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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, 28 Dec 2010 16:33:51 +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/28/t129355395335p7ruyvu9tjt4h.htm/, Retrieved Tue, 28 Dec 2010 17:32:35 +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/28/t129355395335p7ruyvu9tjt4h.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 «

36845 35338 35022 34777 26887 23970 22780 17351 21382 24561 17409 11514 31514 27071 29462 26105 22397 23843 21705 18089 20764 25316 17704 15548 28029 29383 36438 32034 22679 24319 18004 17537 20366 22782 19169 13807 29743 25591 29096 26482 22405 27044 17970 18730 19684 19785 18479 10698 31956 29506 34506 27165 26736 23691 18157 17328 18205 20995 17382 9367 31124 26551 30651 25859 25100 25778 20418 18688 20424 24776 19814 12738 31566 30111 30019 31934 25826 26835 20205 17789 20520 22518 15572 11509

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	1 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.422295	-3.5583	0.000335
2	0.166972	1.4069	0.081905
3	-0.198065	-1.6689	0.049768
4	-0.029929	-0.2522	0.400813
5	-0.032583	-0.2746	0.392229
6	0.074889	0.631	0.265024
7	-0.094539	-0.7966	0.21417
8	0.087473	0.7371	0.231757
9	0.223517	1.8834	0.031872
10	-0.100138	-0.8438	0.200813
11	-0.063439	-0.5345	0.297318
12	-0.201754	-1.7	0.046753
13	-0.093858	-0.7909	0.215828
14	0.092498	0.7794	0.219168
15	0.110794	0.9336	0.176846
16	-0.035186	-0.2965	0.383862
17	0.039869	0.3359	0.368953
18	0.056302	0.4744	0.318331
19	-0.108121	-0.911	0.182677
20	-0.033651	-0.2835	0.388792
21	0.040917	0.3448	0.365644
22	-0.219948	-1.8533	0.033996
23	0.373226	3.1449	0.001213
24	-0.139331	-1.174	0.122154
25	0.144876	1.2208	0.11311
26	-0.079282	-0.668	0.253136
27	0.068345	0.5759	0.283258
28	-0.236698	-1.9945	0.024971
29	0.238082	2.0061	0.024327
30	-0.178382	-1.5031	0.068628
31	0.093926	0.7914	0.215664
32	0.045689	0.385	0.3507
33	-0.083801	-0.7061	0.241212
34	0.071963	0.6064	0.273101
35	-0.009791	-0.0825	0.467241
36	-0.103072	-0.8685	0.194023
37	-0.008692	-0.0732	0.47091
38	-0.002241	-0.0189	0.492493
39	0.016643	0.1402	0.444434
40	0.043072	0.3629	0.358867
41	-0.038966	-0.3283	0.371812
42	-0.029985	-0.2527	0.40063
43	0.041248	0.3476	0.364598
44	0.085644	0.7216	0.23644
45	-0.134805	-1.1359	0.129911
46	0.086742	0.7309	0.233623
47	-0.063439	-0.5345	0.297316
48	0.06629	0.5586	0.289105
49	0.030753	0.2591	0.398142
50	0.039077	0.3293	0.371461
51	-0.118349	-0.9972	0.161021
52	0.122278	1.0303	0.153175
53	-0.079146	-0.6669	0.253499
54	0.068363	0.576	0.283206
55	-0.068336	-0.5758	0.283282
56	-0.029932	-0.2522	0.400802
57	0.02193	0.1848	0.426963
58	0.02836	0.239	0.405909
59	0.007778	0.0655	0.473966
60	-0.075443	-0.6357	0.26351

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.422295	-3.5583	0.000335
2	-0.013827	-0.1165	0.453791
3	-0.161188	-1.3582	0.089351
4	-0.211714	-1.7839	0.039354
5	-0.14869	-1.2529	0.107179
6	-0.019046	-0.1605	0.436477
7	-0.144249	-1.2155	0.114108
8	-0.066302	-0.5587	0.289073
9	0.33026	2.7828	0.00345
10	0.166789	1.4054	0.082133
11	-0.096396	-0.8122	0.209683
12	-0.243318	-2.0502	0.022018
13	-0.307614	-2.592	0.005788
14	-0.205825	-1.7343	0.043602
15	-0.032102	-0.2705	0.393781
16	-0.04668	-0.3933	0.347628
17	-0.108058	-0.9105	0.182816
18	0.000711	0.006	0.497617
19	-0.061193	-0.5156	0.30386
20	-0.094571	-0.7969	0.214092
21	0.270317	2.2777	0.012878
22	-0.043803	-0.3691	0.356578
23	0.106362	0.8962	0.186581
24	-0.085876	-0.7236	0.235843
25	-0.100337	-0.8455	0.20035
26	-0.044454	-0.3746	0.354547
27	0.161214	1.3584	0.089317
28	-0.092586	-0.7801	0.21895
29	0.062206	0.5242	0.300901
30	0.017033	0.1435	0.443141
31	-0.021664	-0.1825	0.427838
32	-0.026696	-0.2249	0.411335
33	-0.067683	-0.5703	0.285136
34	0.006826	0.0575	0.477147
35	0.083894	0.7069	0.240971
36	-0.056814	-0.4787	0.316804
37	-0.011542	-0.0973	0.461398
38	-0.106237	-0.8952	0.186862
39	0.005715	0.0482	0.480863
40	0.046614	0.3928	0.347832
41	-0.096363	-0.812	0.209761
42	-0.041497	-0.3497	0.363814
43	0.018591	0.1567	0.437982
44	0.023783	0.2004	0.420869
45	-0.00429	-0.0362	0.485631
46	0.031796	0.2679	0.394769
47	0.069862	0.5887	0.278977
48	0.013433	0.1132	0.4551
49	0.034069	0.2871	0.387447
50	-0.005536	-0.0466	0.481464
51	0.085477	0.7202	0.236869
52	-0.0701	-0.5907	0.278307
53	-0.091052	-0.7672	0.222747
54	0.055181	0.465	0.321689
55	0.009095	0.0766	0.469563
56	-0.017102	-0.1441	0.442915
57	0.040399	0.3404	0.367276
58	-0.098515	-0.8301	0.204631
59	0.078317	0.6599	0.255723
60	-0.039485	-0.3327	0.370169

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/28/t129355395335p7ruyvu9tjt4h/10ds31293554029.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t129355395335p7ruyvu9tjt4h/10ds31293554029.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t129355395335p7ruyvu9tjt4h/20ds31293554029.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t129355395335p7ruyvu9tjt4h/20ds31293554029.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; 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 <- 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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