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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: Wed, 05 May 2010 15:42:58 +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/May/05/t12730742218kqc1urw54fic3i.htm/, Retrieved Wed, 05 May 2010 17:43:42 +0200

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/May/05/t12730742218kqc1urw54fic3i.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:

KDGP2W21

Dataseries X:

» Textbox « » Textfile « » CSV «

1772.2 1769.5 1768 1794.8 1823.4 1856.9 1866.9 1869.8 1843.8 1837.1 1857.7 1840.3 1914.6 1972.9 2050.1 2086.2 2112.5 2147.6 2190.4 2194.1 2216.2 2218.6 2233.5 2307.2 2350.4 2368.2 2353.8 2316.5 2305.5 2308.4 2334.4 2381.2 2449.7 2490.3 2523.5 2537.6 2526.1 2545.9 2542.7 2584.3 2600.2 2593.9 2618.9 2591.3 2521.2 2536.6 2596.1 2656.6 2710.3 2778.8 2775.5 2785.2 2847.7 2834.4 2839 2802.6 2819.3 2872 2918.4 2977.8 3031.2 3064.7 3093 3100.6 3141.1 3180.4 3240.3 3265 3338.2 3376.6 3422.5 3432 3516.3 3564 3636.3 3724 3815.4 3828.1 3853.3 3884.5 3918.7 3919.6 3950.8 3981 4063 4132 4160.3 4178.3 4244.1 4256.5 4283.4 4263.3 4256.6 4264.3 4302.3 4256.6 4374 4398.8 4433.9 4446.3 4525.8 4633.1 4677.5 4754.5 4876.2 4932.6 4906.3 4953.1 4909.6 4922.2 4873.5 4854.3 4795.3 4831.9 4913.3 4977.5 5090.7 5128.9 5154.1 5191.5 5251.8 5356.1 5451.9 5450.8 5469.4 5684.6 5740.3 5816.2 5825.9 5831.4 5873.3 etc...

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	0.436808	6.9203	0
2	0.328779	5.2088	0
3	0.124619	1.9743	0.02472
4	0.124197	1.9677	0.025105
5	0.037807	0.599	0.274865
6	0.089401	1.4164	0.078952
7	0.039087	0.6193	0.268154
8	0.019912	0.3155	0.376336
9	0.143337	2.2709	0.012001
10	0.125008	1.9805	0.024369
11	0.069568	1.1022	0.135723
12	-0.060738	-0.9623	0.168419
13	-2.6e-05	-4e-04	0.499838
14	0.017543	0.2779	0.390647
15	0.027438	0.4347	0.332077
16	0.088727	1.4057	0.080526
17	0.043565	0.6902	0.245351
18	0.065371	1.0357	0.150677
19	0.107711	1.7065	0.044579
20	0.114562	1.815	0.035358
21	0.037769	0.5984	0.275063
22	0.060143	0.9528	0.170795
23	0.063057	0.999	0.159376
24	0.13128	2.0799	0.019276
25	0.141481	2.2415	0.012935
26	0.083508	1.323	0.093517
27	0.041165	0.6522	0.25744
28	0.094927	1.5039	0.066929
29	0.138109	2.1881	0.014794
30	0.072867	1.1544	0.12471
31	0.110502	1.7507	0.040611
32	0.10132	1.6052	0.054853
33	0.037717	0.5975	0.27534
34	0.061308	0.9713	0.166165
35	-0.006911	-0.1095	0.456453
36	-0.009115	-0.1444	0.442649
37	-0.034663	-0.5492	0.291688
38	0.011853	0.1878	0.425598
39	-0.012369	-0.196	0.4224
40	0.024215	0.3836	0.350788
41	0.027887	0.4418	0.329505
42	0.103554	1.6406	0.051067
43	0.079573	1.2607	0.1043
44	0.08016	1.27	0.102634
45	0.101126	1.6021	0.055191
46	0.018162	0.2877	0.38689
47	0.040018	0.634	0.263329
48	0.034498	0.5465	0.292588

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.436808	6.9203	0
2	0.170512	2.7014	0.003688
3	-0.087806	-1.3911	0.082712
4	0.062867	0.996	0.160105
5	-0.031113	-0.4929	0.31125
6	0.069484	1.1008	0.136011
7	-0.011888	-0.1883	0.425379
8	-0.035535	-0.563	0.286975
9	0.190954	3.0253	0.001371
10	0.013174	0.2087	0.417422
11	-0.071008	-1.125	0.130837
12	-0.126898	-2.0104	0.022727
13	0.067798	1.0741	0.141898
14	0.080567	1.2764	0.101494
15	-0.044376	-0.703	0.24134
16	0.090608	1.4355	0.076196
17	-0.017401	-0.2757	0.391512
18	0.024591	0.3896	0.348582
19	0.069891	1.1073	0.134616
20	-0.005707	-0.0904	0.464016
21	-0.003737	-0.0592	0.47642
22	0.045958	0.7281	0.233614
23	0.025083	0.3974	0.345708
24	0.090724	1.4373	0.075934
25	0.029255	0.4635	0.321709
26	-0.055129	-0.8734	0.191636
27	-0.013819	-0.2189	0.413442
28	0.108894	1.7252	0.042861
29	0.065892	1.0439	0.148762
30	-0.076527	-1.2124	0.113245
31	0.0962	1.5241	0.064372
32	0.060125	0.9526	0.170865
33	-0.12019	-1.9042	0.029016
34	0.021166	0.3353	0.368824
35	-0.078458	-1.243	0.107512
36	0.052697	0.8349	0.202289
37	0.001849	0.0293	0.488329
38	-0.069969	-1.1085	0.134351
39	0.005786	0.0917	0.46352
40	0.030718	0.4867	0.313459
41	0.011066	0.1753	0.430483
42	0.080831	1.2806	0.100759
43	0.009515	0.1507	0.440148
44	0.010388	0.1646	0.434704
45	0.039647	0.6281	0.265246
46	-0.053381	-0.8457	0.199259
47	-0.004822	-0.0764	0.469585
48	-0.019958	-0.3162	0.376056

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/May/05/t12730742218kqc1urw54fic3i/1wwxv1273074174.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/05/t12730742218kqc1urw54fic3i/1wwxv1273074174.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/May/05/t12730742218kqc1urw54fic3i/276ff1273074174.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/05/t12730742218kqc1urw54fic3i/276ff1273074174.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 1 ; 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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