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

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Mon, 15 Nov 2010 12:08:38 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/15/t1289823075imla1fofaehj8md.htm/, Retrieved Mon, 15 Nov 2010 13:11:15 +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/2010/Nov/15/t1289823075imla1fofaehj8md.htm/},
    year = {2010},
}
@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 = {2010},
    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:

KDGP2W11

Dataseries X:

» Textbox « » Textfile « » CSV «

24.3 29.4 31.8 36.7 37.1 37.7 39.4 43.3 39.6 34.3 32 29.6 22.3 28.9 31.7 34.2 38.6 37.2 38.8 43.4 38.8 36.3 33 29.2 22.64 28.44 30.14 34.39 36.82 36.74 38.9 42.8 39.09 37.49 33.17 30.98 21.2 27.8 29 35.4 37.5 34.7 38.4 39.9 35.9 34.7 30.4 29 21.5 28 29.3 34.3 36.6 36.2 37.5 41.6 39.4 37.3 32.7 30.7 22.9 29.1 29.5 37.1 37.7 38.4 39.4 40.6 39.7 36.6 32.8 31.6 24.1 30.3 31.8 38.7 37.8 38.4 40.7 43.8 41.5 39.3 35.9 33.4

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.710033	6.5076	0
2	0.405198	3.7137	0.000183
3	-0.011264	-0.1032	0.459011
4	-0.338724	-3.1045	0.001299
5	-0.592951	-5.4345	0
6	-0.663109	-6.0775	0
7	-0.628773	-5.7628	0
8	-0.377797	-3.4626	0.000422
9	-0.057725	-0.5291	0.29908
10	0.318015	2.9147	0.002282
11	0.595228	5.4554	0
12	0.818544	7.5021	0
13	0.585549	5.3666	0
14	0.336226	3.0816	0.001392
15	-0.021991	-0.2016	0.420376
16	-0.299672	-2.7465	0.003684
17	-0.518078	-4.7483	4e-06
18	-0.575033	-5.2703	1e-06
19	-0.550093	-5.0417	1e-06
20	-0.338402	-3.1015	0.001311
21	-0.070329	-0.6446	0.260479
22	0.240355	2.2029	0.01517
23	0.486125	4.4554	1.3e-05
24	0.66928	6.1341	0
25	0.475706	4.3599	1.8e-05
26	0.274463	2.5155	0.006895
27	-0.035381	-0.3243	0.373269
28	-0.256208	-2.3482	0.010608
29	-0.437087	-4.006	6.6e-05
30	-0.490975	-4.4999	1.1e-05
31	-0.46394	-4.2521	2.7e-05
32	-0.288897	-2.6478	0.004837
33	-0.077639	-0.7116	0.23935
34	0.173409	1.5893	0.057873
35	0.367348	3.3668	0.000575
36	0.516853	4.737	4e-06
37	0.360097	3.3003	0.000709
38	0.192372	1.7631	0.040759
39	-0.045625	-0.4182	0.338449
40	-0.211713	-1.9404	0.027844
41	-0.340789	-3.1234	0.001227
42	-0.375085	-3.4377	0.000457
43	-0.353256	-3.2376	0.000863
44	-0.208267	-1.9088	0.029851
45	-0.04206	-0.3855	0.350427
46	0.15069	1.3811	0.085456
47	0.298026	2.7315	0.003842
48	0.40101	3.6753	0.000209

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.710033	6.5076	0
2	-0.199554	-1.8289	0.035478
3	-0.450929	-4.1328	4.2e-05
4	-0.223396	-2.0475	0.021869
5	-0.261201	-2.3939	0.009447
6	-0.150761	-1.3817	0.085357
7	-0.244195	-2.2381	0.013931
8	0.042014	0.3851	0.350581
9	0.081072	0.743	0.229766
10	0.186124	1.7059	0.045865
11	0.194663	1.7841	0.039008
12	0.473329	4.3381	2e-05
13	-0.525394	-4.8153	3e-06
14	-0.012109	-0.111	0.455947
15	0.134823	1.2357	0.110013
16	0.024969	0.2288	0.409774
17	0.012513	0.1147	0.454483
18	0.127255	1.1663	0.123395
19	0.005327	0.0488	0.480587
20	-0.184134	-1.6876	0.047598
21	-0.065472	-0.6001	0.275041
22	0.011109	0.1018	0.459572
23	0.043551	0.3991	0.345398
24	0.053212	0.4877	0.313519
25	-0.079044	-0.7245	0.2354
26	-0.012286	-0.1126	0.455307
27	-0.080395	-0.7368	0.231637
28	0.011819	0.1083	0.456998
29	-0.005612	-0.0514	0.479551
30	-0.041629	-0.3815	0.351885
31	0.105547	0.9674	0.168073
32	-0.063399	-0.5811	0.281376
33	-0.157459	-1.4431	0.076351
34	-0.028697	-0.263	0.396592
35	-0.084932	-0.7784	0.219257
36	-0.008604	-0.0789	0.468667
37	-0.020223	-0.1853	0.426702
38	-0.073919	-0.6775	0.249981
39	0.092126	0.8444	0.200436
40	-0.092125	-0.8443	0.200439
41	-0.032436	-0.2973	0.383494
42	0.014246	0.1306	0.448215
43	-0.043937	-0.4027	0.344099
44	0.021754	0.1994	0.421225
45	0.036557	0.3351	0.369211
46	-0.016814	-0.1541	0.438951
47	-0.025007	-0.2292	0.409638
48	-0.053854	-0.4936	0.311446

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/15/t1289823075imla1fofaehj8md/1507p1289822915.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/15/t1289823075imla1fofaehj8md/1507p1289822915.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/15/t1289823075imla1fofaehj8md/2507p1289822915.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/15/t1289823075imla1fofaehj8md/2507p1289822915.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; 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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