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paper

*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: Wed, 17 Dec 2008 01:04:31 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/17/t1229501112xv7f0kxjnyf1rrl.htm/, Retrieved Wed, 17 Dec 2008 09:05:12 +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/2008/Dec/17/t1229501112xv7f0kxjnyf1rrl.htm/},
    year = {2008},
}
@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 = {2008},
    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 «

31.58 27.88 27.32 28.89 28.05 28.73 32.00 34.53 33.47 34.09 35.47 34.59 34.32 32.78 28.38 29.18 28.62 28.20 29.33 29.72 26.29 26.82 27.64 27.10 27.05 26.02 25.76 25.94 24.97 21.74 18.16 16.95 16.46 16.44 18.20 16.44 15.70 13.94 12.23 14.75 14.62 15.04 15.50 16.10 15.44 15.14 15.42 15.69 17.57 18.42 17.96 18.39 17.63 17.95 17.79 17.73 18.99 19.83 20.23 20.24 21.12 21.25 21.80 21.84 22.21 22.64 23.54 23.78 23.65 23.93 24.77 26.26 27.69 29.54 29.31 29.26 28.69 26.16 27.12 29.40 30.99 32.96 32.20 31.67 32.49 33.66 32.44 34.38 32.36 30.73 30.31 27.26 25.05 22.33 18.26 18.30 16.00 14.36 14.98 16.88 16.56 13.31 9.61 9.34 7.89 1.71 0.81 0.71

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.93298	9.6958	0
2	0.856611	8.9022	0
3	0.779319	8.0989	0
4	0.710352	7.3822	0
5	0.645474	6.708	0
6	0.578207	6.0089	0
7	0.514667	5.3486	0
8	0.457429	4.7537	3e-06
9	0.396745	4.1231	3.7e-05
10	0.321186	3.3379	0.000579
11	0.240363	2.4979	0.007
12	0.162713	1.691	0.046864
13	0.085491	0.8884	0.188138
14	0.007108	0.0739	0.470627
15	-0.054063	-0.5618	0.287696
16	-0.111982	-1.1638	0.123545
17	-0.166678	-1.7322	0.043049
18	-0.212412	-2.2074	0.014699
19	-0.255845	-2.6588	0.004517
20	-0.294159	-3.057	0.001409
21	-0.314964	-3.2732	0.000714
22	-0.338467	-3.5175	0.000319
23	-0.354418	-3.6832	0.000181
24	-0.368763	-3.8323	0.000107
25	-0.384621	-3.9971	5.9e-05
26	-0.393871	-4.0932	4.1e-05
27	-0.394326	-4.098	4e-05
28	-0.40021	-4.1591	3.2e-05
29	-0.409831	-4.2591	2.2e-05
30	-0.420596	-4.371	1.4e-05
31	-0.428011	-4.448	1.1e-05
32	-0.421598	-4.3814	1.4e-05
33	-0.40887	-4.2491	2.3e-05
34	-0.39327	-4.087	4.2e-05
35	-0.374938	-3.8965	8.5e-05
36	-0.353956	-3.6784	0.000184
37	-0.335363	-3.4852	0.000356
38	-0.317231	-3.2968	0.000662
39	-0.296602	-3.0824	0.001303
40	-0.281515	-2.9256	0.002096
41	-0.262865	-2.7318	0.00368
42	-0.242998	-2.5253	0.006506
43	-0.224566	-2.3338	0.01073
44	-0.202061	-2.0999	0.019034
45	-0.176014	-1.8292	0.035065
46	-0.146438	-1.5218	0.065487
47	-0.116647	-1.2122	0.114035
48	-0.086031	-0.8941	0.186639
49	-0.058774	-0.6108	0.271307
50	-0.027732	-0.2882	0.386874
51	0.005099	0.053	0.478919
52	0.034502	0.3586	0.360313
53	0.063764	0.6627	0.25448
54	0.092985	0.9663	0.168019
55	0.12414	1.2901	0.099885
56	0.157085	1.6325	0.052745
57	0.190591	1.9807	0.025085
58	0.221863	2.3057	0.01152
59	0.254878	2.6488	0.004645
60	0.285105	2.9629	0.001875

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.93298	9.6958	0
2	-0.106832	-1.1102	0.134682
3	-0.043647	-0.4536	0.325517
4	0.022267	0.2314	0.408718
5	-0.01698	-0.1765	0.430133
6	-0.063056	-0.6553	0.256836
7	-0.007446	-0.0774	0.469232
8	0.006737	0.07	0.472155
9	-0.076269	-0.7926	0.214872
10	-0.156021	-1.6214	0.053922
11	-0.075777	-0.7875	0.216357
12	-0.033931	-0.3526	0.36253
13	-0.082275	-0.855	0.197214
14	-0.087981	-0.9143	0.181291
15	0.0732	0.7607	0.224241
16	-0.062285	-0.6473	0.259409
17	-0.06531	-0.6787	0.249384
18	0.023218	0.2413	0.404893
19	-0.026972	-0.2803	0.389891
20	-0.031529	-0.3277	0.371904
21	0.087656	0.911	0.182175
22	-0.066787	-0.6941	0.244565
23	0.008582	0.0892	0.464549
24	-0.048449	-0.5035	0.307819
25	-0.067473	-0.7012	0.242343
26	0.004818	0.0501	0.48008
27	0.010241	0.1064	0.457718
28	-0.116217	-1.2078	0.114889
29	-0.068132	-0.708	0.240221
30	-0.079132	-0.8224	0.206341
31	-0.054521	-0.5666	0.286081
32	0.052925	0.55	0.291724
33	-0.011528	-0.1198	0.45243
34	-0.022358	-0.2323	0.408354
35	0.01709	0.1776	0.429682
36	-0.040947	-0.4255	0.335649
37	-0.032184	-0.3345	0.369338
38	0.008986	0.0934	0.462887
39	-0.011058	-0.1149	0.454362
40	-0.068343	-0.7102	0.239543
41	0.013775	0.1432	0.443217
42	-0.064164	-0.6668	0.253156
43	-0.048286	-0.5018	0.308412
44	-0.010032	-0.1043	0.458579
45	-0.020792	-0.2161	0.414669
46	0.029707	0.3087	0.379065
47	-0.013627	-0.1416	0.443824
48	-0.029428	-0.3058	0.380165
49	-0.006062	-0.063	0.474941
50	0.019217	0.1997	0.421043
51	0.004743	0.0493	0.480391
52	0.019635	0.2041	0.419347
53	0.015541	0.1615	0.435997
54	-0.016279	-0.1692	0.432987
55	0.031921	0.3317	0.370366
56	0.01727	0.1795	0.42895
57	0.020839	0.2166	0.414477
58	0.036543	0.3798	0.352431
59	0.029805	0.3097	0.378679
60	-0.012637	-0.1313	0.447878

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/17/t1229501112xv7f0kxjnyf1rrl/1nh6x1229501067.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/17/t1229501112xv7f0kxjnyf1rrl/1nh6x1229501067.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/17/t1229501112xv7f0kxjnyf1rrl/2l2o91229501067.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/17/t1229501112xv7f0kxjnyf1rrl/2l2o91229501067.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

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 (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='lags',ylab='ACF')

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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