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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 06:19:16 -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/t1262006379mspqktvvxnjwk2t.htm/, Retrieved Mon, 28 Dec 2009 14:19:41 +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/t1262006379mspqktvvxnjwk2t.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	-0.332927	-2.8053	0.003241
2	-0.301441	-2.54	0.006638
3	0.072303	0.6092	0.272157
4	0.129269	1.0892	0.139865
5	-0.205646	-1.7328	0.043736
6	0.323115	2.7226	0.004072
7	-0.260508	-2.1951	0.015714
8	0.162998	1.3734	0.086968
9	0.087264	0.7353	0.232289
10	-0.344227	-2.9005	0.002478
11	-0.165094	-1.3911	0.084269
12	0.704441	5.9357	0
13	-0.266994	-2.2497	0.013784
14	-0.150942	-1.2719	0.103787
15	0.005662	0.0477	0.481041
16	0.019564	0.1649	0.434765
17	-0.049382	-0.4161	0.339297
18	0.217234	1.8304	0.03569
19	-0.213837	-1.8018	0.037909
20	0.152861	1.288	0.100959
21	0.071082	0.5989	0.275557
22	-0.354053	-2.9833	0.001953
23	0.027295	0.23	0.40938
24	0.423427	3.5679	0.000325
25	-0.191314	-1.612	0.055695
26	-0.058977	-0.497	0.310379
27	-0.038757	-0.3266	0.372476
28	-0.000654	-0.0055	0.497809
29	0.002771	0.0234	0.490718
30	0.118043	0.9946	0.161642
31	-0.149896	-1.263	0.105353
32	0.192847	1.625	0.054302
33	-0.040774	-0.3436	0.366093
34	-0.236811	-1.9954	0.024918
35	0.023673	0.1995	0.421233
36	0.299234	2.5214	0.006968
37	-0.105726	-0.8909	0.188005
38	-0.048584	-0.4094	0.341748
39	-0.093546	-0.7882	0.216592
40	0.089876	0.7573	0.225686
41	-0.030862	-0.26	0.39779
42	0.066171	0.5576	0.289446
43	-0.128554	-1.0832	0.141189
44	0.199754	1.6832	0.048368
45	-0.076545	-0.645	0.260508
46	-0.123729	-1.0426	0.150345
47	-0.038785	-0.3268	0.372388
48	0.220658	1.8593	0.033564
49	-0.037944	-0.3197	0.37506
50	-0.061247	-0.5161	0.303702
51	-0.07827	-0.6595	0.25585
52	0.083884	0.7068	0.240997
53	-0.024074	-0.2029	0.419914
54	0.040664	0.3426	0.36644
55	-0.060326	-0.5083	0.306404
56	0.087285	0.7355	0.232236
57	-0.030902	-0.2604	0.397659
58	-0.051343	-0.4326	0.333298
59	-0.039438	-0.3323	0.370318
60	0.114056	0.9611	0.169894

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.332927	-2.8053	0.003241
2	-0.463675	-3.907	0.000105
3	-0.328022	-2.764	0.003634
4	-0.195318	-1.6458	0.052114
5	-0.437926	-3.69	0.000218
6	0.086019	0.7248	0.235476
7	-0.339559	-2.8612	0.00277
8	0.237805	2.0038	0.024455
9	0.348154	2.9336	0.002254
10	-0.189788	-1.5992	0.057111
11	-0.409624	-3.4515	0.000471
12	0.125899	1.0608	0.146178
13	-0.003194	-0.0269	0.489304
14	0.179133	1.5094	0.067817
15	0.000165	0.0014	0.499447
16	-0.067189	-0.5661	0.286541
17	0.005647	0.0476	0.48109
18	-0.141084	-1.1888	0.11924
19	0.09715	0.8186	0.207877
20	-0.061606	-0.5191	0.302652
21	0.044704	0.3767	0.353767
22	-0.10368	-0.8736	0.192634
23	0.099226	0.8361	0.202955
24	0.043625	0.3676	0.357136
25	-0.010424	-0.0878	0.465127
26	0.048909	0.4121	0.340747
27	-0.151314	-1.275	0.103234
28	0.146501	1.2344	0.110555
29	-0.133597	-1.1257	0.132039
30	-0.019899	-0.1677	0.433658
31	-0.080534	-0.6786	0.249802
32	-0.01236	-0.1041	0.458672
33	0.018397	0.155	0.438625
34	0.113542	0.9567	0.170976
35	-0.102391	-0.8628	0.195587
36	0.044899	0.3783	0.35316
37	0.020788	0.1752	0.430725
38	-0.056652	-0.4774	0.317287
39	-0.007238	-0.061	0.47577
40	-0.024646	-0.2077	0.418039
41	0.040606	0.3422	0.366624
42	0.014584	0.1229	0.451272
43	-0.042343	-0.3568	0.361153
44	-0.125056	-1.0537	0.147787
45	-0.010687	-0.09	0.464251
46	-0.059754	-0.5035	0.308086
47	0.064022	0.5395	0.29563
48	-0.03193	-0.269	0.394336
49	-0.051867	-0.437	0.331703
50	-0.049758	-0.4193	0.338144
51	-0.022488	-0.1895	0.425126
52	-0.064369	-0.5424	0.294627
53	-0.057658	-0.4858	0.31429
54	-0.041833	-0.3525	0.362756
55	0.045186	0.3807	0.352266
56	-0.013751	-0.1159	0.454043
57	-0.058248	-0.4908	0.31254
58	0.007292	0.0614	0.475588
59	0.064847	0.5464	0.293249
60	-0.007156	-0.0603	0.476043

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/28/t1262006379mspqktvvxnjwk2t/1sk661262006354.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/28/t1262006379mspqktvvxnjwk2t/1sk661262006354.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/28/t1262006379mspqktvvxnjwk2t/2ft7l1262006354.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/28/t1262006379mspqktvvxnjwk2t/2ft7l1262006354.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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