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workshop 9

*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: Sun, 05 Dec 2010 10:41:36 +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/Dec/05/t1291545631156xadafskn54jk.htm/, Retrieved Sun, 05 Dec 2010 11:40:33 +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/2010/Dec/05/t1291545631156xadafskn54jk.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

2938 2909 3141 2427 3059 2918 2901 2823 2798 2892 2967 2397 3458 3024 3100 2904 3056 2771 2897 2772 2857 3020 2648 2364 3194 3013 2560 3074 2746 2846 3184 2354 3080 2963 2430 2296 2416 2647 2789 2685 2666 2882 2953 2127 2563 3061 2809 2861 2781 2555 3206 2570 2410 3195 2736 2743 2934 2668 2907 2866 2983 2878 3225 2515 3193 2663 2908 2896 2853 3028 3053 2455 3401 2969 3243 2849 3296 3121 3194 3023 2984 3525 3116 2383 3294 2882 2820 2583 2803 2767 2945 2716 2644 2956 2598 2171 2994 2645 2724 2550 2707 2679 2878 2307 2496 2637 2436 2426 2607 2533 2888 2520 2229 2804 2661 2547 2509 2465 2629 2706 2666 2432 2836 2888 2566 2802 2611 2683 2675 2434 2693 2619 2903 2550 2900 2456 2912 2883 2464 2655 2447 2592 2698 2274 2901 2397 3004 2614 2882 2671 2761 2806 2414 2673 2748 2112 2903 2633 2684 2861 2504 2708 2961 2535 2688 2699 2469 2585 2582 2480 2709 etc...

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	0.071299	0.9566	0.170032
2	0.23789	3.1916	0.000835
3	0.36716	4.926	1e-06
4	0.24807	3.3282	0.00053
5	0.263768	3.5388	0.000256
6	0.245414	3.2926	0.000598
7	0.029019	0.3893	0.348746
8	0.40104	5.3805	0
9	0.23367	3.135	0.001004
10	0.054221	0.7274	0.233949
11	0.065207	0.8748	0.191414
12	0.45676	6.1281	0
13	0.005267	0.0707	0.47187
14	0.212363	2.8491	0.002447
15	0.099468	1.3345	0.091863
16	0.080917	1.0856	0.13955
17	0.202221	2.7131	0.003657
18	0.054151	0.7265	0.234234
19	-0.10326	-1.3854	0.083825
20	0.23443	3.1452	0.000971
21	-0.008878	-0.1191	0.452662
22	-0.045965	-0.6167	0.269113
23	0.043993	0.5902	0.277889
24	0.050638	0.6794	0.248885
25	-0.074279	-0.9966	0.160158
26	0.104713	1.4049	0.080892
27	-0.132517	-1.7779	0.038554
28	0.06144	0.8243	0.205427
29	0.016242	0.2179	0.413875
30	-0.122678	-1.6459	0.050765
31	-0.066783	-0.896	0.185728
32	0.091617	1.2292	0.110306
33	-0.150893	-2.0244	0.022201
34	0.018476	0.2479	0.402253
35	-0.071173	-0.9549	0.170457
36	-0.030075	-0.4035	0.343528
37	-0.028164	-0.3779	0.352989
38	-0.058366	-0.7831	0.21731
39	-0.144522	-1.939	0.027034
40	0.097348	1.3061	0.0966
41	-0.078551	-1.0539	0.146677
42	-0.117993	-1.583	0.057583
43	0.029903	0.4012	0.344378
44	0.017602	0.2361	0.406793
45	-0.096587	-1.2959	0.098343
46	0.096115	1.2895	0.099436
47	-0.108751	-1.459	0.073148
48	0.132287	1.7748	0.038809

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.071299	0.9566	0.170032
2	0.233996	3.1394	0.00099
3	0.358858	4.8146	2e-06
4	0.222448	2.9845	0.001618
5	0.162898	2.1855	0.015071
6	0.084726	1.1367	0.128583
7	-0.218152	-2.9268	0.001933
8	0.192165	2.5782	0.005366
9	0.171407	2.2997	0.011307
10	-0.05511	-0.7394	0.23032
11	-0.267665	-3.5911	0.000212
12	0.36118	4.8457	1e-06
13	-0.055632	-0.7464	0.228205
14	0.019143	0.2568	0.3988
15	-0.048351	-0.6487	0.258681
16	-0.089388	-1.1993	0.116
17	-0.092995	-1.2477	0.10689
18	-0.027804	-0.373	0.354782
19	-0.016685	-0.2238	0.411565
20	-0.056773	-0.7617	0.22362
21	-0.071789	-0.9631	0.168383
22	-0.084195	-1.1296	0.130076
23	0.109018	1.4626	0.072656
24	-0.013357	-0.1792	0.42899
25	-0.062324	-0.8362	0.202087
26	0.000651	0.0087	0.496519
27	-0.018886	-0.2534	0.400133
28	0.10383	1.393	0.082666
29	-0.056063	-0.7522	0.226467
30	-0.0571	-0.7661	0.222316
31	-0.037988	-0.5097	0.305454
32	0.089747	1.2041	0.115068
33	-0.006035	-0.081	0.467779
34	0.110966	1.4888	0.06915
35	-0.053033	-0.7115	0.238843
36	-0.022355	-0.2999	0.382291
37	0.006428	0.0862	0.465684
38	-0.035203	-0.4723	0.318643
39	0.011497	0.1542	0.438795
40	-0.002273	-0.0305	0.487853
41	0.02424	0.3252	0.3727
42	-0.080293	-1.0772	0.141408
43	0.152798	2.05	0.020907
44	0.050339	0.6754	0.250154
45	-0.032348	-0.434	0.332406
46	0.03565	0.4783	0.316509
47	0.025007	0.3355	0.368817
48	0.155175	2.0819	0.019383

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/05/t1291545631156xadafskn54jk/174yv1291545693.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/05/t1291545631156xadafskn54jk/174yv1291545693.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/05/t1291545631156xadafskn54jk/274yv1291545693.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/05/t1291545631156xadafskn54jk/274yv1291545693.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 0 ; 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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