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paper d=D=0

*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, 13 Dec 2009 02:08:29 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/13/t12606955504i2ftw0s3s29ufo.htm/, Retrieved Sun, 13 Dec 2009 10:12:32 +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/2009/Dec/13/t12606955504i2ftw0s3s29ufo.htm/},
    year = {2009},
}
@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 = {2009},
    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 «

2.04 2.16 2.75 2.79 2.88 3.36 2.97 3.10 2.49 2.20 2.25 2.09 2.79 3.14 2.93 2.65 2.67 2.26 2.35 2.13 2.18 2.90 2.63 2.67 1.81 1.33 0.88 1.28 1.26 1.26 1.29 1.10 1.37 1.21 1.74 1.76 1.48 1.04 1.62 1.49 1.79 1.80 1.58 1.86 1.74 1.59 1.26 1.13 1.92 2.61 2.26 2.41 2.26 2.03 2.86 2.55 2.27 2.26 2.57 3.07 2.76 2.51 2.87 3.14 3.11 3.16 2.47 2.57 2.89 2.63 2.38 1.69 1.96 2.19 1.87 1.60 1.63 1.22 1.21 1.49 1.64 1.66 1.77 1.82 1.78 1.28 1.29 1.37 1.12 1.51 2.24 2.94 3.09 3.46 3.64 4.39 4.15 5.21 5.80 5.91 5.39 5.46 4.72 3.14 2.63 2.32 1.93 0.62

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	0.901682	9.3706	0
2	0.791674	8.2273	0
3	0.674054	7.005	0
4	0.549069	5.7061	0
5	0.418523	4.3494	1.6e-05
6	0.304702	3.1666	0.001003
7	0.210181	2.1843	0.015553
8	0.123317	1.2815	0.101374
9	0.047492	0.4935	0.311314
10	-0.022137	-0.2301	0.409243
11	-0.081677	-0.8488	0.198932
12	-0.177342	-1.843	0.034036
13	-0.196848	-2.0457	0.021608
14	-0.196074	-2.0377	0.022014
15	-0.199667	-2.075	0.020181
16	-0.202813	-2.1077	0.018686
17	-0.205063	-2.1311	0.017676
18	-0.202956	-2.1092	0.01862
19	-0.209974	-2.1821	0.015634
20	-0.236408	-2.4568	0.007805
21	-0.254949	-2.6495	0.004635
22	-0.260707	-2.7093	0.003921
23	-0.27185	-2.8252	0.002815
24	-0.243152	-2.5269	0.006478
25	-0.198928	-2.0673	0.020547
26	-0.163109	-1.6951	0.046471
27	-0.113319	-1.1776	0.120763
28	-0.068037	-0.7071	0.240525
29	-0.028508	-0.2963	0.383799
30	0.002606	0.0271	0.48922
31	0.025895	0.2691	0.394181
32	0.053586	0.5569	0.28938
33	0.074905	0.7784	0.219009
34	0.08208	0.853	0.197773
35	0.105832	1.0998	0.136924
36	0.12769	1.327	0.093655
37	0.116982	1.2157	0.113373
38	0.11734	1.2194	0.112668
39	0.10948	1.1378	0.128871
40	0.110831	1.1518	0.125976
41	0.119251	1.2393	0.108962
42	0.110084	1.144	0.127571
43	0.102934	1.0697	0.143565
44	0.096317	1.001	0.159543
45	0.094487	0.9819	0.164162
46	0.10316	1.0721	0.143039
47	0.091107	0.9468	0.172923
48	0.06077	0.6315	0.264512
49	0.053108	0.5519	0.291073
50	0.035703	0.371	0.355667
51	0.00807	0.0839	0.466659
52	-0.019431	-0.2019	0.420174
53	-0.056715	-0.5894	0.278411
54	-0.075404	-0.7836	0.217488
55	-0.087154	-0.9057	0.183546
56	-0.089494	-0.93	0.17721
57	-0.085976	-0.8935	0.186792
58	-0.099293	-1.0319	0.152216
59	-0.098583	-1.0245	0.153944
60	-0.101586	-1.0557	0.146728

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.901682	9.3706	0
2	-0.114229	-1.1871	0.118895
3	-0.099318	-1.0321	0.152155
4	-0.106737	-1.1092	0.134894
5	-0.107164	-1.1137	0.133943
6	0.005399	0.0561	0.47768
7	0.015319	0.1592	0.436903
8	-0.049345	-0.5128	0.304566
9	-0.033699	-0.3502	0.363433
10	-0.063896	-0.664	0.254044
11	-0.031896	-0.3315	0.370463
12	-0.279608	-2.9058	0.002223
13	0.363457	3.7772	0.00013
14	0.012251	0.1273	0.449464
15	-0.099942	-1.0386	0.150649
16	-0.059239	-0.6156	0.269718
17	-0.112859	-1.1729	0.121715
18	0.010378	0.1078	0.457158
19	-0.024861	-0.2584	0.398309
20	-0.157987	-1.6418	0.051765
21	0.04951	0.5145	0.30397
22	-0.001611	-0.0167	0.493336
23	-0.01666	-0.1731	0.431436
24	0.010302	0.1071	0.45747
25	0.168768	1.7539	0.041143
26	-0.029965	-0.3114	0.378045
27	0.047946	0.4983	0.309655
28	-0.067321	-0.6996	0.242836
29	-0.065357	-0.6792	0.24923
30	0.046695	0.4853	0.314236
31	0.030976	0.3219	0.37407
32	-0.077322	-0.8036	0.211709
33	0.007751	0.0806	0.467974
34	-0.023634	-0.2456	0.403225
35	0.079391	0.8251	0.205581
36	0.045125	0.4689	0.320025
37	-0.086628	-0.9003	0.184991
38	0.053997	0.5612	0.287928
39	0.026608	0.2765	0.39134
40	0.041307	0.4293	0.334288
41	0.032793	0.3408	0.366958
42	-0.141665	-1.4722	0.071934
43	0.003149	0.0327	0.486978
44	0.017731	0.1843	0.427074
45	0.078719	0.8181	0.207558
46	0.019015	0.1976	0.421861
47	-0.086485	-0.8988	0.185384
48	0.032418	0.3369	0.368426
49	0.022427	0.2331	0.408073
50	-0.027133	-0.282	0.38925
51	-0.07784	-0.8089	0.210165
52	0.017386	0.1807	0.428479
53	0.028725	0.2985	0.38294
54	-0.034248	-0.3559	0.361299
55	-0.01399	-0.1454	0.442336
56	0.053956	0.5607	0.288071
57	0.025721	0.2673	0.394872
58	-0.04863	-0.5054	0.307163
59	0.014934	0.1552	0.438477
60	-0.198368	-2.0615	0.020828

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/13/t12606955504i2ftw0s3s29ufo/19c401260695307.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/13/t12606955504i2ftw0s3s29ufo/19c401260695307.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/13/t12606955504i2ftw0s3s29ufo/2soyi1260695307.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/13/t12606955504i2ftw0s3s29ufo/2soyi1260695307.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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