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	1 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.832984	6.5058	0
2	0.570993	4.4596	1.8e-05
3	0.280832	2.1934	0.016051
4	0.034709	0.2711	0.393621
5	-0.127918	-0.9991	0.160853
6	-0.215637	-1.6842	0.048629
7	-0.24307	-1.8984	0.031186
8	-0.256487	-2.0032	0.024801
9	-0.268654	-2.0983	0.020016
10	-0.282034	-2.2028	0.0157
11	-0.28828	-2.2515	0.013982
12	-0.297646	-2.3247	0.011717
13	-0.264834	-2.0684	0.021424
14	-0.216516	-1.691	0.047966
15	-0.135344	-1.0571	0.147323
16	-0.073083	-0.5708	0.285116
17	-0.02491	-0.1946	0.423194
18	-0.003987	-0.0311	0.487629
19	0.021566	0.1684	0.433398
20	0.05195	0.4057	0.343175
21	0.072287	0.5646	0.287215
22	0.079779	0.6231	0.267772
23	0.086384	0.6747	0.251214
24	0.094061	0.7346	0.232686
25	0.084534	0.6602	0.255796
26	0.082738	0.6462	0.260286
27	0.056061	0.4379	0.33152
28	0.019912	0.1555	0.438464
29	-0.01406	-0.1098	0.456458
30	-0.024608	-0.1922	0.424113
31	-0.012125	-0.0947	0.462432
32	-0.010293	-0.0804	0.468094
33	0.003837	0.03	0.488096
34	0.011255	0.0879	0.465121
35	0.008458	0.0661	0.473774
36	0.015599	0.1218	0.451716
37	0.016963	0.1325	0.447518
38	0.011442	0.0894	0.464543
39	-0.004041	-0.0316	0.487463
40	-0.019641	-0.1534	0.439296
41	-0.01283	-0.1002	0.460254
42	-0.005699	-0.0445	0.48232
43	-0.007163	-0.0559	0.477784
44	-0.007641	-0.0597	0.476305
45	-0.016618	-0.1298	0.448578
46	-0.010668	-0.0833	0.466934
47	-0.009665	-0.0755	0.470038
48	-0.025431	-0.1986	0.42161

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.832984	6.5058	0
2	-0.401351	-3.1347	0.001323
3	-0.200023	-1.5622	0.061704
4	-0.032845	-0.2565	0.399203
5	0.018092	0.1413	0.444049
6	-0.046002	-0.3593	0.36031
7	-0.038762	-0.3027	0.381558
8	-0.133501	-1.0427	0.150607
9	-0.091452	-0.7143	0.238895
10	-0.071404	-0.5577	0.28955
11	-0.056016	-0.4375	0.331646
12	-0.136815	-1.0686	0.144739
13	0.05317	0.4153	0.339699
14	-0.088384	-0.6903	0.246311
15	0.035815	0.2797	0.390317
16	-0.145325	-1.135	0.130402
17	-0.028023	-0.2189	0.413742
18	-0.093735	-0.7321	0.233456
19	0.070574	0.5512	0.291756
20	-0.034794	-0.2717	0.393366
21	-0.067255	-0.5253	0.300647
22	-0.08924	-0.697	0.24423
23	0.041477	0.3239	0.373543
24	-0.021387	-0.167	0.433947
25	-0.050576	-0.395	0.347106
26	0.002722	0.0213	0.491554
27	-0.089219	-0.6968	0.244281
28	-0.066068	-0.516	0.303857
29	0.019812	0.1547	0.43877
30	-0.000432	-0.0034	0.498659
31	0.021762	0.17	0.4328
32	-0.118851	-0.9283	0.178467
33	0.077215	0.6031	0.274349
34	-0.057117	-0.4461	0.328554
35	-0.016613	-0.1298	0.448594
36	0.039649	0.3097	0.378933
37	-0.032076	-0.2505	0.401514
38	-0.025126	-0.1962	0.422536
39	-0.048941	-0.3822	0.351805
40	-0.003603	-0.0281	0.488821
41	0.051694	0.4037	0.343908
42	-0.025909	-0.2024	0.420157
43	-0.04386	-0.3426	0.366555
44	-0.001538	-0.012	0.495226
45	-0.008674	-0.0677	0.473105
46	0.030798	0.2405	0.405358
47	-0.041946	-0.3276	0.372164
48	-0.082975	-0.6481	0.259692

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/14/t1242301590prpfa4aihh5gv1t/1ewvg1242301542.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/14/t1242301590prpfa4aihh5gv1t/1ewvg1242301542.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/14/t1242301590prpfa4aihh5gv1t/2blzm1242301542.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/14/t1242301590prpfa4aihh5gv1t/2blzm1242301542.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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