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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: Mon, 29 Nov 2010 10:18:55 +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/Nov/29/t1291025861bbfebcxk9pbemh3.htm/, Retrieved Mon, 29 Nov 2010 11:17:41 +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/Nov/29/t1291025861bbfebcxk9pbemh3.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 «

15086 20559 39383 68032 42346 40184 29183 18049 24377 48033 61410 40637 37914 22481 17061 21921 34043 36152 38929 36713 27928 14178 19331 35030 37834 45257 39650 33001 22268 34283 63733 54548 31666 32654 28409 16234 19544 33375 30839 27581 28596 28542 14285 20799 28729 30278 31266 38341 24938 15700 17382 34229 29584 33909 29397 24644 14124 18770 32681 30518 34310 24217 15806 12362 13751 25312 23549 30305 30411 15593 17382 15806 29183 33348 33589 30198 23469 15593 16474 27341 26673 33268 26406 23656 15086 18316 27528 30305 34550 34710 23843 12362 21200 27261 31586 33322 32814 21974 17115 14445 26673 31746 28249 29103 21974 17622 21066 28382 32147 35885 40824 28622 24297 30465 47927 51665 57058 48407 30011 21413 30518 41171 37487 44456 41465 28409 34870 29557 44936 44028 45310 39302 28516 19865 30091 38101 44402 52359 71182 60796 43735 63947 89071 86321 90967 54441 36 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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.770708	27.0847	0
2	0.597167	20.986	0
3	0.445563	15.6582	0
4	0.302197	10.62	0
5	0.156159	5.4878	0
6	0.001718	0.0604	0.475938
7	-0.185176	-6.5076	0
8	-0.162872	-5.7237	0
9	-0.171667	-6.0328	0
10	-0.187066	-6.574	0
11	-0.175192	-6.1567	0
12	-0.154351	-5.4243	0
13	-0.144536	-5.0794	0
14	-0.117796	-4.1397	1.9e-05
15	-0.105502	-3.7076	0.000109
16	-0.09028	-3.1727	0.000774
17	-0.070405	-2.4742	0.006743
18	-0.073899	-2.597	0.004758
19	-0.094454	-3.3194	0.000464
20	-0.111709	-3.9257	4.6e-05
21	-0.145841	-5.1252	0
22	-0.138895	-4.8811	1e-06
23	-0.117869	-4.1422	1.8e-05
24	-0.107479	-3.7771	8.3e-05
25	-0.092102	-3.2367	0.000621
26	-0.080607	-2.8327	0.002345
27	-0.058954	-2.0718	0.019246
28	-0.013244	-0.4654	0.320854
29	0.015093	0.5304	0.297963
30	0.027275	0.9585	0.168993
31	0.045356	1.5939	0.055605
32	0.046344	1.6286	0.051822
33	0.058563	2.0581	0.019897
34	0.071279	2.5049	0.006188
35	0.050324	1.7685	0.03861
36	0.023445	0.8239	0.20507
37	0.012915	0.4539	0.325005
38	-0.003073	-0.108	0.457016
39	0.006256	0.2199	0.41301
40	0.009753	0.3428	0.365922
41	0.015232	0.5353	0.296275
42	0.040874	1.4364	0.075567
43	0.077513	2.724	0.00327
44	0.077127	2.7104	0.003406
45	0.088926	3.1251	0.000909
46	0.086093	3.0255	0.001267
47	0.083707	2.9417	0.001663
48	0.07583	2.6649	0.003901
49	0.052573	1.8475	0.032453
50	0.023431	0.8234	0.205215
51	0.019853	0.6977	0.242748
52	0.00355	0.1247	0.450371
53	-0.006929	-0.2435	0.403823
54	-0.014842	-0.5216	0.301026
55	-0.011888	-0.4178	0.338092
56	-0.009806	-0.3446	0.365229
57	-0.010933	-0.3842	0.350442
58	-0.020059	-0.7049	0.240494
59	-0.019656	-0.6908	0.244922
60	-0.008632	-0.3033	0.38084

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.770708	27.0847	0
2	0.007823	0.2749	0.391705
3	-0.042138	-1.4808	0.069453
4	-0.074273	-2.6102	0.00458
5	-0.111085	-3.9038	5e-05
6	-0.14748	-5.1828	0
7	-0.24223	-8.5126	0
8	0.325124	11.4257	0
9	-0.054863	-1.928	0.02704
10	-0.056825	-1.997	0.023023
11	0.0152	0.5342	0.296663
12	-0.032749	-1.1509	0.125004
13	-0.102981	-3.619	0.000154
14	-0.091375	-3.2112	0.000678
15	0.151968	5.3406	0
16	-0.053189	-1.8692	0.030917
17	-0.035502	-1.2476	0.1062
18	-0.021865	-0.7684	0.221204
19	-0.076986	-2.7055	0.003457
20	-0.104229	-3.6629	0.00013
21	-0.114164	-4.012	3.2e-05
22	0.155428	5.4621	0
23	0.007467	0.2624	0.396523
24	-0.034583	-1.2153	0.112234
25	-0.00383	-0.1346	0.446477
26	-0.074936	-2.6335	0.004279
27	-0.046742	-1.6426	0.050356
28	-0.018505	-0.6503	0.257805
29	0.116805	4.1048	2.2e-05
30	-0.011858	-0.4167	0.338482
31	-0.013256	-0.4659	0.320702
32	-0.029782	-1.0466	0.14774
33	-0.02463	-0.8656	0.193446
34	-0.009146	-0.3214	0.373977
35	-0.074671	-2.6241	0.004397
36	0.040306	1.4164	0.078448
37	0.018789	0.6603	0.254599
38	-0.011126	-0.391	0.347932
39	0.027797	0.9769	0.164413
40	-0.013224	-0.4647	0.32111
41	0.022796	0.8011	0.211612
42	-0.015895	-0.5586	0.288276
43	0.091011	3.1984	0.000709
44	-0.0382	-1.3424	0.089851
45	0.005336	0.1875	0.425642
46	0.005161	0.1814	0.428058
47	-0.014795	-0.5199	0.301603
48	0.012627	0.4437	0.328651
49	-0.029861	-1.0494	0.147105
50	0.06322	2.2217	0.013242
51	-0.011407	-0.4009	0.344296
52	-0.004385	-0.1541	0.438772
53	0.016379	0.5756	0.282497
54	-0.003958	-0.1391	0.444701
55	0.05363	1.8847	0.029852
56	-0.043467	-1.5275	0.06344
57	0.014137	0.4968	0.309707
58	-0.024367	-0.8563	0.195993
59	-0.005733	-0.2015	0.420187
60	0.055987	1.9675	0.024673

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/29/t1291025861bbfebcxk9pbemh3/1ce231291025931.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/29/t1291025861bbfebcxk9pbemh3/1ce231291025931.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/29/t1291025861bbfebcxk9pbemh3/2ce231291025931.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/29/t1291025861bbfebcxk9pbemh3/2ce231291025931.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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 <- 7

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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