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Paper Variance Reduction Matrix T1

*Unverified author*

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

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Wed, 24 Dec 2008 07:47:06 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/24/t12301300678zblmy3o9b1h5ff.htm/, Retrieved Wed, 24 Dec 2008 15:47:49 +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/2008/Dec/24/t12301300678zblmy3o9b1h5ff.htm/},
    year = {2008},
}
@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 = {2008},
    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 «

105.7 109.5 105.3 102.8 100.6 97.6 110.3 107.2 107.2 108.1 97.1 92.2 112.2 111.6 115.7 111.3 104.2 103.2 112.7 106.4 102.6 110.6 95.2 89 112.5 116.8 107.2 113.6 101.8 102.6 122.7 110.3 110.5 121.6 100.3 100.7 123.4 127.1 124.1 131.2 111.6 114.2 130.1 125.9 119 133.8 107.5 113.5 134.4 126.8 135.6 139.9 129.8 131 153.1 134.1 144.1 155.9 123.3 128.1 144.3 153 149.9 150.9 141 138.9 157.4 142.9 151.7 161 138.5 135.9 151.5 164 159.1 157 142.1 144.8 152.1 154.6 148.7 157.7 146.4 136.5

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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.486835	4.1309	4.8e-05
2	0.580776	4.928	3e-06
3	0.54696	4.6411	8e-06
4	0.42142	3.5759	0.000314
5	0.420462	3.5677	0.000323
6	0.318614	2.7035	0.004277
7	0.260044	2.2065	0.015268
8	0.170409	1.446	0.076263
9	0.248205	2.1061	0.019342
10	0.036293	0.308	0.379503
11	0.078878	0.6693	0.252723
12	-0.020614	-0.1749	0.430819
13	0.030138	0.2557	0.399443
14	0.051643	0.4382	0.331276
15	-0.010554	-0.0896	0.464445
16	-0.001323	-0.0112	0.495536
17	-0.067888	-0.5761	0.283188
18	0.045451	0.3857	0.350442
19	-0.169679	-1.4398	0.077133
20	-0.102416	-0.869	0.193858
21	-0.108887	-0.9239	0.179303
22	-0.158893	-1.3483	0.090902
23	-0.067821	-0.5755	0.28338
24	-0.246681	-2.0932	0.019929
25	-0.201263	-1.7078	0.045993
26	-0.207477	-1.7605	0.041285
27	-0.227309	-1.9288	0.02885
28	-0.27933	-2.3702	0.01023
29	-0.170743	-1.4488	0.075867
30	-0.311242	-2.641	0.005066
31	-0.220214	-1.8686	0.032875
32	-0.2078	-1.7632	0.041051
33	-0.323614	-2.746	0.003808
34	-0.262034	-2.2234	0.014663
35	-0.311674	-2.6446	0.005016
36	-0.242714	-2.0595	0.021532

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.486835	4.1309	4.8e-05
2	0.450551	3.8231	0.000139
3	0.283279	2.4037	0.009403
4	-0.019039	-0.1616	0.436055
5	-0.011519	-0.0977	0.461206
6	-0.085527	-0.7257	0.235181
7	-0.085433	-0.7249	0.235424
8	-0.132008	-1.1201	0.133192
9	0.168093	1.4263	0.07905
10	-0.151188	-1.2829	0.101826
11	-0.041297	-0.3504	0.363526
12	-0.123572	-1.0485	0.148948
13	0.158148	1.3419	0.091918
14	0.155735	1.3215	0.095266
15	0.044911	0.3811	0.352131
16	-0.088616	-0.7519	0.227271
17	-0.150093	-1.2736	0.103454
18	0.060873	0.5165	0.303535
19	-0.233347	-1.98	0.025762
20	-0.113881	-0.9663	0.16856
21	0.084616	0.718	0.237544
22	0.027958	0.2372	0.406575
23	0.1096	0.93	0.177743
24	-0.224346	-1.9036	0.030477
25	-0.068172	-0.5785	0.282381
26	0.064965	0.5512	0.291586
27	-0.051246	-0.4348	0.33249
28	-0.071836	-0.6095	0.272041
29	0.126125	1.0702	0.14405
30	-0.148426	-1.2594	0.105971
31	-0.095697	-0.812	0.209729
32	-0.106666	-0.9051	0.184218
33	0.042579	0.3613	0.35947
34	-0.047356	-0.4018	0.3445
35	-0.079472	-0.6743	0.251126
36	-0.034444	-0.2923	0.385463

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/24/t12301300678zblmy3o9b1h5ff/1926r1230130024.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/24/t12301300678zblmy3o9b1h5ff/1926r1230130024.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/24/t12301300678zblmy3o9b1h5ff/260401230130024.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/24/t12301300678zblmy3o9b1h5ff/260401230130024.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ;

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ;

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 (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='lags',ylab='ACF')

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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