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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: Thu, 03 Dec 2009 02:44:29 -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/03/t1259833514nc2hvbkuwaehlpo.htm/, Retrieved Thu, 03 Dec 2009 10:45:16 +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/03/t1259833514nc2hvbkuwaehlpo.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 «

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 82.6 89.1

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	0.541662	3.7916	0.000206
2	0.634404	4.4408	2.6e-05
3	0.688667	4.8207	7e-06
4	0.411375	2.8796	0.002944
5	0.413385	2.8937	0.002834
6	0.386242	2.7037	0.0047
7	0.173017	1.2111	0.115829
8	0.216613	1.5163	0.067936
9	0.080599	0.5642	0.287599
10	0.049626	0.3474	0.364896
11	0.072526	0.5077	0.306978
12	-0.045937	-0.3216	0.374577
13	0.009404	0.0658	0.47389
14	0.005534	0.0387	0.484628
15	-0.043201	-0.3024	0.38181
16	-0.071463	-0.5002	0.309572
17	-0.002461	-0.0172	0.493163
18	-0.092116	-0.6448	0.261028
19	-0.095253	-0.6668	0.254022
20	-0.042749	-0.2992	0.38301
21	-0.115617	-0.8093	0.211123
22	-0.200366	-1.4026	0.083526
23	-0.026699	-0.1869	0.426257
24	-0.223632	-1.5654	0.06196
25	-0.160312	-1.1222	0.133626
26	-0.121284	-0.849	0.200008
27	-0.23025	-1.6117	0.05672
28	-0.190716	-1.335	0.094021
29	-0.172903	-1.2103	0.11598
30	-0.250831	-1.7558	0.042684
31	-0.189723	-1.3281	0.095155
32	-0.23557	-1.649	0.052774
33	-0.246954	-1.7287	0.045082
34	-0.195329	-1.3673	0.088885
35	-0.258386	-1.8087	0.038317
36	-0.191868	-1.3431	0.092718

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.541662	3.7916	0.000206
2	0.4826	3.3782	0.000719
3	0.460241	3.2217	0.001133
4	-0.239446	-1.6761	0.050042
5	-0.319859	-2.239	0.014864
6	-0.073206	-0.5124	0.305322
7	-0.073657	-0.5156	0.304227
8	0.089366	0.6256	0.267252
9	-0.106469	-0.7453	0.22983
10	0.070014	0.4901	0.313126
11	0.167083	1.1696	0.123914
12	-0.019572	-0.137	0.445796
13	-0.024708	-0.173	0.431698
14	-0.032677	-0.2287	0.410011
15	0.056741	0.3972	0.346478
16	-0.260476	-1.8233	0.037178
17	-0.008358	-0.0585	0.476792
18	0.03285	0.2299	0.409545
19	0.002112	0.0148	0.494133
20	0.060265	0.4219	0.337489
21	-0.028736	-0.2012	0.420705
22	-0.241808	-1.6927	0.048436
23	0.186227	1.3036	0.099233
24	-0.045469	-0.3183	0.375811
25	-0.028313	-0.1982	0.421857
26	-0.098735	-0.6911	0.246368
27	-0.012485	-0.0874	0.465358
28	-0.085409	-0.5979	0.276341
29	-0.022078	-0.1545	0.438908
30	0.030083	0.2106	0.417045
31	-0.064155	-0.4491	0.327675
32	-0.020571	-0.144	0.443047
33	-0.043935	-0.3075	0.379867
34	-0.041817	-0.2927	0.385487
35	0.061239	0.4287	0.335019
36	0.088158	0.6171	0.27001

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259833514nc2hvbkuwaehlpo/1382m1259833467.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259833514nc2hvbkuwaehlpo/1382m1259833467.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259833514nc2hvbkuwaehlpo/24kzv1259833467.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259833514nc2hvbkuwaehlpo/24kzv1259833467.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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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