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WS8:1.2 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 10:37:11 -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/t1259343580xncu4p0tj920lws.htm/, Retrieved Fri, 27 Nov 2009 18:39:42 +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/t1259343580xncu4p0tj920lws.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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.136959	0.9489	0.173717
2	0.285333	1.9768	0.026909
3	0.458114	3.1739	0.001313
4	0.227546	1.5765	0.060742
5	0.229029	1.5868	0.059567
6	0.247559	1.7151	0.046385
7	-0.062838	-0.4354	0.332628
8	0.164839	1.142	0.129551
9	0.070573	0.4889	0.313554
10	-0.124099	-0.8598	0.197092
11	-0.090699	-0.6284	0.266366
12	-0.1348	-0.9339	0.177509
13	-0.172894	-1.1978	0.11843
14	-0.004619	-0.032	0.487303
15	-0.157912	-1.094	0.139698
16	-0.243692	-1.6883	0.048916
17	-0.026078	-0.1807	0.428693
18	-0.048175	-0.3338	0.370005
19	-0.181492	-1.2574	0.107344
20	-0.11948	-0.8278	0.205945
21	0.03753	0.26	0.397982
22	-0.205655	-1.4248	0.08034
23	0.097045	0.6723	0.252293
24	-0.090868	-0.6296	0.265986
25	-0.192269	-1.3321	0.094563
26	0.043144	0.2989	0.38315
27	-0.06096	-0.4223	0.337329
28	-0.131346	-0.91	0.183687
29	-0.011959	-0.0829	0.467155
30	-0.145577	-1.0086	0.159115
31	-0.04151	-0.2876	0.387449
32	-0.046485	-0.3221	0.374403
33	-0.177925	-1.2327	0.111845
34	-0.064471	-0.4467	0.328561
35	0.012185	0.0844	0.466538
36	-0.122634	-0.8496	0.199873

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.136959	0.9489	0.173717
2	0.271672	1.8822	0.03294
3	0.431816	2.9917	0.002185
4	0.150432	1.0422	0.151265
5	0.019744	0.1368	0.445884
6	-0.025566	-0.1771	0.430076
7	-0.358845	-2.4862	0.008223
8	-0.078525	-0.544	0.294467
9	0.008785	0.0609	0.47586
10	-0.044689	-0.3096	0.379097
11	-0.141012	-0.977	0.166743
12	-0.166757	-1.1553	0.126838
13	-0.05837	-0.4044	0.343858
14	0.234778	1.6266	0.055186
15	0.25818	1.7887	0.039986
16	-0.049552	-0.3433	0.366433
17	-0.110921	-0.7685	0.222983
18	-0.018656	-0.1293	0.448849
19	-0.07835	-0.5428	0.294881
20	-0.151808	-1.0518	0.149089
21	0.176471	1.2226	0.11372
22	-0.216817	-1.5022	0.069804
23	0.014592	0.1011	0.459947
24	-0.039108	-0.2709	0.393798
25	-0.118065	-0.818	0.208705
26	0.019715	0.1366	0.445962
27	0.029878	0.207	0.418444
28	0.076827	0.5323	0.298497
29	-0.064499	-0.4469	0.328492
30	-0.022925	-0.1588	0.437235
31	-0.052366	-0.3628	0.359172
32	-0.149118	-1.0331	0.153363
33	-0.032447	-0.2248	0.411546
34	0.081799	0.5667	0.286774
35	0.090799	0.6291	0.266142
36	0.011694	0.081	0.467883

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259343580xncu4p0tj920lws/1gvu61259343429.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259343580xncu4p0tj920lws/1gvu61259343429.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259343580xncu4p0tj920lws/2pa841259343429.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259343580xncu4p0tj920lws/2pa841259343429.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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