Home » date » 2009 » Dec » 19 »

ACF met: d=1, D=0, 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: Sat, 19 Dec 2009 04:10:28 -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/Dec/19/t12612211753bgcdloinhlkyt4.htm/, Retrieved Sat, 19 Dec 2009 12:12:57 +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/Dec/19/t12612211753bgcdloinhlkyt4.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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.51713	-4.0057	8.7e-05
2	0.020061	0.1554	0.438517
3	0.127917	0.9908	0.162871
4	-0.068124	-0.5277	0.299831
5	-0.058358	-0.452	0.326435
6	0.028156	0.2181	0.414047
7	-0.086167	-0.6674	0.253523
8	0.062953	0.4876	0.313795
9	0.097432	0.7547	0.226688
10	-0.11204	-0.8679	0.194465
11	-0.044101	-0.3416	0.36692
12	0.164646	1.2753	0.103552
13	-0.14442	-1.1187	0.133869
14	0.030366	0.2352	0.407421
15	0.106715	0.8266	0.205867
16	-0.180097	-1.395	0.084075
17	0.203754	1.5783	0.05988
18	-0.087433	-0.6773	0.250424
19	-0.070845	-0.5488	0.292601
20	-0.03613	-0.2799	0.390272
21	0.138396	1.072	0.144004
22	-0.117385	-0.9093	0.183425
23	-0.055885	-0.4329	0.333325
24	0.090494	0.701	0.243017
25	0.094864	0.7348	0.232658
26	-0.157373	-1.219	0.113806
27	0.16129	1.2493	0.108195
28	-0.098956	-0.7665	0.223189
29	0.048922	0.3789	0.353032
30	0.013176	0.1021	0.459523
31	-0.135362	-1.0485	0.149304
32	0.132489	1.0263	0.154446
33	-0.024108	-0.1867	0.426249
34	0.009913	0.0768	0.469525
35	-0.088602	-0.6863	0.247581
36	0.087284	0.6761	0.250789
37	-0.018809	-0.1457	0.442325
38	-0.070529	-0.5463	0.293439
39	0.11605	0.8989	0.186144
40	-0.084076	-0.6512	0.258687
41	0.017564	0.1361	0.446118
42	0.097755	0.7572	0.225944
43	-0.11456	-0.8874	0.18921
44	0.014906	0.1155	0.454231
45	-0.002697	-0.0209	0.4917
46	-0.003138	-0.0243	0.490344
47	-0.030601	-0.237	0.406717
48	0.041901	0.3246	0.373319
49	-0.024572	-0.1903	0.424844
50	0.034542	0.2676	0.394977
51	-0.00082	-0.0064	0.497476
52	-0.031869	-0.2469	0.402931
53	0.04603	0.3565	0.361342
54	-0.009556	-0.074	0.47062
55	-0.054992	-0.426	0.335827
56	0.064897	0.5027	0.308512
57	-0.025679	-0.1989	0.421504
58	0.001526	0.0118	0.495305
59	0.000418	0.0032	0.498713
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.51713	-4.0057	8.7e-05
2	-0.337661	-2.6155	0.005626
3	-0.050567	-0.3917	0.348337
4	0.00598	0.0463	0.481603
5	-0.085301	-0.6607	0.255654
6	-0.111594	-0.8644	0.195405
7	-0.214556	-1.6619	0.05087
8	-0.127977	-0.9913	0.162759
9	0.11175	0.8656	0.195076
10	0.065265	0.5055	0.307516
11	-0.147619	-1.1435	0.128696
12	-0.027509	-0.2131	0.415993
13	-0.065814	-0.5098	0.306034
14	-0.018154	-0.1406	0.44432
15	0.145647	1.1282	0.131868
16	-0.064761	-0.5016	0.308878
17	0.077732	0.6021	0.274686
18	0.025997	0.2014	0.420544
19	-0.027539	-0.2133	0.415903
20	-0.209725	-1.6245	0.054753
21	-0.044137	-0.3419	0.366817
22	0.012867	0.0997	0.460471
23	-0.153338	-1.1878	0.119805
24	-0.180806	-1.4005	0.083254
25	0.09817	0.7604	0.22499
26	-0.064951	-0.5031	0.308365
27	0.07015	0.5434	0.29444
28	0.07453	0.5773	0.282946
29	0.00424	0.0328	0.486953
30	0.010783	0.0835	0.466855
31	-0.095233	-0.7377	0.231795
32	0.065275	0.5056	0.30749
33	0.048556	0.3761	0.35408
34	0.106922	0.8282	0.205416
35	-0.041921	-0.3247	0.373261
36	-0.107388	-0.8318	0.204404
37	0.009009	0.0698	0.472299
38	-0.054886	-0.4251	0.336127
39	0.023937	0.1854	0.426763
40	0.021838	0.1692	0.433121
41	-0.055418	-0.4293	0.334634
42	-0.104242	-0.8075	0.211296
43	-0.001143	-0.0089	0.496482
44	-0.006461	-0.05	0.480125
45	-0.046886	-0.3632	0.358874
46	-0.087219	-0.6756	0.250947
47	-0.034773	-0.2694	0.394292
48	0.024814	0.1922	0.424114
49	-0.048778	-0.3778	0.353446
50	0.041888	0.3245	0.373358
51	-0.035828	-0.2775	0.391167
52	0.000369	0.0029	0.498863
53	0.062454	0.4838	0.315157
54	-0.047197	-0.3656	0.357979
55	-0.054708	-0.4238	0.336625
56	0.037682	0.2919	0.38569
57	-0.039047	-0.3025	0.381675
58	0.008453	0.0655	0.474006
59	-0.028388	-0.2199	0.413352
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/19/t12612211753bgcdloinhlkyt4/1vjnf1261221026.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t12612211753bgcdloinhlkyt4/1vjnf1261221026.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t12612211753bgcdloinhlkyt4/2sz5h1261221026.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t12612211753bgcdloinhlkyt4/2sz5h1261221026.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 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; 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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