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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: Tue, 15 Dec 2009 06:32:12 -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/15/t12608840153vm85669hbq6wjt.htm/, Retrieved Tue, 15 Dec 2009 14:33:37 +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/15/t12608840153vm85669hbq6wjt.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 «

558 564 581 597 587 536 524 537 536 533 528 516 502 506 518 534 528 478 469 490 493 508 517 514 510 527 542 565 555 499 511 526 532 549 561 557 566 588 620 626 620 573 573 574 580 590 593 597 595 612 628 629 621 569 567 573 584 589 591 595

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	0.8884	6.8815	0
2	0.724491	5.6119	0
3	0.614834	4.7625	6e-06
4	0.572351	4.4334	2e-05
5	0.576027	4.4619	1.8e-05
6	0.56586	4.3831	2.4e-05
7	0.508864	3.9416	0.000107
8	0.4132	3.2006	0.001097
9	0.352172	2.7279	0.004174
10	0.349085	2.704	0.00445
11	0.400334	3.101	0.001469
12	0.410441	3.1793	0.001168
13	0.268581	2.0804	0.020883
14	0.098194	0.7606	0.224936
15	-0.019332	-0.1497	0.440734
16	-0.073801	-0.5717	0.284844
17	-0.085607	-0.6631	0.254901
18	-0.106471	-0.8247	0.206398
19	-0.159959	-1.239	0.110078
20	-0.243602	-1.8869	0.032005
21	-0.292432	-2.2652	0.013563
22	-0.289211	-2.2402	0.014396
23	-0.23785	-1.8424	0.035181
24	-0.215635	-1.6703	0.050035
25	-0.295867	-2.2918	0.012722
26	-0.391813	-3.035	0.001777
27	-0.437655	-3.3901	0.00062
28	-0.433817	-3.3603	0.000679
29	-0.401522	-3.1102	0.00143
30	-0.371411	-2.8769	0.002777
31	-0.356623	-2.7624	0.003803
32	-0.370571	-2.8704	0.002827
33	-0.361048	-2.7967	0.003464
34	-0.310675	-2.4065	0.009602
35	-0.238869	-1.8503	0.0346
36	-0.191277	-1.4816	0.071837

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.8884	6.8815	0
2	-0.30731	-2.3804	0.010243
3	0.243201	1.8838	0.032218
4	0.131126	1.0157	0.156926
5	0.150575	1.1664	0.124044
6	-0.06308	-0.4886	0.313448
7	-0.087407	-0.6771	0.250487
8	-0.116957	-0.9059	0.184294
9	0.160369	1.2422	0.109496
10	0.060678	0.47	0.320027
11	0.208576	1.6156	0.055711
12	-0.251267	-1.9463	0.028153
13	-0.591153	-4.5791	1.2e-05
14	0.139901	1.0837	0.141423
15	-0.044175	-0.3422	0.366707
16	-0.082816	-0.6415	0.261825
17	-0.078253	-0.6061	0.273351
18	-0.125042	-0.9686	0.168323
19	0.120163	0.9308	0.17785
20	0.021375	0.1656	0.434526
21	-0.005742	-0.0445	0.482335
22	-0.039177	-0.3035	0.381295
23	-0.003528	-0.0273	0.489143
24	0.058906	0.4563	0.324916
25	0.022536	0.1746	0.431006
26	-0.054239	-0.4201	0.337946
27	0.055163	0.4273	0.335349
28	-0.082353	-0.6379	0.262983
29	0.008529	0.0661	0.473773
30	0.060583	0.4693	0.320286
31	0.077393	0.5995	0.275554
32	-0.069183	-0.5359	0.297008
33	-0.000874	-0.0068	0.49731
34	0.015522	0.1202	0.452349
35	-0.089908	-0.6964	0.244427
36	0.064932	0.503	0.308418

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/15/t12608840153vm85669hbq6wjt/1thsm1260883930.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/15/t12608840153vm85669hbq6wjt/1thsm1260883930.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/15/t12608840153vm85669hbq6wjt/2o8rv1260883930.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/15/t12608840153vm85669hbq6wjt/2o8rv1260883930.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = MA ; 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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