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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, 24 Nov 2009 12:18:22 -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/Nov/24/t12590905193j3xytlrtjk8sjq.htm/, Retrieved Tue, 24 Nov 2009 20:22:01 +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/Nov/24/t12590905193j3xytlrtjk8sjq.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 «

111,4 87,4 96,8 114,1 110,3 103,9 101,6 94,6 95,9 104,7 102,8 98,1 113,9 80,9 95,7 113,2 105,9 108,8 102,3 99 100,7 115,5 100,7 109,9 114,6 85,4 100,5 114,8 116,5 112,9 102 106 105,3 118,8 106,1 109,3 117,2 92,5 104,2 112,5 122,4 113,3 100 110,7 112,8 109,8 117,3 109,1 115,9 96 99,8 116,8 115,7 99,4 94,3 91 93,2 103,1 94,1 91,8 102,7

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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.184382	1.4401	0.07748
2	-0.108061	-0.844	0.200988
3	0.06272	0.4899	0.312995
4	0.036447	0.2847	0.388435
5	0.267016	2.0855	0.020609
6	0.274498	2.1439	0.018018
7	0.109123	0.8523	0.198696
8	-0.086283	-0.6739	0.251464
9	-0.060259	-0.4706	0.319788
10	-0.225612	-1.7621	0.041532
11	-0.001372	-0.0107	0.495744
12	0.500638	3.9101	0.000117
13	-0.057407	-0.4484	0.327741
14	-0.278035	-2.1715	0.016895
15	-0.165825	-1.2951	0.100077
16	-0.100767	-0.787	0.217159
17	0.109223	0.8531	0.198483
18	0.074058	0.5784	0.282558
19	-0.014618	-0.1142	0.454738
20	-0.178312	-1.3927	0.084389
21	-0.111285	-0.8692	0.194083
22	-0.230739	-1.8021	0.038233
23	-0.056723	-0.443	0.32966
24	0.278403	2.1744	0.016782
25	-0.073004	-0.5702	0.285324
26	-0.295539	-2.3082	0.012196
27	-0.228202	-1.7823	0.039837
28	-0.058965	-0.4605	0.323385
29	0.039744	0.3104	0.378654
30	-0.004529	-0.0354	0.48595
31	-0.042367	-0.3309	0.370928
32	-0.178323	-1.3927	0.084376
33	-0.087695	-0.6849	0.247995
34	-0.091136	-0.7118	0.239653
35	-0.087286	-0.6817	0.248997
36	0.162	1.2653	0.105295
37	-0.026025	-0.2033	0.419804
38	-0.189118	-1.4771	0.072402
39	-0.122088	-0.9535	0.172041
40	0.029282	0.2287	0.409933
41	0.052735	0.4119	0.340938
42	0.057458	0.4488	0.327596
43	0.019387	0.1514	0.440072
44	-0.036985	-0.2889	0.386833
45	0.036997	0.289	0.386798
46	0.036079	0.2818	0.389532
47	0.034141	0.2667	0.395318
48	0.158284	1.2362	0.110555
49	0.046228	0.3611	0.359653
50	-0.051591	-0.4029	0.344202
51	0.000752	0.0059	0.497667
52	0.048462	0.3785	0.353187
53	0.042269	0.3301	0.371216
54	0.041045	0.3206	0.374817
55	-0.008131	-0.0635	0.474785
56	-0.017821	-0.1392	0.444881
57	0.050825	0.397	0.346391
58	0.033969	0.2653	0.395833
59	-0.009324	-0.0728	0.471093
60	-0.00274	-0.0214	0.491499

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.184382	1.4401	0.07748
2	-0.147057	-1.1486	0.127612
3	0.119234	0.9312	0.177698
4	-0.019877	-0.1552	0.43857
5	0.307786	2.4039	0.009638
6	0.167384	1.3073	0.098007
7	0.130885	1.0222	0.155352
8	-0.131518	-1.0272	0.154193
9	-0.037446	-0.2925	0.385463
10	-0.42738	-3.3379	0.000721
11	-0.021401	-0.1671	0.433904
12	0.437999	3.4209	0.00056
13	-0.150392	-1.1746	0.12236
14	-0.065343	-0.5103	0.305827
15	-0.105059	-0.8205	0.207552
16	0.014282	0.1115	0.455776
17	-0.090158	-0.7042	0.242008
18	-0.06843	-0.5345	0.297483
19	0.099719	0.7788	0.219546
20	-0.052348	-0.4089	0.342041
21	0.018425	0.1439	0.443027
22	-0.109849	-0.858	0.197139
23	-0.027135	-0.2119	0.416433
24	-0.096302	-0.7521	0.227428
25	0.020459	0.1598	0.436788
26	-0.138793	-1.084	0.141314
27	-0.025767	-0.2012	0.420588
28	0.040736	0.3182	0.375727
29	-0.074229	-0.5797	0.282111
30	-0.053777	-0.42	0.337977
31	-0.00973	-0.076	0.469838
32	-0.005263	-0.0411	0.483672
33	-0.044045	-0.344	0.366013
34	0.108692	0.8489	0.199626
35	-0.174723	-1.3646	0.088691
36	-0.051535	-0.4025	0.344362
37	-0.117636	-0.9188	0.180919
38	0.055512	0.4336	0.333068
39	-0.021159	-0.1653	0.434643
40	-0.002272	-0.0177	0.49295
41	0.014948	0.1167	0.453722
42	0.04123	0.322	0.374271
43	-0.042941	-0.3354	0.369244
44	0.088337	0.6899	0.246425
45	-0.04141	-0.3234	0.373742
46	-0.006107	-0.0477	0.481056
47	0.058445	0.4565	0.324836
48	-0.072448	-0.5658	0.28679
49	-0.079316	-0.6195	0.268955
50	-0.012787	-0.0999	0.460389
51	-0.001153	-0.009	0.496423
52	-0.109608	-0.8561	0.197656
53	-0.048171	-0.3762	0.354027
54	0.025901	0.2023	0.42018
55	-0.0615	-0.4803	0.316357
56	0.017429	0.1361	0.446084
57	0.042048	0.3284	0.371864
58	0.074984	0.5856	0.280139
59	-0.120592	-0.9419	0.174991
60	-0.071753	-0.5604	0.288626

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/24/t12590905193j3xytlrtjk8sjq/1wf6g1259090300.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t12590905193j3xytlrtjk8sjq/1wf6g1259090300.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t12590905193j3xytlrtjk8sjq/2c8tq1259090300.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t12590905193j3xytlrtjk8sjq/2c8tq1259090300.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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