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*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: Wed, 29 Dec 2010 09:18:37 +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/29/t1293614177nyvxkffqjcq2kwe.htm/, Retrieved Wed, 29 Dec 2010 10:16:19 +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/29/t1293614177nyvxkffqjcq2kwe.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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.757034	8.6977	0
2	0.418846	4.8122	2e-06
3	0.021998	0.2527	0.400433
4	-0.412141	-4.7351	3e-06
5	-0.703433	-8.0818	0
6	-0.799131	-9.1813	0
7	-0.700894	-8.0527	0
8	-0.375755	-4.3171	1.5e-05
9	0.041699	0.4791	0.316334
10	0.386944	4.4457	9e-06
11	0.712122	8.1817	0
12	0.870232	9.9982	0
13	0.672075	7.7216	0
14	0.377204	4.3337	1.4e-05
15	0.001478	0.017	0.49324
16	-0.379379	-4.3587	1.3e-05
17	-0.636754	-7.3157	0
18	-0.730319	-8.3907	0
19	-0.634052	-7.2847	0
20	-0.335979	-3.8601	8.8e-05
21	0.014935	0.1716	0.432012
22	0.329454	3.7851	0.000116
23	0.636412	7.3118	0
24	0.751006	8.6284	0
25	0.602774	6.9253	0
26	0.324422	3.7273	0.000143
27	-0.012065	-0.1386	0.444982
28	-0.336351	-3.8644	8.7e-05
29	-0.566861	-6.5127	0
30	-0.661028	-7.5946	0
31	-0.563365	-6.4726	0
32	-0.307084	-3.5281	0.000288
33	-0.000437	-0.005	0.498002
34	0.296024	3.4011	0.000444
35	0.55343	6.3584	0
36	0.653614	7.5095	0
37	0.540477	6.2096	0
38	0.274011	3.1481	0.001016
39	-0.014362	-0.165	0.434597
40	-0.29778	-3.4212	0.000415
41	-0.508023	-5.8367	0
42	-0.589519	-6.7731	0
43	-0.492095	-5.6537	0
44	-0.280399	-3.2215	0.000803
45	-0.002967	-0.0341	0.486431
46	0.266454	3.0613	0.001335
47	0.472619	5.43	0
48	0.582579	6.6933	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.757034	8.6977	0
2	-0.361335	-4.1514	2.9e-05
3	-0.36672	-4.2133	2.3e-05
4	-0.501885	-5.7662	0
5	-0.270246	-3.1049	0.001165
6	-0.182532	-2.0971	0.018945
7	-0.122052	-1.4023	0.08159
8	0.156497	1.798	0.03723
9	0.165915	1.9062	0.029398
10	-0.070244	-0.807	0.210545
11	0.327518	3.7629	0.000126
12	0.414136	4.7581	3e-06
13	-0.306581	-3.5223	0.000294
14	0.020781	0.2388	0.405831
15	0.161908	1.8602	0.032542
16	0.163587	1.8795	0.031193
17	-0.048511	-0.5574	0.289115
18	0.051858	0.5958	0.276165
19	0.07494	0.861	0.195402
20	-0.118003	-1.3557	0.088747
21	-0.13629	-1.5659	0.059889
22	0.077984	0.896	0.18595
23	0.122854	1.4115	0.080227
24	-0.085599	-0.9835	0.163591
25	-0.053017	-0.6091	0.271746
26	-0.126372	-1.4519	0.074451
27	0.047203	0.5423	0.294256
28	0.034814	0.4	0.34491
29	0.010462	0.1202	0.452255
30	-0.035798	-0.4113	0.340762
31	0.028314	0.3253	0.372733
32	-0.110162	-1.2657	0.103932
33	0.008572	0.0985	0.46085
34	0.092397	1.0616	0.145188
35	-0.038259	-0.4396	0.330486
36	-0.020084	-0.2307	0.408936
37	0.029329	0.337	0.368338
38	-0.092387	-1.0614	0.145214
39	0.013111	0.1506	0.440245
40	0.035782	0.4111	0.34083
41	0.03918	0.4501	0.326674
42	-0.064192	-0.7375	0.23106
43	0.030799	0.3539	0.362006
44	-0.041895	-0.4813	0.315539
45	-0.010433	-0.1199	0.452384
46	0.048372	0.5558	0.289661
47	-0.05633	-0.6472	0.259319
48	0.069641	0.8001	0.21254

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293614177nyvxkffqjcq2kwe/1oi601293614315.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293614177nyvxkffqjcq2kwe/1oi601293614315.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293614177nyvxkffqjcq2kwe/2oi601293614315.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293614177nyvxkffqjcq2kwe/2oi601293614315.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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