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Paper - 9

*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: Thu, 10 Dec 2009 08:28:07 -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/10/t1260459001tsvtl9mo8u9o8ow.htm/, Retrieved Thu, 10 Dec 2009 16:30:04 +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/10/t1260459001tsvtl9mo8u9o8ow.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 «

62.7 62.3 61.9 62 62.3 62.8 62.4 62.3 62.7 62.7 62.9 63 62.2 62.3 62.8 62.8 62.8 62.2 62.6 62.8 62.5 62.4 62.3 61.9 61.7 62 62.1 61.7 61.8 61.8 61.8 61.3 61.3 61.3 61.2 61.4 62.2 62.9 63.1 63.5 63.6 64.4 64.1 65.1 65.8 65.9 65.4 65.5 64.8 63.2 62.7 62.1 61.9 60.6 60.7 59.8 59 58.3 59.3 59 59.1

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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.218104	1.6894	0.048164
2	0.210878	1.6335	0.053805
3	0.174644	1.3528	0.0906
4	0.31971	2.4765	0.008053
5	-0.036778	-0.2849	0.388358
6	0.061927	0.4797	0.316598
7	0.103134	0.7989	0.213758
8	-0.037995	-0.2943	0.384768
9	-0.221989	-1.7195	0.045337
10	-0.166926	-1.293	0.100484
11	0.034473	0.267	0.395182
12	-0.418752	-3.2436	0.000965
13	-0.280031	-2.1691	0.017024
14	-0.14662	-1.1357	0.130296
15	0.019555	0.1515	0.440057
16	-0.216757	-1.679	0.049177
17	-0.056151	-0.4349	0.332581
18	-0.030096	-0.2331	0.40823
19	-0.033825	-0.262	0.397105
20	-0.121471	-0.9409	0.175262
21	0.001968	0.0152	0.493943
22	0.143667	1.1128	0.135107
23	-0.015721	-0.1218	0.451741
24	-0.068402	-0.5298	0.299089
25	0.097384	0.7543	0.2268
26	0.075265	0.583	0.281038
27	-0.04864	-0.3768	0.353838
28	0.038798	0.3005	0.382406
29	0.085833	0.6649	0.254345
30	0.048045	0.3722	0.355546
31	-0.059026	-0.4572	0.324584
32	0.070241	0.5441	0.2942
33	0.114944	0.8904	0.188416
34	-0.000544	-0.0042	0.498326
35	-0.10619	-0.8225	0.207012
36	0.081611	0.6322	0.264843
37	-0.023517	-0.1822	0.428034
38	-0.041751	-0.3234	0.373758
39	0.001528	0.0118	0.495298
40	0.033023	0.2558	0.399493
41	-0.098653	-0.7642	0.223882
42	-0.083605	-0.6476	0.259856
43	-0.038125	-0.2953	0.384387
44	0.000104	8e-04	0.499681
45	-0.064621	-0.5005	0.30926
46	-0.093991	-0.7281	0.234707
47	0.038125	0.2953	0.384387
48	-0.028412	-0.2201	0.413278
49	0.000104	8e-04	0.499681
50	0.026677	0.2066	0.418496
51	-0.009557	-0.074	0.470617
52	-0.043331	-0.3356	0.369157
53	0.03569	0.2765	0.391574
54	0.040637	0.3148	0.377013
55	0.04157	0.322	0.374287
56	-0.008003	-0.062	0.475388
57	-0.016395	-0.127	0.449685
58	0.001761	0.0136	0.49458
59	-0.003522	-0.0273	0.489162
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.218104	1.6894	0.048164
2	0.171465	1.3282	0.094577
3	0.107244	0.8307	0.204716
4	0.258154	1.9997	0.025036
5	-0.198862	-1.5404	0.064363
6	-0.004273	-0.0331	0.486851
7	0.074472	0.5769	0.283096
8	-0.15811	-1.2247	0.112734
9	-0.181622	-1.4068	0.082317
10	-0.143872	-1.1144	0.134771
11	0.149462	1.1577	0.125782
12	-0.391856	-3.0353	0.001775
13	-0.082325	-0.6377	0.263051
14	0.079763	0.6178	0.26951
15	0.129796	1.0054	0.159372
16	0.083592	0.6475	0.259888
17	-0.064217	-0.4974	0.310354
18	-0.02985	-0.2312	0.408967
19	-0.015448	-0.1197	0.452576
20	-0.039075	-0.3027	0.381593
21	-0.149572	-1.1586	0.12561
22	0.019707	0.1526	0.439594
23	0.075132	0.582	0.281383
24	-0.23071	-1.7871	0.039489
25	0.035717	0.2767	0.391496
26	-0.053277	-0.4127	0.340656
27	0.089615	0.6942	0.245132
28	0.104332	0.8082	0.211098
29	-0.051969	-0.4026	0.344355
30	0.037421	0.2899	0.38646
31	-0.086417	-0.6694	0.25291
32	0.07247	0.5613	0.288325
33	-0.054018	-0.4184	0.338566
34	-0.004404	-0.0341	0.486451
35	-0.05989	-0.4639	0.322198
36	-0.079764	-0.6178	0.269507
37	-0.040852	-0.3164	0.376383
38	-0.034835	-0.2698	0.394109
39	0.144229	1.1172	0.134183
40	-0.046045	-0.3567	0.361299
41	-0.044189	-0.3423	0.366665
42	0.023567	0.1826	0.427883
43	-0.105527	-0.8174	0.208464
44	0.058924	0.4564	0.324867
45	-0.046398	-0.3594	0.360281
46	0.012271	0.095	0.462296
47	-0.029138	-0.2257	0.411102
48	-0.046047	-0.3567	0.361291
49	0.046161	0.3576	0.360962
50	-0.021954	-0.1701	0.432769
51	-0.029565	-0.229	0.409819
52	-0.02333	-0.1807	0.428601
53	0.037901	0.2936	0.385045
54	-0.011575	-0.0897	0.464428
55	-0.080707	-0.6252	0.267119
56	-0.016236	-0.1258	0.45017
57	-0.0222	-0.172	0.432024
58	-0.013631	-0.1056	0.458133
59	-0.013111	-0.1016	0.459725
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/10/t1260459001tsvtl9mo8u9o8ow/1h2q61260458885.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/10/t1260459001tsvtl9mo8u9o8ow/1h2q61260458885.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/10/t1260459001tsvtl9mo8u9o8ow/2cfm71260458885.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/10/t1260459001tsvtl9mo8u9o8ow/2cfm71260458885.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; 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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