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BEL20-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: Mon, 20 Dec 2010 11:53:46 +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/20/t1292845912rn8sfp9qsb1c3i8.htm/, Retrieved Mon, 20 Dec 2010 12:51:56 +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/20/t1292845912rn8sfp9qsb1c3i8.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 «

3030 2803 2768 2883 2863 2897 3013 3143 3033 3046 3111 3013 2987 2996 2833 2849 2795 2845 2915 2893 2604 2642 2660 2639 2720 2746 2736 2812 2799 2555 2305 2215 2066 1940 2042 1995 1947 1766 1635 1833 1910 1960 1970 2061 2093 2121 2175 2197 2350 2440 2409 2473 2408 2455 2448 2498 2646 2757 2849 2921 2982 3081 3106 3119 3061 3097 3162 3257 3277 3295 3364 3494 3667 3813 3918 3896 3801 3570 3702 3862 3970 4139 4200 4291 4444 4503 4357 4591 4697 4621 4563 4203 4296 4435 4105 4117 3844 3721 3674 3858 3801 3504 3033 3047 2962 2198 2014 1863 1905 1811 1670 1864 2052 2030 2071 2293 2443 2513 2467 2503 2540 2483 2626 2656 2447 2467 2462 2505 2579 2649 2637

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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.272701	3.1093	0.001152
2	0.059557	0.679	0.249157
3	0.214089	2.441	0.007997
4	0.17184	1.9593	0.02611
5	0.18402	2.0982	0.018914
6	0.016199	0.1847	0.426878
7	0.000389	0.0044	0.498234
8	0.123823	1.4118	0.080199
9	0.042348	0.4828	0.315011
10	-0.099417	-1.1335	0.129539
11	0.088115	1.0047	0.158462
12	0.023795	0.2713	0.393294
13	-0.040977	-0.4672	0.320566
14	0.052143	0.5945	0.276599
15	0.00142	0.0162	0.493552
16	0.06245	0.712	0.238859
17	-0.080824	-0.9215	0.17924
18	-0.105552	-1.2035	0.115489
19	0.059963	0.6837	0.247696
20	-0.128769	-1.4682	0.072234
21	-0.12514	-1.4268	0.078015
22	-0.08598	-0.9803	0.164373
23	-0.128159	-1.4612	0.073181
24	-0.088012	-1.0035	0.158745
25	-0.075433	-0.8601	0.195667
26	-0.147382	-1.6804	0.04764
27	-0.036825	-0.4199	0.337636
28	0.01517	0.173	0.431476
29	-0.036253	-0.4133	0.340018
30	0.017652	0.2013	0.420403
31	-0.081718	-0.9317	0.176602
32	-0.008937	-0.1019	0.459496
33	-0.017948	-0.2046	0.419089
34	-0.073673	-0.84	0.201226
35	-0.097476	-1.1114	0.134224
36	-0.040263	-0.4591	0.323475
37	-0.071726	-0.8178	0.207484
38	-0.070243	-0.8009	0.212328
39	-0.011711	-0.1335	0.446992
40	-0.050074	-0.5709	0.284515
41	-0.01935	-0.2206	0.412865
42	-0.037649	-0.4293	0.334219
43	-0.091065	-1.0383	0.15053
44	0.000402	0.0046	0.498176
45	-0.063197	-0.7206	0.236238
46	-0.08089	-0.9223	0.179044
47	-0.061343	-0.6994	0.242772
48	-0.048087	-0.5483	0.292219
49	-0.077377	-0.8822	0.18964
50	-0.074867	-0.8536	0.197445
51	-0.08489	-0.9679	0.167446
52	-0.116289	-1.3259	0.093598
53	-0.019449	-0.2218	0.412426
54	-0.026513	-0.3023	0.381456
55	-0.03242	-0.3696	0.356126
56	0.003092	0.0353	0.485966
57	-0.04126	-0.4704	0.319414
58	-0.041828	-0.4769	0.317112
59	-0.013552	-0.1545	0.43872
60	0.019919	0.2271	0.410346

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.272701	3.1093	0.001152
2	-0.015999	-0.1824	0.427769
3	0.218231	2.4882	0.007051
4	0.064469	0.7351	0.231813
5	0.141331	1.6114	0.054756
6	-0.115286	-1.3145	0.095502
7	-0.010086	-0.115	0.454312
8	0.061385	0.6999	0.242621
9	-0.020302	-0.2315	0.408655
10	-0.122997	-1.4024	0.081593
11	0.153755	1.7531	0.040973
12	-0.072489	-0.8265	0.205016
13	-0.010171	-0.116	0.453928
14	0.060054	0.6847	0.247369
15	0.001034	0.0118	0.495308
16	0.032154	0.3666	0.357252
17	-0.13957	-1.5913	0.056981
18	-0.017439	-0.1988	0.421352
19	0.041655	0.4749	0.317812
20	-0.187261	-2.1351	0.017314
21	0.034487	0.3932	0.347403
22	-0.076345	-0.8705	0.192825
23	-0.062405	-0.7115	0.239016
24	-0.012256	-0.1397	0.444539
25	0.025776	0.2939	0.384653
26	-0.074516	-0.8496	0.198551
27	0.025637	0.2923	0.385258
28	0.072337	0.8248	0.205505
29	0.047873	0.5458	0.293059
30	-0.043846	-0.4999	0.30899
31	-0.036762	-0.4192	0.337897
32	0.04046	0.4613	0.32267
33	-0.107353	-1.224	0.11158
34	0.012646	0.1442	0.442786
35	-0.108557	-1.2377	0.109022
36	0.05587	0.637	0.262617
37	-0.091439	-1.0426	0.149543
38	0.012783	0.1457	0.442173
39	0.063543	0.7245	0.235031
40	-0.058068	-0.6621	0.254547
41	-0.014105	-0.1608	0.436244
42	0.01731	0.1974	0.421926
43	-0.157479	-1.7955	0.037446
44	0.027342	0.3117	0.377867
45	-0.080503	-0.9179	0.180192
46	-0.025626	-0.2922	0.385305
47	-0.071115	-0.8108	0.209471
48	0.005191	0.0592	0.476448
49	-0.03754	-0.428	0.334673
50	-0.011021	-0.1257	0.450097
51	-0.070211	-0.8005	0.212433
52	-0.033891	-0.3864	0.349912
53	-0.010794	-0.1231	0.451121
54	0.060741	0.6925	0.244914
55	-0.078834	-0.8988	0.185199
56	0.07027	0.8012	0.212239
57	-0.103767	-1.1831	0.119458
58	-0.072805	-0.8301	0.204
59	0.015239	0.1738	0.431164
60	0.003835	0.0437	0.482597

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292845912rn8sfp9qsb1c3i8/1xahx1292846024.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292845912rn8sfp9qsb1c3i8/1xahx1292846024.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292845912rn8sfp9qsb1c3i8/28jhi1292846024.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292845912rn8sfp9qsb1c3i8/28jhi1292846024.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292845912rn8sfp9qsb1c3i8/38jhi1292846024.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292845912rn8sfp9qsb1c3i8/38jhi1292846024.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; 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 (par8 != '') par8 <- as.numeric(par8)

ox <- x

if (par8 == '') {

if (par2 == 0) {

x <- log(x)

} else {

x <- (x ^ par2 - 1) / par2

}

} else {

x <- log(x,base=par8)

}

if (par3 > 0) x <- diff(x,lag=1,difference=par3)

if (par4 > 0) x <- diff(x,lag=par5,difference=par4)

bitmap(file='picts.png')

op <- par(mfrow=c(2,1))

plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')

if (par8=='') {

mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')

mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')

} else {

mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')

mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')

}

plot(x,type='l', main=mytitle,xlab='time',ylab='value')

par(op)

dev.off()

bitmap(file='pic1.png')

racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)

dev.off()

bitmap(file='pic2.png')

rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)

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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