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*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: Fri, 10 Dec 2010 21:12:03 +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/t1292015384c6soorz463z4tqw.htm/, Retrieved Fri, 10 Dec 2010 22:09:44 +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/t1292015384c6soorz463z4tqw.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	2 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.10433	0.7152	0.238996
2	0.259034	1.7758	0.041116
3	0.270825	1.8567	0.034815
4	0.250403	1.7167	0.046312
5	0.187696	1.2868	0.102237
6	0.034221	0.2346	0.407767
7	0.018322	0.1256	0.45029
8	0.101258	0.6942	0.24549
9	0.011592	0.0795	0.468498
10	0.10551	0.7233	0.236528
11	-0.002928	-0.0201	0.492035
12	-0.005246	-0.036	0.485731
13	-0.030627	-0.21	0.4173
14	0.013404	0.0919	0.463586
15	0.065485	0.4489	0.327769
16	-0.067201	-0.4607	0.323567
17	-0.009536	-0.0654	0.474076
18	0.023007	0.1577	0.437672
19	0.08691	0.5958	0.277076
20	-0.087798	-0.6019	0.275063
21	-0.035969	-0.2466	0.40315
22	-0.140491	-0.9632	0.170199
23	0.154399	1.0585	0.147617
24	-0.169409	-1.1614	0.12567
25	-0.061021	-0.4183	0.338802
26	0.033122	0.2271	0.410676
27	-0.036857	-0.2527	0.400809
28	-0.015191	-0.1041	0.45875
29	-0.038194	-0.2618	0.397294
30	-0.065585	-0.4496	0.327523
31	-0.037182	-0.2549	0.399954
32	-0.23086	-1.5827	0.060099
33	-0.0196	-0.1344	0.446841
34	-0.198737	-1.3625	0.089771
35	-0.18093	-1.2404	0.110494
36	-0.146053	-1.0013	0.160906
37	-0.173051	-1.1864	0.120718
38	-0.136776	-0.9377	0.1766
39	-0.131957	-0.9046	0.185133
40	-0.062417	-0.4279	0.335335
41	-0.123973	-0.8499	0.199841
42	0.009357	0.0641	0.474563
43	-0.030258	-0.2074	0.418283
44	-0.017011	-0.1166	0.453828
45	0.009235	0.0633	0.474893
46	0.016747	0.1148	0.454542
47	NA	NA	NA
48	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.10433	0.7152	0.238996
2	0.25088	1.7199	0.046011
3	0.242115	1.6599	0.051801
4	0.183767	1.2598	0.106973
5	0.073709	0.5053	0.307846
6	-0.140596	-0.9639	0.17002
7	-0.17255	-1.1829	0.121391
8	0.005759	0.0395	0.484338
9	0.018062	0.1238	0.450991
10	0.168991	1.1585	0.126248
11	0.046904	0.3216	0.374607
12	-0.069137	-0.474	0.318854
13	-0.160083	-1.0975	0.139012
14	-0.062944	-0.4315	0.33403
15	0.121707	0.8344	0.204143
16	0.047917	0.3285	0.371996
17	0.051246	0.3513	0.363458
18	-0.005609	-0.0385	0.484744
19	0.042239	0.2896	0.386708
20	-0.170509	-1.1689	0.12416
21	-0.095337	-0.6536	0.258278
22	-0.184163	-1.2626	0.106489
23	0.27698	1.8989	0.031864
24	0.014649	0.1004	0.460217
25	0.011254	0.0772	0.469413
26	0.05147	0.3529	0.362885
27	-0.099295	-0.6807	0.249691
28	-0.101325	-0.6947	0.245347
29	-0.078285	-0.5367	0.297004
30	0.016967	0.1163	0.453946
31	0.025958	0.178	0.42976
32	-0.154754	-1.0609	0.147069
33	-0.052188	-0.3578	0.361053
34	-0.165169	-1.1323	0.131617
35	-0.088235	-0.6049	0.274074
36	0.010557	0.0724	0.471305
37	0.035955	0.2465	0.403186
38	-0.03204	-0.2197	0.413546
39	0.100596	0.6897	0.246902
40	0.097917	0.6713	0.252663
41	-0.098083	-0.6724	0.252304
42	0.013797	0.0946	0.462523
43	0.038814	0.2661	0.395666
44	-0.026448	-0.1813	0.428447
45	0.018568	0.1273	0.449626
46	-0.037374	-0.2562	0.399447
47	NA	NA	NA
48	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/10/t1292015384c6soorz463z4tqw/1k0g11292015520.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t1292015384c6soorz463z4tqw/1k0g11292015520.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t1292015384c6soorz463z4tqw/2k0g11292015520.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t1292015384c6soorz463z4tqw/2k0g11292015520.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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