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R Software Module: /rwasp_autocorrelation.wasp (opens new window with default values)

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Sat, 29 May 2010 11:09:47 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/May/29/t1275131446yynzgxde35usd86.htm/, Retrieved Sat, 29 May 2010 13:10:47 +0200

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/2010/May/29/t1275131446yynzgxde35usd86.htm/},
    year = {2010},
}
@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 = {2010},
    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:

KDGP2W21

Dataseries X:

» Textbox « » Textfile « » CSV «

589 561 640 656 727 697 640 599 568 577 553 582 600 566 653 673 742 716 660 617 583 587 565 598 628 618 688 705 770 736 678 639 604 611 594 634 658 622 709 722 782 756 702 653 615 621 602 635 677 635 736 755 811 798 735 697 661 667 645 688 713 667 762 784 837 817 767 722 681 687 660 698 717 696 775 796 858 826 783 740 701 706 677 711 734 690 785 805 871 845 801 764 725 723 690 734 750 707 807 824 886 859 819 783 740 747 711 751 804 756 860 878 942 913 869 834 790 800 763 800 826 799 890 900 961 935 894 855 809 810 766 805 821 773 883 898 957 924 881 837 784 791 760 802 828 778 889 902 969 947 908 867 815 812 773 813 834 782 892 903 966 937 896 858 817 827 797 843

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.022553	0.2915	0.385534
2	0.25625	3.3115	0.000569
3	-0.114132	-1.4749	0.07106
4	-0.359139	-4.6411	3e-06
5	-0.057959	-0.749	0.227459
6	-0.501727	-6.4837	0
7	-0.032898	-0.4251	0.335642
8	-0.346924	-4.4832	7e-06
9	-0.08174	-1.0563	0.146175
10	0.233301	3.0149	0.001486
11	0.028109	0.3632	0.358442
12	0.910586	11.7674	0
13	0.030501	0.3942	0.346982
14	0.238269	3.0791	0.001214
15	-0.103146	-1.3329	0.092183
16	-0.329524	-4.2584	1.7e-05
17	-0.057527	-0.7434	0.229139
18	-0.463908	-5.995	0
19	-0.031392	-0.4057	0.342751
20	-0.32044	-4.141	2.7e-05
21	-0.07893	-1.02	0.154603
22	0.20804	2.6885	0.003953
23	0.028397	0.367	0.357055
24	0.832515	10.7585	0
25	0.028815	0.3724	0.355046
26	0.222166	2.871	0.002311
27	-0.08626	-1.1147	0.133285
28	-0.300429	-3.8824	7.4e-05
29	-0.056451	-0.7295	0.233357
30	-0.422362	-5.4581	0
31	-0.022996	-0.2972	0.383353
32	-0.29715	-3.84	8.7e-05
33	-0.07935	-1.0254	0.153321
34	0.188218	2.4323	0.008029
35	0.021601	0.2792	0.390237
36	0.762202	9.8498	0
37	0.024604	0.318	0.37546
38	0.20885	2.6989	0.003836
39	-0.07113	-0.9192	0.179656
40	-0.26438	-3.4165	0.000398
41	-0.053541	-0.6919	0.244978
42	-0.384723	-4.9717	1e-06
43	-0.022098	-0.2856	0.387779
44	-0.278814	-3.6031	0.000207
45	-0.079719	-1.0302	0.152205
46	0.166151	2.1471	0.016612
47	0.016273	0.2103	0.416849
48	0.698978	9.0328	0
49	0.018926	0.2446	0.403541
50	0.194647	2.5154	0.006417
51	-0.066641	-0.8612	0.195184
52	-0.23046	-2.9782	0.001666
53	-0.049417	-0.6386	0.261975
54	-0.347197	-4.4868	7e-06
55	-0.012835	-0.1659	0.434232
56	-0.259865	-3.3582	0.000486
57	-0.067934	-0.8779	0.190628
58	0.139894	1.8078	0.036216
59	0.020152	0.2604	0.397429
60	0.619128	8.0009	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.022553	0.2915	0.385534
2	0.255872	3.3066	0.000578
3	-0.132972	-1.7184	0.043791
4	-0.453911	-5.8658	0
5	0.027237	0.352	0.362649
6	-0.36238	-4.683	3e-06
7	-0.170976	-2.2095	0.01425
8	-0.44249	-5.7182	0
9	-0.463537	-5.9902	0
10	-0.238682	-3.0845	0.001194
11	-0.581055	-7.5089	0
12	0.638319	8.2489	0
13	-0.030479	-0.3939	0.347088
14	-0.345868	-4.4696	7e-06
15	0.023528	0.3041	0.380734
16	0.185647	2.3991	0.008769
17	-0.011448	-0.1479	0.441283
18	0.093607	1.2097	0.114057
19	-0.068238	-0.8818	0.189569
20	0.066537	0.8599	0.195552
21	0.013492	0.1744	0.430898
22	-0.037472	-0.4842	0.314423
23	0.023215	0.3	0.382272
24	0.066334	0.8572	0.196276
25	-0.129152	-1.669	0.048495
26	-0.042958	-0.5551	0.289772
27	0.04966	0.6418	0.260957
28	-0.007559	-0.0977	0.461152
29	-0.096409	-1.2459	0.107276
30	0.011021	0.1424	0.443458
31	0.056909	0.7354	0.231555
32	-0.013081	-0.169	0.432983
33	-0.081184	-1.0491	0.147818
34	0.055783	0.7209	0.235996
35	0.024364	0.3148	0.376634
36	-0.019837	-0.2564	0.398996
37	-0.031753	-0.4103	0.341042
38	0.037765	0.488	0.313083
39	0.025131	0.3248	0.372881
40	0.052104	0.6733	0.250835
41	-0.000175	-0.0023	0.499098
42	0.040734	0.5264	0.299653
43	-0.009164	-0.1184	0.452938
44	-0.003084	-0.0399	0.484128
45	0.052283	0.6756	0.250099
46	0.032587	0.4211	0.337106
47	-0.047081	-0.6084	0.271867
48	0.024583	0.3177	0.375563
49	-0.000799	-0.0103	0.495889
50	-0.026944	-0.3482	0.364067
51	-0.093656	-1.2103	0.113937
52	-0.005795	-0.0749	0.470198
53	0.012481	0.1613	0.436028
54	-0.058986	-0.7623	0.223487
55	-0.034853	-0.4504	0.326504
56	0.028351	0.3664	0.357274
57	0.050118	0.6477	0.259044
58	-0.046631	-0.6026	0.273793
59	0.05099	0.6589	0.255423
60	-0.053953	-0.6972	0.243314

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/May/29/t1275131446yynzgxde35usd86/1qp611275131383.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/29/t1275131446yynzgxde35usd86/1qp611275131383.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/May/29/t1275131446yynzgxde35usd86/20g541275131383.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/29/t1275131446yynzgxde35usd86/20g541275131383.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; 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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