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paper ACF

*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, 10 Dec 2010 10:47:04 +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/Dec/10/t1291977912pvcd3o4y4w6i3ma.htm/, Retrieved Fri, 10 Dec 2010 11:45:13 +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/Dec/10/t1291977912pvcd3o4y4w6i3ma.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

1.579 2.146 2.462 3.695 4.831 5.134 6.250 5.760 6.249 2.917 1.741 2.359 1.511 2.059 2.635 2.867 4.403 5.720 4.502 5.749 5.627 2.846 1.762 2.429 1.169 2.154 2.249 2.687 4.359 5.382 4.459 6.398 4.596 3.024 1.887 2.070 1.351 2.218 2.461 3.028 4.784 4.975 4.607 6.249 4.809 3.157 1.910 2.228 1.594 2.467 2.222 3.607 4.685 4.962 5.770 5.480 5.000 3.228 1.993 2.288 1.580 2.111 2.192 3.601 4.665 4.876 5.813 5.589 5.331 3.075 2.002 2.306 1.507 1.992 2.487 3.490 4.647 5.594 5.611 5.788 6.204 3.013 1.931 2.549 1.504 2.090 2.702 2.939 4.500 6.208 6.415 5.657 5.964 3.163 1.997 2.422 1.376 2.202 2.683 3.303 5.202 5.231 4.880 7.998 4.977 3.531 2.025 2.205 1.442 2.238 2.179 3.218 5.139 4.990 4.914 6.084 5.672 3.548 1.793 2.086

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.721997	7.9091	0
2	0.378118	4.1421	3.2e-05
3	0.00147	0.0161	0.493589
4	-0.427046	-4.6781	4e-06
5	-0.715973	-7.8431	0
6	-0.798206	-8.7439	0
7	-0.71598	-7.8432	0
8	-0.385985	-4.2283	2.3e-05
9	0.029647	0.3248	0.372961
10	0.357428	3.9154	7.5e-05
11	0.678533	7.433	0
12	0.84901	9.3004	0
13	0.657996	7.208	0
14	0.358114	3.9229	7.3e-05
15	-0.009708	-0.1063	0.457743
16	-0.390924	-4.2824	1.9e-05
17	-0.621464	-6.8078	0
18	-0.713787	-7.8191	0
19	-0.634949	-6.9555	0
20	-0.333587	-3.6543	0.000192
21	0.002538	0.0278	0.488933
22	0.311611	3.4135	0.000438
23	0.61844	6.7747	0
24	0.728595	7.9814	0
25	0.579497	6.3481	0
26	0.31685	3.4709	0.000361
27	-0.011895	-0.1303	0.448273
28	-0.339402	-3.718	0.000153
29	-0.560649	-6.1416	0
30	-0.632975	-6.9339	0
31	-0.541916	-5.9364	0
32	-0.283434	-3.1049	0.001188
33	-0.000692	-0.0076	0.496984
34	0.278363	3.0493	0.001411
35	0.524252	5.7429	0
36	0.627578	6.8748	0
37	0.516192	5.6546	0
38	0.254208	2.7847	0.003114
39	-0.013812	-0.1513	0.439994
40	-0.278256	-3.0481	0.001416
41	-0.482412	-5.2846	0
42	-0.549872	-6.0235	0
43	-0.466124	-5.1061	1e-06
44	-0.262502	-2.8756	0.002387
45	-0.000387	-0.0042	0.498311
46	0.25155	2.7556	0.003386
47	0.437646	4.7942	2e-06
48	0.539029	5.9048	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.721997	7.9091	0
2	-0.299049	-3.2759	0.000689
3	-0.314878	-3.4493	0.000388
4	-0.508132	-5.5663	0
5	-0.343824	-3.7664	0.000129
6	-0.265166	-2.9047	0.002188
7	-0.330766	-3.6234	0.000214
8	-0.012209	-0.1337	0.446917
9	-0.005084	-0.0557	0.477842
10	-0.191771	-2.1007	0.018879
11	0.161486	1.769	0.039718
12	0.343592	3.7639	0.00013
13	-0.160301	-1.756	0.040819
14	-0.050542	-0.5537	0.290421
15	0.025427	0.2785	0.39054
16	0.102107	1.1185	0.132788
17	0.138645	1.5188	0.065724
18	0.050298	0.551	0.291332
19	0.072732	0.7967	0.213588
20	0.018497	0.2026	0.419885
21	-0.11584	-1.269	0.103454
22	0.042491	0.4655	0.321221
23	0.182866	2.0032	0.023704
24	0.037292	0.4085	0.34181
25	-0.092168	-1.0097	0.157346
26	-0.08763	-0.9599	0.169509
27	0.090692	0.9935	0.161237
28	0.015724	0.1722	0.431766
29	-0.123171	-1.3493	0.089895
30	0.131917	1.4451	0.075522
31	0.060084	0.6582	0.25584
32	-0.083436	-0.914	0.181276
33	-0.057407	-0.6289	0.265318
34	0.039238	0.4298	0.334045
35	-0.056313	-0.6169	0.269242
36	0.019394	0.2124	0.416059
37	0.05141	0.5632	0.287187
38	-0.111281	-1.219	0.112614
39	0.034111	0.3737	0.354654
40	0.027416	0.3003	0.382222
41	0.004119	0.0451	0.482041
42	-0.02351	-0.2575	0.398602
43	-0.028106	-0.3079	0.379351
44	-0.054615	-0.5983	0.275391
45	0.031014	0.3397	0.367323
46	0.084467	0.9253	0.178336
47	-0.080816	-0.8853	0.188884
48	-0.02429	-0.2661	0.395317

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/10/t1291977912pvcd3o4y4w6i3ma/1kc2g1291978020.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t1291977912pvcd3o4y4w6i3ma/1kc2g1291978020.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t1291977912pvcd3o4y4w6i3ma/2v3j11291978020.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t1291977912pvcd3o4y4w6i3ma/2v3j11291978020.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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