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TIJDREEKS B - STAP 17

*Unverified author*

R Software Module: /rwasp_autocorrelation.wasp (opens new window with default values)

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Mon, 16 Aug 2010 19:04:51 +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/Aug/16/t12819855158j4ai7nega788u9.htm/, Retrieved Mon, 16 Aug 2010 21:05:15 +0200

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/Aug/16/t12819855158j4ai7nega788u9.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:

De Cock Nicola

Dataseries X:

» Textbox « » Textfile « » CSV «

76 75 74 72 70 69 70 72 73 73 74 76 74 67 66 58 55 58 64 68 66 76 75 88 85 83 77 66 65 65 63 62 57 68 69 79 74 76 82 75 75 76 78 77 67 74 68 87 76 88 95 96 96 105 108 113 101 107 102 116 105 121 134 140 131 141 131 128 123 129 125 144 135 141 156 159 146 154 145 133 126 127 122 148

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	0.941533	8.6293	0
2	0.919964	8.4316	0
3	0.877235	8.04	0
4	0.843374	7.7296	0
5	0.795304	7.2891	0
6	0.762084	6.9846	0
7	0.716607	6.5678	0
8	0.69748	6.3925	0
9	0.662839	6.075	0
10	0.634445	5.8148	0
11	0.601538	5.5132	0
12	0.595127	5.4544	0
13	0.533818	4.8925	2e-06
14	0.499269	4.5759	8e-06
15	0.446387	4.0912	4.9e-05
16	0.404561	3.7079	0.000187
17	0.344899	3.161	0.001093
18	0.300026	2.7498	0.00365
19	0.245738	2.2522	0.013458
20	0.210969	1.9336	0.028267
21	0.162894	1.493	0.069598
22	0.125113	1.1467	0.127384
23	0.084932	0.7784	0.219256
24	0.078776	0.722	0.236151
25	0.036472	0.3343	0.369503
26	0.018919	0.1734	0.431378
27	-0.012555	-0.1151	0.454331
28	-0.03364	-0.3083	0.379303
29	-0.075707	-0.6939	0.244842
30	-0.109492	-1.0035	0.159249
31	-0.147094	-1.3481	0.090619
32	-0.173552	-1.5906	0.057725
33	-0.202044	-1.8518	0.033786
34	-0.224054	-2.0535	0.021568
35	-0.244035	-2.2366	0.013981
36	-0.238963	-2.1901	0.015643
37	-0.259487	-2.3782	0.009832
38	-0.256877	-2.3543	0.010445
39	-0.263235	-2.4126	0.009008
40	-0.263488	-2.4149	0.008955
41	-0.279248	-2.5593	0.006139
42	-0.296288	-2.7155	0.004016
43	-0.314342	-2.881	0.002515
44	-0.329115	-3.0164	0.001692
45	-0.34336	-3.1469	0.001142
46	-0.357948	-3.2806	0.000755
47	-0.366326	-3.3574	0.000592
48	-0.359716	-3.2969	0.000717

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.941533	8.6293	0
2	0.294939	2.7032	0.004155
3	-0.107745	-0.9875	0.163117
4	-0.024737	-0.2267	0.410598
5	-0.116804	-1.0705	0.143725
6	0.04651	0.4263	0.3355
7	-0.052375	-0.48	0.31623
8	0.166942	1.53	0.064881
9	-0.019146	-0.1755	0.430565
10	-0.067376	-0.6175	0.269284
11	-0.033062	-0.303	0.381312
12	0.196392	1.8	0.037729
13	-0.407679	-3.7364	0.00017
14	-0.069745	-0.6392	0.262207
15	-0.002815	-0.0258	0.48974
16	-0.022214	-0.2036	0.419583
17	-0.132547	-1.2148	0.11392
18	0.018112	0.166	0.434278
19	0.044823	0.4108	0.341129
20	-0.068573	-0.6285	0.265697
21	-0.05628	-0.5158	0.30367
22	0.040144	0.3679	0.356927
23	-0.011559	-0.1059	0.457941
24	0.147268	1.3497	0.090363
25	-0.036131	-0.3311	0.370678
26	-0.00155	-0.0142	0.494349
27	-0.021838	-0.2001	0.420924
28	-0.044979	-0.4122	0.340608
29	-0.108328	-0.9928	0.16182
30	-0.096836	-0.8875	0.188668
31	0.087366	0.8007	0.212775
32	-0.043203	-0.396	0.346567
33	0.05895	0.5403	0.295215
34	0.041753	0.3827	0.351463
35	0.038145	0.3496	0.363755
36	-0.030858	-0.2828	0.389005
37	-0.065583	-0.6011	0.274702
38	0.048323	0.4429	0.329493
39	0.00546	0.05	0.480104
40	-0.08925	-0.818	0.207838
41	-0.005566	-0.051	0.479717
42	-0.103459	-0.9482	0.172869
43	-0.008127	-0.0745	0.470399
44	-0.061868	-0.567	0.286104
45	0.04415	0.4046	0.343385
46	-0.020809	-0.1907	0.424603
47	0.026059	0.2388	0.405908
48	0.006357	0.0583	0.47684

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/16/t12819855158j4ai7nega788u9/1o55y1281985488.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/16/t12819855158j4ai7nega788u9/1o55y1281985488.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/16/t12819855158j4ai7nega788u9/2o55y1281985488.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/16/t12819855158j4ai7nega788u9/2o55y1281985488.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; 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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