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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: Wed, 09 Dec 2009 02:55:24 -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/09/t126035259460w2huw91ht7vxe.htm/, Retrieved Wed, 09 Dec 2009 10:56:36 +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/09/t126035259460w2huw91ht7vxe.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:

KDGP2W21

Dataseries X:

» Textbox « » Textfile « » CSV «

8,82000 8,80000 8,82000 8,58000 8,54000 8,42000 8,43000 8,44000 8,09000 7,69000 7,56000 7,54000 7,40000 7,39000 7,37000 7,31000 7,35000 7,26000 7,37000 7,35000 7,33000 7,32000 7,31000 7,33000 7,32000 7,27000 7,48000 7,70000 7,77000 7,80000 7,84000 7,81000 7,78000 7,82000 7,80000 7,81000 7,80000 7,66000 7,41000 7,35000 7,39000 7,32000 7,32000 7,30000 7,29000 7,26000 7,22000 7,21000 7,21000 7,21000 7,20000 7,19000 7,18000 7,12000 7,12000 7,07000 7,08000 7,05000 7,06000 7,07000 7,08000 7,08000 7,09000 7,07000 7,06000 6,99000 6,99000 6,99000 6,98000 6,96000 6,95000 6,91000 6,91000 6,87000 6,91000 6,89000 6,88000 6,90000 6,91000 6,85000 6,86000 6,82000 6,80000 6,83000 6,84000 6,89000 7,14000 7,21000 7,25000 7,31000 7,30000 7,48000 7,49000 7,40000 7,44000 7,42000 7,14000 7,24000 7,33000 7,61000 7,66000 7,69000 7,70000 7,68000 7,71000 7,71000 7,72000 7,68000 7,72000 7,74000 7,76000 7,90000 7,97000 7,96000 etc...

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	0.945419	10.862	0
2	0.881221	10.1245	0
3	0.81083	9.3157	0
4	0.744749	8.5565	0
5	0.677645	7.7855	0
6	0.612952	7.0423	0
7	0.543052	6.2392	0
8	0.473921	5.4449	0
9	0.420191	4.8276	2e-06
10	0.383522	4.4063	1.1e-05
11	0.355912	4.0891	3.7e-05
12	0.329438	3.7849	0.000116
13	0.307831	3.5367	0.00028
14	0.282325	3.2437	0.000747
15	0.254412	2.923	0.00204
16	0.233362	2.6811	0.004137
17	0.209987	2.4126	0.008607
18	0.19314	2.219	0.014097
19	0.177872	2.0436	0.021492
20	0.167582	1.9254	0.028167
21	0.160868	1.8482	0.033403
22	0.159874	1.8368	0.034243
23	0.159825	1.8363	0.034285
24	0.159325	1.8305	0.034715
25	0.160912	1.8487	0.033367
26	0.161109	1.851	0.033202
27	0.149292	1.7152	0.044324
28	0.127272	1.4622	0.073025
29	0.100811	1.1582	0.12443
30	0.068386	0.7857	0.216728
31	0.03184	0.3658	0.357543
32	-0.003405	-0.0391	0.484427
33	-0.036769	-0.4224	0.336694
34	-0.067706	-0.7779	0.219016
35	-0.098314	-1.1295	0.130358
36	-0.128431	-1.4756	0.071221
37	-0.166675	-1.9149	0.028831
38	-0.20083	-2.3074	0.011296
39	-0.225336	-2.5889	0.005354
40	-0.250064	-2.873	0.00237
41	-0.27685	-3.1808	0.000916
42	-0.297125	-3.4137	0.000426
43	-0.317722	-3.6504	0.000188
44	-0.336605	-3.8673	8.6e-05
45	-0.353898	-4.066	4.1e-05
46	-0.367828	-4.226	2.2e-05
47	-0.372605	-4.2809	1.8e-05
48	-0.374836	-4.3065	1.6e-05

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.945419	10.862	0
2	-0.118635	-1.363	0.0876
3	-0.085691	-0.9845	0.163333
4	0.011281	0.1296	0.448538
5	-0.052168	-0.5994	0.274978
6	-0.019737	-0.2268	0.410478
7	-0.090613	-1.0411	0.149875
8	-0.033279	-0.3823	0.35141
9	0.108889	1.251	0.106566
10	0.098699	1.134	0.129432
11	0.021952	0.2522	0.400637
12	-0.032651	-0.3751	0.354083
13	0.024807	0.285	0.388042
14	-0.060962	-0.7004	0.242456
15	-0.061414	-0.7056	0.240842
16	0.03806	0.4373	0.331315
17	-0.047574	-0.5466	0.292792
18	0.075012	0.8618	0.195174
19	0.022982	0.264	0.396081
20	0.033478	0.3846	0.350563
21	0.039534	0.4542	0.32521
22	0.025332	0.291	0.385739
23	-0.0185	-0.2125	0.416003
24	-0.025759	-0.2959	0.383868
25	0.020354	0.2338	0.407734
26	-0.014879	-0.1709	0.432263
27	-0.113074	-1.2991	0.098084
28	-0.066602	-0.7652	0.222758
29	-0.024551	-0.2821	0.389164
30	-0.040359	-0.4637	0.321815
31	-0.043944	-0.5049	0.307244
32	-0.01095	-0.1258	0.450038
33	0.015663	0.18	0.428732
34	0.004329	0.0497	0.480206
35	-0.048182	-0.5536	0.290404
36	-0.071421	-0.8206	0.206686
37	-0.136887	-1.5727	0.059089
38	-0.012125	-0.1393	0.44471
39	0.035776	0.411	0.340856
40	-0.06304	-0.7243	0.235088
41	-0.038875	-0.4466	0.327932
42	0.055554	0.6383	0.262203
43	-0.025158	-0.289	0.386502
44	-0.037763	-0.4339	0.332547
45	-0.072232	-0.8299	0.204051
46	-0.044681	-0.5133	0.304285
47	0.057045	0.6554	0.256678
48	-0.029287	-0.3365	0.368523

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/09/t126035259460w2huw91ht7vxe/1tcri1260352522.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/09/t126035259460w2huw91ht7vxe/1tcri1260352522.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/09/t126035259460w2huw91ht7vxe/26pmj1260352522.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/09/t126035259460w2huw91ht7vxe/26pmj1260352522.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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