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Workshop 9

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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: Fri, 10 Dec 2010 19:48:20 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/10/t12920104599o7dyqnh29d14m1.htm/, Retrieved Fri, 10 Dec 2010 20:47:41 +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/2010/Dec/10/t12920104599o7dyqnh29d14m1.htm/},
    year = {2010},
}
@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 = {2010},
    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 «

493 514 522 490 484 506 501 462 465 454 464 427 460 473 465 422 415 413 420 363 376 380 384 346 389 407 393 346 348 353 364 305 307 312 312 286 324 336 327 302 299 311 315 264 278 278 287 279 324 354 354 360 363 385 412 370 389 395 417 404

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	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.917339	7.1057	0
2	0.842738	6.5278	0
3	0.790225	6.1211	0
4	0.76739	5.9442	0
5	0.678015	5.2519	1e-06
6	0.593392	4.5964	1.1e-05
7	0.539659	4.1802	4.8e-05
8	0.522544	4.0476	7.5e-05
9	0.44126	3.418	0.000569
10	0.386486	2.9937	0.001999
11	0.350401	2.7142	0.004331
12	0.344758	2.6705	0.004866
13	0.24272	1.8801	0.032476
14	0.153343	1.1878	0.119798
15	0.093653	0.7254	0.235504
16	0.06657	0.5156	0.303997
17	-0.010505	-0.0814	0.46771
18	-0.073697	-0.5709	0.285116
19	-0.114238	-0.8849	0.189875
20	-0.114971	-0.8906	0.188361
21	-0.165516	-1.2821	0.102372
22	-0.198128	-1.5347	0.065058
23	-0.211392	-1.6374	0.053387
24	-0.201761	-1.5628	0.061676
25	-0.263563	-2.0415	0.0228
26	-0.318492	-2.467	0.008248
27	-0.348523	-2.6997	0.004503
28	-0.347574	-2.6923	0.004592
29	-0.383286	-2.9689	0.002145
30	-0.416041	-3.2226	0.001027
31	-0.43166	-3.3436	0.000714
32	-0.410617	-3.1806	0.001163
33	-0.414125	-3.2078	0.001074
34	-0.408291	-3.1626	0.001227
35	-0.393662	-3.0493	0.001705
36	-0.357932	-2.7725	0.003699
37	-0.363818	-2.8181	0.003266
38	-0.366473	-2.8387	0.003087
39	-0.352558	-2.7309	0.00414
40	-0.32075	-2.4845	0.00789
41	-0.302192	-2.3408	0.011293
42	-0.286157	-2.2166	0.015228
43	-0.258478	-2.0022	0.024897
44	-0.204491	-1.584	0.059227
45	-0.167474	-1.2973	0.099755
46	-0.125284	-0.9704	0.167861
47	-0.085628	-0.6633	0.254849
48	-0.03679	-0.285	0.388323

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.917339	7.1057	0
2	0.007743	0.06	0.476188
3	0.101161	0.7836	0.218182
4	0.172082	1.3329	0.093795
5	-0.411097	-3.1843	0.001151
6	0.008781	0.068	0.473
7	0.120271	0.9316	0.177635
8	0.085081	0.659	0.256197
9	-0.29258	-2.2663	0.013526
10	0.252843	1.9585	0.027411
11	-0.028689	-0.2222	0.412446
12	-0.038995	-0.3021	0.381828
13	-0.478496	-3.7064	0.00023
14	0.120825	0.9359	0.176536
15	0.007408	0.0574	0.477216
16	-0.097034	-0.7516	0.227607
17	0.087476	0.6776	0.250318
18	0.110856	0.8587	0.196965
19	-0.107935	-0.8361	0.20322
20	-0.066933	-0.5185	0.303021
21	0.110116	0.853	0.198539
22	-0.100156	-0.7758	0.220457
23	-0.00801	-0.062	0.475366
24	-0.06603	-0.5115	0.30545
25	-0.106556	-0.8254	0.206213
26	-0.086719	-0.6717	0.25217
27	0.020852	0.1615	0.436113
28	-0.01647	-0.1276	0.449457
29	0.066299	0.5135	0.304728
30	-0.100598	-0.7792	0.219454
31	-0.023575	-0.1826	0.427859
32	0.006196	0.048	0.480941
33	0.123265	0.9548	0.171754
34	-0.067497	-0.5228	0.301508
35	-0.051504	-0.399	0.345673
36	0.061954	0.4799	0.316523
37	-0.018204	-0.141	0.444168
38	-0.073507	-0.5694	0.28561
39	0.047459	0.3676	0.357227
40	0.009141	0.0708	0.471894
41	0.055654	0.4311	0.333973
42	-0.032441	-0.2513	0.401226
43	0.079346	0.6146	0.270567
44	0.02282	0.1768	0.430144
45	-0.063508	-0.4919	0.312281
46	0.068393	0.5298	0.299114
47	-0.038204	-0.2959	0.384154
48	0.009839	0.0762	0.469753

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/10/t12920104599o7dyqnh29d14m1/1mus51292010495.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t12920104599o7dyqnh29d14m1/1mus51292010495.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t12920104599o7dyqnh29d14m1/2mus51292010495.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t12920104599o7dyqnh29d14m1/2mus51292010495.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; 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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