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WS8: 1.3 The long run trend

*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: Fri, 27 Nov 2009 10:42:52 -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/27/t125934384511sj5cekm9us9pa.htm/, Retrieved Fri, 27 Nov 2009 18:44:07 +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/27/t125934384511sj5cekm9us9pa.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 «

14,3 14,2 15,9 15,3 15,5 15,1 15 12,1 15,8 16,9 15,1 13,7 14,8 14,7 16 15,4 15 15,5 15,1 11,7 16,3 16,7 15 14,9 14,6 15,3 17,9 16,4 15,4 17,9 15,9 13,9 17,8 17,9 17,4 16,7 16 16,6 19,1 17,8 17,2 18,6 16,3 15,1 19,2 17,7 19,1 18 17,5 17,8 21,1 17,2 19,4 19,8 17,6 16,2 19,5 19,9 20 17,3

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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.568775	-3.8993	0.000153
2	0.02165	0.1484	0.44132
3	0.189403	1.2985	0.100229
4	-0.121623	-0.8338	0.204304
5	0.002925	0.0201	0.492044
6	0.195647	1.3413	0.093136
7	-0.301014	-2.0636	0.022299
8	0.119333	0.8181	0.208713
9	0.134049	0.919	0.181397
10	-0.161572	-1.1077	0.136818
11	0.066298	0.4545	0.325775
12	-0.019951	-0.1368	0.445895
13	-0.107315	-0.7357	0.232781
14	0.148459	1.0178	0.156996
15	-0.000541	-0.0037	0.498527
16	-0.195388	-1.3395	0.093423
17	0.13675	0.9375	0.176644
18	0.064013	0.4389	0.33139
19	-0.075859	-0.5201	0.302731
20	-0.075547	-0.5179	0.30347
21	0.235423	1.614	0.056613
22	-0.321235	-2.2023	0.016294
23	0.296923	2.0356	0.023725
24	-0.044048	-0.302	0.382001
25	-0.18803	-1.2891	0.101841
26	0.170173	1.1666	0.124619
27	-0.010347	-0.0709	0.471875
28	-0.09189	-0.63	0.265884
29	0.103712	0.711	0.240295
30	-0.09904	-0.679	0.25024
31	0.01244	0.0853	0.466198
32	0.095935	0.6577	0.256971
33	-0.134371	-0.9212	0.180826
34	-0.002385	-0.0164	0.493512
35	0.100878	0.6916	0.2463
36	-0.130401	-0.894	0.187942

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.568775	-3.8993	0.000153
2	-0.446204	-3.059	0.00183
3	-0.085968	-0.5894	0.279218
4	0.006941	0.0476	0.481124
5	0.002222	0.0152	0.493955
6	0.282199	1.9347	0.029532
7	-0.02393	-0.1641	0.435194
8	-0.167232	-1.1465	0.1287
9	0.001487	0.0102	0.495956
10	0.05553	0.3807	0.352572
11	0.073198	0.5018	0.309067
12	-0.046137	-0.3163	0.376588
13	-0.195964	-1.3435	0.092787
14	-0.151774	-1.0405	0.151712
15	0.042082	0.2885	0.387115
16	-0.037545	-0.2574	0.398998
17	-0.086878	-0.5956	0.277148
18	0.087999	0.6033	0.274608
19	0.183922	1.2609	0.106783
20	-0.155168	-1.0638	0.146433
21	0.182568	1.2516	0.108451
22	-0.059004	-0.4045	0.343837
23	0.04921	0.3374	0.36867
24	0.141616	0.9709	0.168292
25	-0.002524	-0.0173	0.493134
26	-0.031974	-0.2192	0.41372
27	-0.127745	-0.8758	0.192804
28	-0.036122	-0.2476	0.402746
29	-0.09127	-0.6257	0.267264
30	-0.063517	-0.4355	0.332614
31	0.095872	0.6573	0.257108
32	-0.035664	-0.2445	0.403953
33	-0.111131	-0.7619	0.224969
34	-0.101941	-0.6989	0.244039
35	-0.026921	-0.1846	0.427183
36	-0.04179	-0.2865	0.387877

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/27/t125934384511sj5cekm9us9pa/1n6fs1259343770.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t125934384511sj5cekm9us9pa/1n6fs1259343770.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t125934384511sj5cekm9us9pa/29lod1259343770.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t125934384511sj5cekm9us9pa/29lod1259343770.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 1 ; 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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