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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: Thu, 16 Dec 2010 18:20:33 +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/16/t12925235140l38ck1ddctcgzk.htm/, Retrieved Thu, 16 Dec 2010 19:18:35 +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/16/t12925235140l38ck1ddctcgzk.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 «

1775 2197 2920 4240 5415 6136 6719 6234 7152 3646 2165 2803 1615 2350 3350 3536 5834 6767 5993 7276 5641 3477 2247 2466 1567 2237 2598 3729 5715 5776 5852 6878 5488 3583 2054 2282 1552 2261 2446 3519 5161 5085 5711 6057 5224 3363 1899 2115 1491 2061 2419 3430 4778 4862 6176 5664 5529 3418 1941 2402 1579 2146 2462 3695 4831 5134 6250 5760 6249 2917 1741 2359 1511 2059 2635 2867 4403 5720 4502 5749 5627 2846 1762 2429 1169 2154 2249 2687 4359 5382 4459 6398 4596 3024 1887 2070 1351 2218 2461 3028 4784 4975 4607 6249 4809 3157 1910 2228 1594 2467 2222 3607 4685 4962 5770 5480 5000 3228 1993 2288 1588 2105 2191 3591 4668 4885 5822 5599 5340 3082 2010 2301

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

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.267951	-2.9353	0.001997
2	0.173517	1.9008	0.029865
3	0.312866	3.4273	0.000418
4	-0.146369	-1.6034	0.055738
5	0.1846	2.0222	0.02269
6	0.190251	2.0841	0.019637
7	-0.174742	-1.9142	0.028988
8	0.114826	1.2579	0.105444
9	0.228714	2.5054	0.006785
10	-0.155867	-1.7074	0.045163
11	0.147725	1.6182	0.054117
12	0.00026	0.0029	0.498864
13	-0.204691	-2.2423	0.01339
14	0.274382	3.0057	0.001614
15	-0.105528	-1.156	0.124989
16	-0.114803	-1.2576	0.105489
17	0.11134	1.2197	0.112491
18	-0.053778	-0.5891	0.27845
19	-0.136572	-1.4961	0.068631
20	0.083052	0.9098	0.182379
21	-0.072389	-0.793	0.214676
22	-0.225909	-2.4747	0.007366
23	0.257527	2.8211	0.002802
24	-0.252359	-2.7645	0.003301
25	-0.07406	-0.8113	0.209403
26	0.060479	0.6625	0.254457
27	-0.138834	-1.5208	0.065465
28	-0.032848	-0.3598	0.359803
29	0.029821	0.3267	0.372241
30	-0.120622	-1.3213	0.09445
31	0.002489	0.0273	0.489147
32	0.096789	1.0603	0.145576
33	-0.12767	-1.3986	0.082263
34	-0.021295	-0.2333	0.407973
35	0.157143	1.7214	0.043876
36	-0.267321	-2.9284	0.002039
37	0.273448	2.9955	0.001665
38	-0.095191	-1.0428	0.149576
39	-0.098241	-1.0762	0.142004
40	0.154249	1.6897	0.046839
41	0.004524	0.0496	0.480281
42	-0.063039	-0.6906	0.245588
43	0.104039	1.1397	0.128343
44	0.026583	0.2912	0.385699
45	-0.038073	-0.4171	0.338685
46	0.192678	2.1107	0.018438
47	-0.01245	-0.1364	0.445872
48	-0.077238	-0.8461	0.199591

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.267951	-2.9353	0.001997
2	0.109587	1.2005	0.116162
3	0.418327	4.5825	6e-06
4	0.02429	0.2661	0.395315
5	0.0136	0.149	0.44091
6	0.185603	2.0332	0.02212
7	-0.086203	-0.9443	0.173457
8	-0.151796	-1.6628	0.049477
9	0.242407	2.6554	0.004498
10	0.085384	0.9353	0.175748
11	-0.090524	-0.9916	0.161685
12	-0.120803	-1.3233	0.094121
13	-0.175479	-1.9223	0.028471
14	0.124989	1.3692	0.086749
15	0.063094	0.6912	0.245401
16	-0.077592	-0.85	0.198516
17	-0.088147	-0.9656	0.168094
18	0.073723	0.8076	0.21046
19	-0.140122	-1.535	0.063713
20	-0.17074	-1.8704	0.031935
21	0.18094	1.9821	0.024877
22	-0.061777	-0.6767	0.249938
23	0.013039	0.1428	0.443329
24	-0.076283	-0.8356	0.202509
25	-0.098773	-1.082	0.140711
26	-0.094766	-1.0381	0.150654
27	0.147385	1.6145	0.054521
28	0.034385	0.3767	0.353543
29	-0.080392	-0.8807	0.190132
30	0.060772	0.6657	0.253431
31	0.05245	0.5746	0.283333
32	-0.050571	-0.554	0.290313
33	0.057675	0.6318	0.264361
34	-0.040914	-0.4482	0.327413
35	0.136409	1.4943	0.068864
36	-0.121854	-1.3348	0.092227
37	0.056352	0.6173	0.269102
38	-0.037282	-0.4084	0.341854
39	0.003915	0.0429	0.482933
40	-0.017076	-0.1871	0.425965
41	0.038601	0.4228	0.336581
42	0.061533	0.6741	0.250785
43	-0.043617	-0.4778	0.316831
44	0.002667	0.0292	0.488369
45	0.120029	1.3149	0.095533
46	-0.012914	-0.1415	0.443868
47	0.069698	0.7635	0.22333
48	-0.104444	-1.1441	0.127424

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/16/t12925235140l38ck1ddctcgzk/15nne1292523630.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t12925235140l38ck1ddctcgzk/15nne1292523630.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t12925235140l38ck1ddctcgzk/25nne1292523630.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t12925235140l38ck1ddctcgzk/25nne1292523630.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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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