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acf

*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: Mon, 28 Dec 2009 06:23:40 -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/28/t1262006646umnpze439qy74mv.htm/, Retrieved Mon, 28 Dec 2009 14:24:08 +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/28/t1262006646umnpze439qy74mv.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 «

14.3 14.2 15.9 15.3 15.5 15.1 15 12.1 15.8 16.9 15.1 13.7 14.8 14.7 16 15.4 15 15.5 15.1 11.7 16.3 16.7 15 14.9 14.6 15.3 17.9 16.4 15.4 17.9 15.9 13.9 17.8 17.9 17.4 16.7 16 16.6 19.1 17.8 17.2 18.6 16.3 15.1 19.2 17.7 19.1 18 17.5 17.8 21.1 17.2 19.4 19.8 17.6 16.2 19.5 19.9 20 17.3 18.9 18.6 21.4 18.6 19.8 20.8 19.6 17.7 19.8 22.2 20.7 17.9

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	-0.592816	-4.5535	1.3e-05
2	-0.041597	-0.3195	0.375234
3	0.312207	2.3981	0.009831
4	-0.185668	-1.4261	0.079548
5	-0.05669	-0.4354	0.332416
6	0.287572	2.2089	0.01554
7	-0.373639	-2.87	0.002845
8	0.156224	1.2	0.117471
9	0.141826	1.0894	0.140206
10	-0.210122	-1.614	0.055935
11	0.078607	0.6038	0.274147
12	0.000291	0.0022	0.499112
13	-0.095825	-0.736	0.232309
14	0.188551	1.4483	0.076416
15	-0.077338	-0.594	0.277378
16	-0.202424	-1.5548	0.062666
17	0.3093	2.3758	0.010389
18	-0.164929	-1.2668	0.105095
19	0.023079	0.1773	0.429949
20	-0.034921	-0.2682	0.394728
21	0.158324	1.2161	0.114393
22	-0.291343	-2.2378	0.01451
23	0.341174	2.6206	0.005572
24	-0.155405	-1.1937	0.118688
25	-0.146325	-1.1239	0.132795
26	0.213349	1.6388	0.053292
27	-0.03609	-0.2772	0.391293
28	-0.135671	-1.0421	0.150807
29	0.184228	1.4151	0.081151
30	-0.16143	-1.24	0.109948
31	0.064189	0.493	0.311904
32	0.106168	0.8155	0.209036
33	-0.199923	-1.5356	0.064986
34	0.078201	0.6007	0.275179
35	0.123231	0.9466	0.173864
36	-0.199617	-1.5333	0.065275
37	0.138032	1.0602	0.146678
38	0.018482	0.142	0.443798
39	-0.191267	-1.4692	0.073552
40	0.248985	1.9125	0.030336
41	-0.112316	-0.8627	0.195894
42	-0.0785	-0.603	0.274419
43	0.131642	1.0112	0.158034
44	-0.031631	-0.243	0.404438
45	-0.073572	-0.5651	0.287069
46	0.088689	0.6812	0.249194
47	-0.046874	-0.36	0.36005
48	-0.020699	-0.159	0.437108
49	0.052614	0.4041	0.343786
50	-0.037198	-0.2857	0.388045
51	-0.01271	-0.0976	0.46128
52	0.037085	0.2849	0.388376
53	-0.033692	-0.2588	0.398348
54	0.01892	0.1453	0.442475
55	-0.010306	-0.0792	0.468586
56	0.008955	0.0688	0.472697
57	0.000609	0.0047	0.498141
58	2e-06	0	0.499993
59	NA	NA	NA
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.592816	-4.5535	1.3e-05
2	-0.605993	-4.6547	9e-06
3	-0.211106	-1.6215	0.055117
4	-0.01837	-0.1411	0.444134
5	-0.055751	-0.4282	0.33502
6	0.310106	2.382	0.010232
7	-0.02466	-0.1894	0.425209
8	-0.201234	-1.5457	0.063762
9	-0.135895	-1.0438	0.150411
10	-0.006565	-0.0504	0.479978
11	0.115326	0.8858	0.189652
12	-0.098956	-0.7601	0.225112
13	-0.282747	-2.1718	0.01695
14	-0.138624	-1.0648	0.145655
15	0.176613	1.3566	0.09004
16	-0.001518	-0.0117	0.495367
17	0.005579	0.0429	0.482983
18	-0.152522	-1.1715	0.123045
19	0.008958	0.0688	0.472687
20	-0.214433	-1.6471	0.052428
21	0.326081	2.5047	0.007519
22	-0.033871	-0.2602	0.397819
23	-0.025379	-0.1949	0.423054
24	0.010085	0.0775	0.469258
25	-0.118524	-0.9104	0.183159
26	-0.024109	-0.1852	0.426861
27	-0.146182	-1.1228	0.133026
28	-0.004568	-0.0351	0.486063
29	0.024648	0.1893	0.425243
30	0.004924	0.0378	0.484977
31	0.047688	0.3663	0.357727
32	0.033892	0.2603	0.397757
33	-0.068168	-0.5236	0.301255
34	-0.166355	-1.2778	0.103163
35	0.063056	0.4843	0.314968
36	0.038017	0.292	0.385651
37	0.088255	0.6779	0.250242
38	-0.135369	-1.0398	0.15134
39	0.056503	0.434	0.332932
40	-0.017412	-0.1337	0.44703
41	0.086124	0.6615	0.255424
42	-0.060841	-0.4673	0.320993
43	0.001193	0.0092	0.496358
44	-0.043342	-0.3329	0.37019
45	-0.015584	-0.1197	0.452563
46	0.036175	0.2779	0.391045
47	0.012354	0.0949	0.462362
48	0.04338	0.3332	0.37008
49	-0.127133	-0.9765	0.166395
50	-0.094945	-0.7293	0.234356
51	-0.03271	-0.2513	0.401246
52	-0.065833	-0.5057	0.307484
53	0.016176	0.1242	0.45077
54	0.017765	0.1365	0.445964
55	0.005363	0.0412	0.483641
56	-0.037364	-0.287	0.387558
57	0.117862	0.9053	0.18449
58	-0.12386	-0.9514	0.172645
59	NA	NA	NA
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/28/t1262006646umnpze439qy74mv/1ktah1262006618.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/28/t1262006646umnpze439qy74mv/1ktah1262006618.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/28/t1262006646umnpze439qy74mv/235kp1262006618.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/28/t1262006646umnpze439qy74mv/235kp1262006618.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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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