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*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: Tue, 29 Dec 2009 13:21:47 -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/29/t1262118162wnewnewn26qbjdf.htm/, Retrieved Tue, 29 Dec 2009 21:22:44 +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/29/t1262118162wnewnewn26qbjdf.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 «

100.44 100.51 101.00 100.88 100.55 100.83 101.51 102.16 102.39 102.54 102.85 103.47 103.57 103.69 103.50 103.47 103.45 103.48 103.93 103.89 104.40 104.79 104.77 105.13 105.26 104.96 104.75 105.01 105.15 105.20 105.77 105.78 106.26 106.13 106.12 106.57 106.44 106.54 107.10 108.10 108.40 108.84 109.62 110.42 110.67 111.66 112.28 112.87 112.18 112.36 112.16 111.49 111.25 111.36 111.74 111.10 111.33 111.25 111.04 110.97 111.31 111.02 111.07 111.36

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	0.961991	7.6959	0
2	0.921791	7.3743	0
3	0.881785	7.0543	0
4	0.835598	6.6848	0
5	0.784857	6.2789	0
6	0.734347	5.8748	0
7	0.686389	5.4911	0
8	0.639614	5.1169	2e-06
9	0.594648	4.7572	6e-06
10	0.546769	4.3742	2.3e-05
11	0.501715	4.0137	8e-05
12	0.459287	3.6743	0.000245
13	0.415817	3.3265	0.00073
14	0.369734	2.9579	0.002168
15	0.320344	2.5628	0.006374
16	0.269644	2.1572	0.017377
17	0.215574	1.7246	0.044714
18	0.16332	1.3066	0.098019
19	0.116051	0.9284	0.178342
20	0.07221	0.5777	0.282754
21	0.032932	0.2635	0.396524
22	-0.00155	-0.0124	0.495071
23	-0.034501	-0.276	0.391715
24	-0.063797	-0.5104	0.305771
25	-0.092572	-0.7406	0.23083
26	-0.120004	-0.96	0.170327
27	-0.147392	-1.1791	0.121355
28	-0.173299	-1.3864	0.085219
29	-0.199712	-1.5977	0.057518
30	-0.224578	-1.7966	0.038557
31	-0.246516	-1.9721	0.02646
32	-0.269629	-2.157	0.017382
33	-0.288967	-2.3117	0.012011
34	-0.311489	-2.4919	0.007653
35	-0.332796	-2.6624	0.004901
36	-0.352044	-2.8164	0.003225
37	-0.37411	-2.9929	0.001962
38	-0.395368	-3.1629	0.001194
39	-0.414736	-3.3179	0.000749
40	-0.429973	-3.4398	0.000515
41	-0.443316	-3.5465	0.000368
42	-0.451783	-3.6143	0.000297
43	-0.454854	-3.6388	0.000274
44	-0.450776	-3.6062	0.000305
45	-0.442229	-3.5378	0.000378
46	-0.427065	-3.4165	0.000553
47	-0.404893	-3.2391	0.000951
48	-0.379001	-3.032	0.001753
49	-0.357677	-2.8614	0.002846
50	-0.334798	-2.6784	0.004695
51	-0.313694	-2.5096	0.007315
52	-0.296567	-2.3725	0.010341
53	-0.28078	-2.2462	0.014074
54	-0.261039	-2.0883	0.020377
55	-0.237463	-1.8997	0.03099
56	-0.217451	-1.7396	0.043367
57	-0.194688	-1.5575	0.062141
58	-0.169478	-1.3558	0.08996
59	-0.142589	-1.1407	0.12912
60	-0.114551	-0.9164	0.181447

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.961991	7.6959	0
2	-0.048743	-0.3899	0.348938
3	-0.017515	-0.1401	0.444503
4	-0.10452	-0.8362	0.203087
5	-0.08269	-0.6615	0.255328
6	-0.023833	-0.1907	0.424697
7	0.010909	0.0873	0.465364
8	-0.004542	-0.0363	0.485564
9	-0.001221	-0.0098	0.496117
10	-0.075068	-0.6005	0.275133
11	0.002389	0.0191	0.492404
12	-0.00226	-0.0181	0.492815
13	-0.038977	-0.3118	0.378096
14	-0.065062	-0.5205	0.302258
15	-0.085711	-0.6857	0.247692
16	-0.058728	-0.4698	0.320039
17	-0.078805	-0.6304	0.265326
18	-0.005675	-0.0454	0.481963
19	0.035647	0.2852	0.388215
20	0.009145	0.0732	0.470955
21	0.016748	0.134	0.446918
22	0.011281	0.0902	0.464187
23	-0.03405	-0.2724	0.393095
24	0.001524	0.0122	0.495156
25	-0.045028	-0.3602	0.359934
26	-0.018874	-0.151	0.440229
27	-0.041004	-0.328	0.371979
28	-0.016808	-0.1345	0.446729
29	-0.034118	-0.2729	0.392887
30	-0.003423	-0.0274	0.489121
31	0.007225	0.0578	0.477045
32	-0.050084	-0.4007	0.344997
33	0.003687	0.0295	0.488281
34	-0.102401	-0.8192	0.207854
35	-0.041516	-0.3321	0.370439
36	-0.028574	-0.2286	0.409957
37	-0.084034	-0.6723	0.251916
38	-0.029026	-0.2322	0.408557
39	-0.01676	-0.1341	0.44688
40	0.016887	0.1351	0.446481
41	0.002623	0.021	0.491662
42	0.0274	0.2192	0.413596
43	0.036312	0.2905	0.386189
44	0.054883	0.4391	0.331046
45	0.017196	0.1376	0.445505
46	0.061058	0.4885	0.313445
47	0.061334	0.4907	0.312669
48	0.03869	0.3095	0.378966
49	-0.080882	-0.6471	0.259954
50	0.01182	0.0946	0.462481
51	-0.03812	-0.305	0.380692
52	-0.059929	-0.4794	0.316632
53	-0.022245	-0.178	0.42966
54	0.044761	0.3581	0.360729
55	0.034012	0.2721	0.393213
56	-0.063859	-0.5109	0.3056
57	0.004804	0.0384	0.484733
58	0.007491	0.0599	0.476199
59	0.000679	0.0054	0.497841
60	0.008023	0.0642	0.474513

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/29/t1262118162wnewnewn26qbjdf/1umdu1262118104.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/29/t1262118162wnewnewn26qbjdf/1umdu1262118104.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/29/t1262118162wnewnewn26qbjdf/2v5cr1262118104.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/29/t1262118162wnewnewn26qbjdf/2v5cr1262118104.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; 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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