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CPI-ACF

*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, 21 Dec 2010 15:45:37 +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/21/t12929463221fqad6o86dhma3n.htm/, Retrieved Tue, 21 Dec 2010 16:45:23 +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/21/t12929463221fqad6o86dhma3n.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 «

104.8 105.2 105.6 105.8 106.1 106.5 106.71 106.68 107.41 107.15 107.5 107.22 107.11 107.57 107.81 108.75 109.43 109.62 109.54 109.53 109.84 109.67 109.79 109.56 110.22 110.4 110.69 110.72 110.89 110.58 110.94 110.91 111.22 111.09 111 111.06 111.55 112.32 112.64 112.36 112.04 112.37 112.59 112.89 113.22 112.85 113.06 112.99 113.32 113.74 113.91 114.52 114.96 114.91 115.3 115.44 115.52 116.08 115.94 115.56 115.88 116.66 117.41 117.68 117.85 118.21 118.92 119.03 119.17 118.95 118.92 118.9 118.92 119.44 119.40 119.98 120.43 120.41 120.82 120.97 120.63 120.38 120.68 120.84 120.90 121.56 121.57 122.12 121.97 121.96 122.48 122.33 122.44 123.08 124.23 124.58 125.08 125.98 126.90 127.19 128.33 129.04 129.72 128.92 129.13 128.90 128.13 127.85 127.98 128.42 127.68 127.95 127.85 127.61 127.53 127.92 127.59 127.65 127.98 128.19 128.77 129.31 129.80 130.24 130.76 130.75 130.81 130.89 131.30 131.4 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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.177372	2.0224	0.022596
2	0.1377	1.57	0.059421
3	0.065481	0.7466	0.228326
4	0.066067	0.7533	0.226321
5	-0.057991	-0.6612	0.254827
6	-0.069507	-0.7925	0.214755
7	0.018557	0.2116	0.416381
8	-0.110292	-1.2575	0.105409
9	-0.12572	-1.4334	0.077068
10	-0.069809	-0.7959	0.213759
11	0.0635	0.724	0.235179
12	-0.065534	-0.7472	0.228146
13	-0.143239	-1.6332	0.052426
14	-0.074465	-0.849	0.198714
15	-0.089953	-1.0256	0.153489
16	-0.214918	-2.4504	0.007799
17	-0.133417	-1.5212	0.065321
18	-0.132496	-1.5107	0.066648
19	-0.042895	-0.4891	0.312807
20	-0.071422	-0.8143	0.208472
21	-0.014757	-0.1683	0.43332
22	0.137481	1.5675	0.059711
23	-0.026158	-0.2982	0.382997
24	0.167681	1.9119	0.029048
25	0.032028	0.3652	0.357787
26	0.02391	0.2726	0.392792
27	0.016016	0.1826	0.427693
28	-0.02226	-0.2538	0.400026
29	-0.002897	-0.033	0.486851
30	-0.015534	-0.1771	0.429845
31	-0.068216	-0.7778	0.219054
32	-0.031986	-0.3647	0.357964
33	0.073438	0.8373	0.201975
34	0.054713	0.6238	0.266919
35	0.049413	0.5634	0.28707
36	0.22651	2.5826	0.005456
37	-0.008795	-0.1003	0.460141
38	0.033019	0.3765	0.353587
39	0.002668	0.0304	0.487891
40	-0.073924	-0.8429	0.200425
41	-0.001597	-0.0182	0.49275
42	-0.055292	-0.6304	0.264762
43	-0.075198	-0.8574	0.196403
44	-0.062833	-0.7164	0.237513
45	-0.024646	-0.281	0.389577
46	0.082044	0.9354	0.175648
47	0.102254	1.1659	0.1229
48	0.038789	0.4423	0.329516
49	0.018485	0.2108	0.416702
50	-0.01402	-0.1599	0.436623
51	-0.01808	-0.2061	0.418502
52	-0.046639	-0.5318	0.297899
53	-0.048123	-0.5487	0.292079
54	-0.115051	-1.3118	0.095952
55	-0.121747	-1.3881	0.083736
56	-0.048617	-0.5543	0.290156
57	0.034313	0.3912	0.348133
58	0.099661	1.1363	0.128959
59	-0.002097	-0.0239	0.490482
60	0.088726	1.0116	0.156798

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.177372	2.0224	0.022596
2	0.10969	1.2507	0.106653
3	0.025374	0.2893	0.386401
4	0.038541	0.4394	0.330537
5	-0.088324	-1.007	0.157891
6	-0.063933	-0.7289	0.233673
7	0.054661	0.6232	0.267112
8	-0.108341	-1.2353	0.109477
9	-0.092776	-1.0578	0.146052
10	-0.012509	-0.1426	0.443402
11	0.102887	1.1731	0.121453
12	-0.063883	-0.7284	0.233847
13	-0.150572	-1.7168	0.0442
14	-0.052833	-0.6024	0.273984
15	-0.055268	-0.6302	0.264851
16	-0.175936	-2.006	0.023467
17	-0.071763	-0.8182	0.207364
18	-0.122561	-1.3974	0.082335
19	0.014009	0.1597	0.436674
20	-0.024432	-0.2786	0.390511
21	-0.06207	-0.7077	0.240195
22	0.089141	1.0164	0.155673
23	-0.105678	-1.2049	0.115213
24	0.140171	1.5982	0.056214
25	-0.080576	-0.9187	0.179975
26	-0.113199	-1.2907	0.099555
27	0.034377	0.392	0.347864
28	-0.090882	-1.0362	0.151013
29	-0.049706	-0.5667	0.285936
30	-0.031257	-0.3564	0.361063
31	-0.166895	-1.9029	0.029633
32	-0.021522	-0.2454	0.403272
33	0.027263	0.3109	0.378206
34	-0.015549	-0.1773	0.429781
35	-0.011059	-0.1261	0.449928
36	0.191655	2.1852	0.015333
37	-0.09036	-1.0303	0.152399
38	0.015364	0.1752	0.430605
39	-0.023551	-0.2685	0.394362
40	-0.09966	-1.1363	0.12896
41	0.044171	0.5036	0.307689
42	-0.00341	-0.0389	0.484524
43	-0.146384	-1.669	0.048758
44	-0.049796	-0.5678	0.285586
45	0.017696	0.2018	0.420208
46	0.051125	0.5829	0.280479
47	0.077413	0.8826	0.189529
48	-0.052017	-0.5931	0.277076
49	0.013424	0.1531	0.439297
50	0.031774	0.3623	0.358868
51	-0.001278	-0.0146	0.494199
52	0.000142	0.0016	0.499357
53	-0.038846	-0.4429	0.329284
54	-0.071167	-0.8114	0.209301
55	-0.087665	-0.9995	0.159697
56	-0.011829	-0.1349	0.446463
57	-0.001385	-0.0158	0.493713
58	0.027804	0.317	0.375869
59	0.030797	0.3511	0.363024
60	-0.061073	-0.6963	0.24373

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/21/t12929463221fqad6o86dhma3n/1mumf1292946333.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t12929463221fqad6o86dhma3n/1mumf1292946333.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t12929463221fqad6o86dhma3n/2x34i1292946333.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t12929463221fqad6o86dhma3n/2x34i1292946333.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t12929463221fqad6o86dhma3n/3x34i1292946333.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t12929463221fqad6o86dhma3n/3x34i1292946333.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; 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 (par8 != '') par8 <- as.numeric(par8)

ox <- x

if (par8 == '') {

if (par2 == 0) {

x <- log(x)

} else {

x <- (x ^ par2 - 1) / par2

}

} else {

x <- log(x,base=par8)

}

if (par3 > 0) x <- diff(x,lag=1,difference=par3)

if (par4 > 0) x <- diff(x,lag=par5,difference=par4)

bitmap(file='picts.png')

op <- par(mfrow=c(2,1))

plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')

if (par8=='') {

mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')

mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')

} else {

mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')

mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')

}

plot(x,type='l', main=mytitle,xlab='time',ylab='value')

par(op)

dev.off()

bitmap(file='pic1.png')

racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)

dev.off()

bitmap(file='pic2.png')

rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)

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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