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WS 8

*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 11:29:00 -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/t1259087384qmlf71af39mvpfo.htm/, Retrieved Tue, 24 Nov 2009 19:29:46 +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/t1259087384qmlf71af39mvpfo.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:

WS 8- methode 1 link 2

Dataseries X:

» Textbox « » Textfile « » CSV «

162 161 149 139 135 130 127 122 117 112 113 149 157 157 147 137 132 125 123 117 114 111 112 144 150 149 134 123 116 117 111 105 102 95 93 124 130 124 115 106 105 105 101 95 93 84 87 116 120 117 109 105 107 109 109 108 107 99 103 131 137

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	0.905819	6.3407	0
2	0.817637	5.7235	0
3	0.701326	4.9093	5e-06
4	0.585342	4.0974	7.8e-05
5	0.464135	3.2489	0.001048
6	0.357685	2.5038	0.007833
7	0.273006	1.911	0.030929
8	0.198672	1.3907	0.085299
9	0.132645	0.9285	0.178846
10	0.0635	0.4445	0.329318
11	0.018681	0.1308	0.448247
12	-0.054694	-0.3829	0.351742
13	-0.100704	-0.7049	0.242097
14	-0.158184	-1.1073	0.136788
15	-0.225422	-1.578	0.060505
16	-0.274695	-1.9229	0.03016
17	-0.321131	-2.2479	0.014558
18	-0.369448	-2.5861	0.006364
19	-0.410786	-2.8755	0.002977
20	-0.431412	-3.0199	0.002004
21	-0.456823	-3.1978	0.001214
22	-0.441281	-3.089	0.001653
23	-0.421473	-2.9503	0.002429
24	-0.360477	-2.5233	0.007459
25	-0.320362	-2.2425	0.014742
26	-0.2776	-1.9432	0.028874
27	-0.242394	-1.6968	0.048044
28	-0.209428	-1.466	0.074519
29	-0.188238	-1.3177	0.096871
30	-0.160036	-1.1203	0.134034
31	-0.124585	-0.8721	0.193705
32	-0.108676	-0.7607	0.225232
33	-0.051984	-0.3639	0.358754
34	-0.005423	-0.038	0.484937
35	0.038571	0.27	0.394149
36	0.060108	0.4208	0.337888

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.905819	6.3407	0
2	-0.015992	-0.1119	0.455663
3	-0.204313	-1.4302	0.079504
4	-0.077896	-0.5453	0.29402
5	-0.082942	-0.5806	0.282087
6	0.002728	0.0191	0.49242
7	0.061491	0.4304	0.334383
8	-0.018944	-0.1326	0.447523
9	-0.05006	-0.3504	0.363763
10	-0.103224	-0.7226	0.23669
11	0.058268	0.4079	0.34257
12	-0.195676	-1.3697	0.088507
13	0.057946	0.4056	0.343394
14	-0.075408	-0.5279	0.299991
15	-0.180018	-1.2601	0.106797
16	0.046787	0.3275	0.372339
17	-0.043912	-0.3074	0.379926
18	-0.131852	-0.923	0.180275
19	-0.035636	-0.2495	0.402026
20	0.019847	0.1389	0.445038
21	-0.116141	-0.813	0.210078
22	0.12793	0.8955	0.187446
23	0.048665	0.3407	0.367411
24	0.089333	0.6253	0.267328
25	-0.137636	-0.9634	0.170027
26	-0.025419	-0.1779	0.429755
27	-0.088259	-0.6178	0.269781
28	0.014556	0.1019	0.459629
29	-0.001327	-0.0093	0.496314
30	0.023949	0.1676	0.433776
31	0.007937	0.0556	0.477961
32	-0.091536	-0.6408	0.262334
33	0.1529	1.0703	0.144864
34	0.02806	0.1964	0.422548
35	-0.118484	-0.8294	0.205453
36	-0.099842	-0.6989	0.243962

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259087384qmlf71af39mvpfo/17u4m1259087338.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259087384qmlf71af39mvpfo/17u4m1259087338.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259087384qmlf71af39mvpfo/2neqd1259087338.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259087384qmlf71af39mvpfo/2neqd1259087338.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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