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Paper 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: Sat, 19 Dec 2009 09:26:13 -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/19/t1261240024f5ryncanr31q6ka.htm/, Retrieved Sat, 19 Dec 2009 17:27:07 +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/19/t1261240024f5ryncanr31q6ka.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 «

13.4 13.5 14.8 14.3 14.3 14 13.2 12.2 14.3 15.7 14.2 14.6 14.5 14.3 15.3 14.4 13.7 14.2 13.5 11.9 14.6 15.6 14.1 14.9 14.2 14.6 17.2 15.4 14.3 17.5 14.5 14.4 16.6 16.7 16.6 16.9 15.7 16.4 18.4 16.9 16.5 18.3 15.1 15.7 18.1 16.8 18.9 19 18.1 17.8 21.5 17.1 18.7 19 16.4 16.9 18.6 19.3 19.4 17.6 18.6 18.1 20.4 18.1 19.6 19.9 19.2 17.8 19.2 22 21.1 19.5

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	0.750925	6.3718	0
2	0.659293	5.5943	0
3	0.70873	6.0138	0
4	0.615435	5.2221	1e-06
5	0.616211	5.2287	1e-06
6	0.670587	5.6901	0
7	0.534363	4.5342	1.1e-05
8	0.504513	4.2809	2.8e-05
9	0.539045	4.5739	1e-05
10	0.407743	3.4598	0.000456
11	0.466824	3.9611	8.7e-05
12	0.575869	4.8864	3e-06
13	0.399545	3.3903	0.000568
14	0.351545	2.983	0.001947
15	0.358867	3.0451	0.001624
16	0.273175	2.318	0.011648
17	0.30115	2.5553	0.00636
18	0.323702	2.7467	0.0038
19	0.205993	1.7479	0.042372
20	0.176313	1.4961	0.069504
21	0.174765	1.4829	0.071229
22	0.044443	0.3771	0.353599
23	0.10977	0.9314	0.177373
24	0.12293	1.0431	0.150196
25	-0.015879	-0.1347	0.446598
26	-0.062866	-0.5334	0.297689
27	-0.067463	-0.5724	0.284402
28	-0.136972	-1.1622	0.124486
29	-0.11026	-0.9356	0.176307
30	-0.096186	-0.8162	0.208549
31	-0.169481	-1.4381	0.07737
32	-0.169066	-1.4346	0.07787
33	-0.206838	-1.7551	0.04175
34	-0.268596	-2.2791	0.012813
35	-0.202502	-1.7183	0.045021
36	-0.180312	-1.53	0.065199
37	-0.255955	-2.1719	0.016581
38	-0.295499	-2.5074	0.00721
39	-0.302329	-2.5653	0.006195
40	-0.329396	-2.795	0.003324
41	-0.312176	-2.6489	0.004959
42	-0.299552	-2.5418	0.006591
43	-0.347978	-2.9527	0.002126
44	-0.332803	-2.8239	0.003066
45	-0.36181	-3.0701	0.001509
46	-0.398944	-3.3852	0.000577
47	-0.359156	-3.0475	0.001612
48	-0.308942	-2.6215	0.005338
49	-0.337855	-2.8668	0.002717
50	-0.36197	-3.0714	0.001503
51	-0.338331	-2.8708	0.002686
52	-0.331386	-2.8119	0.003171
53	-0.284782	-2.4165	0.009104
54	-0.256674	-2.178	0.016343
55	-0.259938	-2.2056	0.015301
56	-0.251712	-2.1359	0.018046
57	-0.251916	-2.1376	0.017973
58	-0.24782	-2.1028	0.019489
59	-0.225243	-1.9112	0.029977
60	-0.200242	-1.6991	0.046808

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.750925	6.3718	0
2	0.218762	1.8563	0.033754
3	0.379733	3.2221	0.000956
4	-0.067465	-0.5725	0.284396
5	0.202017	1.7142	0.0454
6	0.175661	1.4905	0.070227
7	-0.214391	-1.8192	0.036522
8	0.019211	0.163	0.435485
9	0.023194	0.1968	0.422267
10	-0.199497	-1.6928	0.047409
11	0.257081	2.1814	0.01621
12	0.244468	2.0744	0.02081
13	-0.297386	-2.5234	0.006915
14	-0.098615	-0.8368	0.202743
15	-0.118551	-1.0059	0.158907
16	0.025219	0.214	0.41558
17	-0.001942	-0.0165	0.493448
18	-0.028129	-0.2387	0.406016
19	0.033533	0.2845	0.388407
20	-0.145081	-1.2311	0.111154
21	-0.027462	-0.233	0.408201
22	-0.101658	-0.8626	0.195611
23	0.074742	0.6342	0.263977
24	-0.147203	-1.2491	0.107844
25	-0.06797	-0.5767	0.282956
26	-0.12945	-1.0984	0.137841
27	0.059663	0.5063	0.307111
28	-0.012485	-0.1059	0.457963
29	-0.030127	-0.2556	0.399479
30	0.040638	0.3448	0.365616
31	0.060189	0.5107	0.305553
32	-0.014269	-0.1211	0.451982
33	-0.116857	-0.9916	0.162364
34	0.082308	0.6984	0.243587
35	-0.032931	-0.2794	0.39036
36	0.077363	0.6564	0.256815
37	-0.009626	-0.0817	0.467563
38	-0.070428	-0.5976	0.275992
39	-0.003249	-0.0276	0.489041
40	-0.033089	-0.2808	0.389846
41	-0.045717	-0.3879	0.349608
42	0.014919	0.1266	0.449809
43	-0.059451	-0.5045	0.30774
44	0.043491	0.369	0.356592
45	0.014225	0.1207	0.452131
46	-0.093186	-0.7907	0.215854
47	0.001746	0.0148	0.494109
48	0.015941	0.1353	0.446391
49	0.04446	0.3773	0.353546
50	-0.046813	-0.3972	0.34619
51	0.058885	0.4997	0.30942
52	0.043649	0.3704	0.356097
53	0.045813	0.3887	0.349309
54	-0.028004	-0.2376	0.406426
55	0.044092	0.3741	0.354703
56	-0.034755	-0.2949	0.384457
57	-0.028599	-0.2427	0.404477
58	0.070697	0.5999	0.275233
59	-0.073668	-0.6251	0.266943
60	-0.106755	-0.9058	0.18402

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261240024f5ryncanr31q6ka/1ygnx1261239970.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261240024f5ryncanr31q6ka/1ygnx1261239970.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261240024f5ryncanr31q6ka/2pw9r1261239970.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261240024f5ryncanr31q6ka/2pw9r1261239970.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 0.0 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 0.0 ; par3 = 0 ; 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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