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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 09:54:26 +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/t12910243468hueudrh3ikzi71.htm/, Retrieved Mon, 29 Nov 2010 10:52:26 +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/t12910243468hueudrh3ikzi71.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 «

1483509 8036554 4623093 5528662 4221032 8061847 7640066 2935533 8161548 2543967 13163450 3348436 3997440 2322911 2019457 3047748 5728767 2605173 5646743 13121544 3453409 1878333 4247362 23022552 7646203 9016602 3606568 3173510 17568772 10805045 31056269 15623385 6663443 35435745 2823250 5197089 4120632 8832767 3695374 8385805 3777904 5199532 5297275 14847382 5900158 4416718 3926429 4876884 2795297 3385527 3877941 3556729 4982836 2976325 2295026 2218752 4146062 3302091 3864505 5454794 1749836 6684048 2809918 4092664 5070470 9814477 6665318 3912554 6188129 3627991 3308767 3820332 4932979 5567917 5020814 3803273 3999984 4883104 13731747 47531824 8415570 22178158 61211654 18223748 17678085 49299580 25899948 34121754 9859231 29740892 21085212 43003866 59549247 18026465 4680597 5564728 11792347 10371624 3728446 5732978 4067638 2395508 5018801 22068888 7678580 15510095 6471239 14349204 35151574 8210488 50226 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	0.508807	9.5461	0
2	0.412072	7.7312	0
3	0.405474	7.6074	0
4	0.336241	6.3084	0
5	0.35884	6.7324	0
6	0.327088	6.1367	0
7	0.287409	5.3923	0
8	0.251502	4.7186	2e-06
9	0.223538	4.1939	1.7e-05
10	0.243978	4.5774	3e-06
11	0.209398	3.9287	5.1e-05
12	0.176693	3.3151	0.000506
13	0.223993	4.2025	1.7e-05
14	0.211979	3.9771	4.2e-05
15	0.083986	1.5757	0.057994
16	0.075178	1.4105	0.079642
17	0.094775	1.7781	0.038123
18	0.059991	1.1255	0.130566
19	0.079409	1.4898	0.068581
20	0.060523	1.1355	0.128467
21	0.074288	1.3938	0.082133
22	0.050717	0.9515	0.170991
23	0.06729	1.2625	0.103807
24	0.084587	1.587	0.056706
25	0.084675	1.5886	0.056519
26	0.128968	2.4197	0.008021
27	0.072937	1.3684	0.086026
28	0.087007	1.6324	0.051744
29	0.128806	2.4166	0.008087
30	0.144375	2.7087	0.003542
31	0.141676	2.6581	0.004109
32	0.105573	1.9807	0.0242
33	0.091536	1.7174	0.043396
34	0.136354	2.5582	0.005469
35	0.17579	3.2981	0.000536
36	0.138382	2.5963	0.004909
37	0.123893	2.3244	0.010335
38	0.054709	1.0264	0.152695
39	0.053227	0.9986	0.159332
40	0.062911	1.1803	0.119334
41	0.043697	0.8198	0.206433
42	0.073918	1.3868	0.083185
43	0.05014	0.9407	0.17375
44	0.024059	0.4514	0.325991
45	0.042106	0.79	0.215036
46	0.005436	0.102	0.45941
47	-0.017508	-0.3285	0.371369
48	-0.00715	-0.1341	0.446683
49	0.023746	0.4455	0.328109
50	-0.073498	-1.3789	0.084393
51	-0.047276	-0.887	0.187847
52	-0.035659	-0.669	0.251958
53	-0.065701	-1.2327	0.109261
54	-0.041997	-0.7879	0.215631
55	-0.035916	-0.6738	0.250428
56	-0.015016	-0.2817	0.389163
57	-0.065611	-1.231	0.109578
58	-0.060625	-1.1374	0.128068
59	-0.028126	-0.5277	0.299023
60	-0.073142	-1.3723	0.085428

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.508807	9.5461	0
2	0.206698	3.878	6.3e-05
3	0.188846	3.5431	0.000224
4	0.056353	1.0573	0.145557
5	0.134721	2.5276	0.005961
6	0.05285	0.9915	0.16105
7	0.023999	0.4503	0.326402
8	-0.008686	-0.163	0.435319
9	-0.001102	-0.0207	0.491762
10	0.057749	1.0835	0.139671
11	-0.005606	-0.1052	0.458147
12	-0.017667	-0.3315	0.370249
13	0.084371	1.5829	0.057166
14	0.038345	0.7194	0.236182
15	-0.156246	-2.9314	0.001797
16	-0.053822	-1.0098	0.156645
17	0.021948	0.4118	0.340372
18	-0.027514	-0.5162	0.303015
19	0.014605	0.274	0.392118
20	-0.003812	-0.0715	0.471512
21	0.058115	1.0903	0.138154
22	-0.009373	-0.1759	0.430252
23	0.027454	0.5151	0.30341
24	0.023755	0.4457	0.328053
25	0.049025	0.9198	0.179158
26	0.08075	1.515	0.065335
27	-0.074023	-1.3888	0.082886
28	0.039167	0.7348	0.231462
29	0.096691	1.8141	0.035258
30	0.054204	1.017	0.154935
31	-0.011667	-0.2189	0.413434
32	-0.033624	-0.6308	0.264277
33	-0.026327	-0.4939	0.310827
34	0.050842	0.9539	0.170398
35	0.070376	1.3204	0.093786
36	-0.035529	-0.6666	0.252736
37	-0.01419	-0.2662	0.395112
38	-0.10948	-2.054	0.020355
39	-0.050388	-0.9454	0.172561
40	-0.021769	-0.4084	0.341607
41	0.014203	0.2665	0.395017
42	0.029512	0.5537	0.290069
43	-0.030652	-0.5751	0.2828
44	-0.017684	-0.3318	0.370127
45	0.030469	0.5716	0.283965
46	-0.004453	-0.0835	0.466732
47	-0.057679	-1.0822	0.139962
48	-0.022804	-0.4278	0.334515
49	0.05935	1.1135	0.133126
50	-0.111892	-2.0993	0.018252
51	0.033117	0.6213	0.267395
52	0.037655	0.7065	0.24018
53	-0.010064	-0.1888	0.425176
54	-0.018008	-0.3379	0.367838
55	-0.010353	-0.1942	0.423054
56	0.029777	0.5587	0.288374
57	-0.042228	-0.7923	0.214367
58	-0.012983	-0.2436	0.403846
59	-0.000424	-0.008	0.496828
60	-0.049338	-0.9257	0.177629

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/29/t12910243468hueudrh3ikzi71/1tor91291024459.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/29/t12910243468hueudrh3ikzi71/1tor91291024459.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/29/t12910243468hueudrh3ikzi71/2mf8c1291024459.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/29/t12910243468hueudrh3ikzi71/2mf8c1291024459.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 = 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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