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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, 05 May 2010 15:19:03 +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/May/05/t1273072789xc2ez0ms22qwt88.htm/, Retrieved Wed, 05 May 2010 17:19:51 +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/2010/May/05/t1273072789xc2ez0ms22qwt88.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:

KDGP2W21

Dataseries X:

» Textbox « » Textfile « » CSV «

1954 2302 3054 2414 2226 2725 2589 3470 2400 3180 4009 3924 2072 2434 2956 2828 2687 2629 3150 4119 3030 3055 3821 4001 2529 2472 3134 2789 2758 2993 3282 3437 2804 3076 3782 3889 2271 2452 3084 2522 2769 3438 2839 3746 2632 2851 3871 3618 2389 2344 2678 2492 2858 2246 2800 3869 3007 3023 3907 4209 2353 2570 2903 2910 3782 2759 2931 3641 2794 3070 3576 4106 2452 2206 2488 2416 2534 2521 3093 3903 2907 3025 3812 4209

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	-0.21929	-1.9978	0.024505
2	-0.436622	-3.9778	7.4e-05
3	0.123812	1.128	0.131289
4	0.21715	1.9783	0.025604
5	-0.025762	-0.2347	0.407508
6	-0.214599	-1.9551	0.026969
7	-0.121599	-1.1078	0.13557
8	0.265832	2.4218	0.00881
9	0.188824	1.7203	0.044555
10	-0.446027	-4.0635	5.5e-05
11	-0.18253	-1.6629	0.050049
12	0.674908	6.1487	0
13	-0.103302	-0.9411	0.174686
14	-0.316423	-2.8828	0.002509
15	0.074335	0.6772	0.250075
16	0.162051	1.4764	0.071816
17	-0.020379	-0.1857	0.426582
18	-0.138452	-1.2614	0.105357
19	-0.143844	-1.3105	0.096825
20	0.195858	1.7843	0.039011
21	0.187372	1.707	0.045777
22	-0.36681	-3.3418	0.000625
23	-0.120655	-1.0992	0.137425
24	0.524502	4.7784	4e-06
25	-0.078858	-0.7184	0.237255
26	-0.230134	-2.0966	0.019536
27	0.007566	0.0689	0.472607
28	0.150689	1.3728	0.08675
29	0.01467	0.1337	0.447
30	-0.095315	-0.8684	0.193852
31	-0.165835	-1.5108	0.067315
32	0.164325	1.4971	0.069084
33	0.185678	1.6916	0.047236
34	-0.298228	-2.717	0.004008
35	-0.174877	-1.5932	0.057457
36	0.454899	4.1443	4.1e-05
37	-0.056577	-0.5154	0.303806
38	-0.145157	-1.3224	0.094827
39	-0.02966	-0.2702	0.393832
40	0.064833	0.5907	0.278179
41	0.120438	1.0972	0.137855
42	-0.13197	-1.2023	0.116332
43	-0.168587	-1.5359	0.064183
44	0.146044	1.3305	0.093495
45	0.192077	1.7499	0.041915
46	-0.24151	-2.2003	0.015284
47	-0.144649	-1.3178	0.095596
48	0.303654	2.7664	0.003492

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.21929	-1.9978	0.024505
2	-0.509197	-4.639	6e-06
3	-0.187705	-1.7101	0.045494
4	-0.030359	-0.2766	0.391393
5	0.068732	0.6262	0.266459
6	-0.097906	-0.892	0.187494
7	-0.286418	-2.6094	0.005379
8	-0.055079	-0.5018	0.308569
9	0.182799	1.6654	0.049804
10	-0.22965	-2.0922	0.019738
11	-0.402797	-3.6697	0.000214
12	0.345324	3.146	0.001149
13	0.032012	0.2916	0.385644
14	0.085008	0.7745	0.220431
15	0.10082	0.9185	0.180506
16	0.034167	0.3113	0.378184
17	-0.160909	-1.466	0.07322
18	-0.003679	-0.0335	0.486673
19	0.023485	0.214	0.415551
20	-0.101604	-0.9257	0.178654
21	-0.102727	-0.9359	0.176023
22	-0.072807	-0.6633	0.254487
23	-0.0479	-0.4364	0.331844
24	0.12633	1.1509	0.126535
25	0.089126	0.812	0.209565
26	0.084322	0.7682	0.22227
27	-0.112837	-1.028	0.15347
28	0.00641	0.0584	0.476787
29	0.017179	0.1565	0.438006
30	0.067875	0.6184	0.269013
31	-0.005334	-0.0486	0.480679
32	-0.023161	-0.211	0.416698
33	-0.038201	-0.348	0.364351
34	0.028383	0.2586	0.3983
35	-0.121959	-1.1111	0.134866
36	0.085964	0.7832	0.217879
37	-0.099745	-0.9087	0.183064
38	0.02676	0.2438	0.403997
39	-0.024949	-0.2273	0.410375
40	-0.047173	-0.4298	0.334239
41	0.112852	1.0281	0.153438
42	-0.121585	-1.1077	0.135596
43	-0.007674	-0.0699	0.472216
44	-0.046227	-0.4212	0.337367
45	0.002193	0.02	0.492055
46	-0.012055	-0.1098	0.456406
47	0.058418	0.5322	0.298001
48	-0.079036	-0.72	0.236759

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/May/05/t1273072789xc2ez0ms22qwt88/1wxov1273072741.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/05/t1273072789xc2ez0ms22qwt88/1wxov1273072741.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/May/05/t1273072789xc2ez0ms22qwt88/266ng1273072741.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/05/t1273072789xc2ez0ms22qwt88/266ng1273072741.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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