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ACF met: d=1, D=1, lambda=1

*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, 26 Nov 2009 03:10:06 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/26/t1259230249ij5hzxsdj84otcs.htm/, Retrieved Thu, 26 Nov 2009 11:10:51 +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/26/t1259230249ij5hzxsdj84otcs.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 «

1919 1911 1870 2263 1802 1863 1989 2197 2409 2502 2593 2598 2053 2213 2238 2359 2151 2474 3079 2312 2565 1972 2484 2202 2151 1976 2012 2114 1772 1957 2070 1990 2182 2008 1916 2397 2114 1778 1641 2186 1773 1785 2217 2153 1895 2475 1793 2308 2051 1898 2142 1874 1560 1808 1575 1525 1997 1753 1623 2251 1890

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	-0.531404	-3.6817	0.000293
2	0.121571	0.8423	0.201907
3	-0.06376	-0.4417	0.33033
4	0.094536	0.655	0.257809
5	-0.187874	-1.3016	0.099628
6	0.095275	0.6601	0.256177
7	-0.018754	-0.1299	0.448581
8	0.046874	0.3248	0.37339
9	-0.023328	-0.1616	0.436142
10	-0.014478	-0.1003	0.460261
11	0.196162	1.3591	0.090241
12	-0.367193	-2.544	0.007117
13	0.152388	1.0558	0.148177
14	-0.002995	-0.0208	0.491765
15	0.029399	0.2037	0.419731
16	-0.15667	-1.0854	0.141574
17	0.195231	1.3526	0.09126
18	-0.062142	-0.4305	0.334367
19	0.041577	0.2881	0.387273
20	-0.155282	-1.0758	0.143692
21	0.155047	1.0742	0.144053
22	-0.14971	-1.0372	0.152415
23	0.139159	0.9641	0.169909
24	-0.139277	-0.9649	0.169706
25	0.180006	1.2471	0.109203
26	-0.129564	-0.8976	0.186927
27	0.098977	0.6857	0.248091
28	-0.021283	-0.1475	0.441696
29	-0.021456	-0.1487	0.441226
30	-0.039309	-0.2723	0.393264
31	-0.023557	-0.1632	0.435521
32	0.149306	1.0344	0.153062
33	-0.087823	-0.6085	0.272878
34	0.044944	0.3114	0.378429
35	-0.047835	-0.3314	0.370888
36	0.087734	0.6078	0.273079

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.531404	-3.6817	0.000293
2	-0.224104	-1.5526	0.06354
3	-0.152249	-1.0548	0.148396
4	0.013914	0.0964	0.461802
5	-0.178663	-1.2378	0.110903
6	-0.146628	-1.0159	0.157392
7	-0.0819	-0.5674	0.286536
8	0.00461	0.0319	0.487328
9	0.033538	0.2324	0.408623
10	-0.047927	-0.332	0.370651
11	0.255297	1.7687	0.041645
12	-0.194574	-1.348	0.091985
13	-0.211097	-1.4625	0.075058
14	-0.081524	-0.5648	0.287416
15	-0.011138	-0.0772	0.469407
16	-0.148739	-1.0305	0.153971
17	-0.111158	-0.7701	0.2225
18	-0.019046	-0.132	0.447787
19	0.037142	0.2573	0.399014
20	-0.163328	-1.1316	0.131718
21	-0.071635	-0.4963	0.310974
22	-0.172085	-1.1922	0.119514
23	0.129528	0.8974	0.186993
24	-0.188628	-1.3069	0.098744
25	-0.081524	-0.5648	0.287414
26	-0.05371	-0.3721	0.355723
27	0.053066	0.3676	0.357376
28	-0.028848	-0.1999	0.421214
29	-0.094133	-0.6522	0.2587
30	-0.023634	-0.1637	0.435311
31	-0.108756	-0.7535	0.22742
32	-0.019737	-0.1367	0.445903
33	0.06851	0.4746	0.318595
34	-0.030412	-0.2107	0.417008
35	0.059021	0.4089	0.342213
36	-0.103034	-0.7138	0.239392

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259230249ij5hzxsdj84otcs/18arj1259230205.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259230249ij5hzxsdj84otcs/18arj1259230205.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259230249ij5hzxsdj84otcs/2lvzu1259230205.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259230249ij5hzxsdj84otcs/2lvzu1259230205.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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