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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: Thu, 16 Dec 2010 14:18:31 +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/t1292509075alhxjan0mnbmk6b.htm/, Retrieved Thu, 16 Dec 2010 15:17:56 +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/t1292509075alhxjan0mnbmk6b.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 «

2260 2498 2695 2799 2947 2930 2318 2540 2570 2669 2450 2842 3440 2678 2981 2260 2844 2546 2456 2295 2379 2479 2057 2280 2351 2276 2548 2311 2201 2725 2408 2139 1898 2539 2069 2063 2565 2442 2194 2798 2074 2628 2289 2154 2466 2137 1846 2072 1786 1754 2226 1947 1823 2521 2072 2368 2164 2095 1834 1856 2017

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	-0.541364	-3.7507	0.000237
2	0.149042	1.0326	0.153484
3	0.078705	0.5453	0.294042
4	-0.073534	-0.5095	0.306383
5	-0.039528	-0.2739	0.392684
6	0.016578	0.1149	0.45452
7	-0.046255	-0.3205	0.375004
8	0.156853	1.0867	0.141296
9	-0.087564	-0.6067	0.273467
10	-0.014466	-0.1002	0.460293
11	0.271007	1.8776	0.03326
12	-0.408874	-2.8328	0.003364
13	0.174186	1.2068	0.116713
14	-0.009705	-0.0672	0.473334
15	-0.090865	-0.6295	0.265992
16	-0.011981	-0.083	0.467097
17	0.09338	0.647	0.260371
18	-0.048649	-0.3371	0.368774
19	0.072198	0.5002	0.309609
20	-0.181216	-1.2555	0.107687
21	0.166441	1.1531	0.127282
22	-0.150442	-1.0423	0.151249
23	0.085689	0.5937	0.27776
24	-0.075989	-0.5265	0.300495
25	0.124741	0.8642	0.19588
26	-0.065335	-0.4527	0.326419
27	0.014318	0.0992	0.460696
28	0.068167	0.4723	0.319436
29	-0.08778	-0.6082	0.272974
30	0.034239	0.2372	0.406751
31	-0.07606	-0.527	0.300324
32	0.101969	0.7065	0.241659
33	-0.022403	-0.1552	0.438653
34	0.026879	0.1862	0.426527
35	0.011297	0.0783	0.468969
36	0.041326	0.2863	0.387934
37	-0.07447	-0.5159	0.304131
38	0.01601	0.1109	0.456072
39	-0.00448	-0.031	0.487684
40	-0.063761	-0.4418	0.330326
41	0.035221	0.244	0.404128
42	-0.036665	-0.254	0.400281
43	0.0249	0.1725	0.431879
44	0.008411	0.0583	0.476886
45	-0.040456	-0.2803	0.390231
46	0.021618	0.1498	0.440786
47	-0.041335	-0.2864	0.387912
48	NA	NA	NA
49	NA	NA	NA
50	NA	NA	NA
51	NA	NA	NA
52	NA	NA	NA
53	NA	NA	NA
54	NA	NA	NA
55	NA	NA	NA
56	NA	NA	NA
57	NA	NA	NA
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.541364	-3.7507	0.000237
2	-0.203745	-1.4116	0.082261
3	0.096713	0.67	0.25302
4	0.073795	0.5113	0.305753
5	-0.086401	-0.5986	0.276126
6	-0.116276	-0.8056	0.212228
7	-0.105289	-0.7295	0.234631
8	0.18575	1.2869	0.102147
9	0.162159	1.1235	0.133413
10	-0.045811	-0.3174	0.376162
11	0.256553	1.7775	0.040915
12	-0.189036	-1.3097	0.098269
13	-0.228834	-1.5854	0.05972
14	-0.058444	-0.4049	0.343671
15	0.019121	0.1325	0.447581
16	-0.083582	-0.5791	0.282623
17	-0.016954	-0.1175	0.453494
18	-0.001786	-0.0124	0.495088
19	0.010711	0.0742	0.470576
20	-0.149256	-1.0341	0.153142
21	0.001403	0.0097	0.496141
22	-0.121994	-0.8452	0.201097
23	0.245732	1.7025	0.047567
24	-0.019414	-0.1345	0.446784
25	0.010089	0.0699	0.472283
26	0.040524	0.2808	0.39005
27	-0.02866	-0.1986	0.421721
28	0.022465	0.1556	0.438483
29	-0.003205	-0.0222	0.491187
30	0.046065	0.3191	0.3755
31	-0.084726	-0.587	0.279977
32	-0.086641	-0.6003	0.275576
33	0.139814	0.9687	0.168786
34	-0.007017	-0.0486	0.480714
35	0.133123	0.9223	0.180491
36	-0.069176	-0.4793	0.316963
37	-0.029857	-0.2069	0.418499
38	0.002724	0.0189	0.492511
39	-0.007985	-0.0553	0.478057
40	-0.072649	-0.5033	0.308518
41	-0.059723	-0.4138	0.340441
42	-0.100692	-0.6976	0.244392
43	-0.098461	-0.6822	0.24921
44	-0.080632	-0.5586	0.289504
45	0.11463	0.7942	0.2155
46	-0.086464	-0.599	0.275981
47	0.009858	0.0683	0.472916
48	NA	NA	NA
49	NA	NA	NA
50	NA	NA	NA
51	NA	NA	NA
52	NA	NA	NA
53	NA	NA	NA
54	NA	NA	NA
55	NA	NA	NA
56	NA	NA	NA
57	NA	NA	NA
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292509075alhxjan0mnbmk6b/1bsl51292509108.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292509075alhxjan0mnbmk6b/1bsl51292509108.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292509075alhxjan0mnbmk6b/2bsl51292509108.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292509075alhxjan0mnbmk6b/2bsl51292509108.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; 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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