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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, 03 Dec 2009 08:49:35 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/03/t1259855865p38h02seubi8lz8.htm/, Retrieved Thu, 03 Dec 2009 16:57:47 +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/2009/Dec/03/t1259855865p38h02seubi8lz8.htm/},
    year = {2009},
}
@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 = {2009},
    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 «

8.1 7.7 7.5 7.6 7.8 7.8 7.8 7.5 7.5 7.1 7.5 7.5 7.6 7.7 7.7 7.9 8.1 8.2 8.2 8.2 7.9 7.3 6.9 6.6 6.7 6.9 7 7.1 7.2 7.1 6.9 7 6.8 6.4 6.7 6.6 6.4 6.3 6.2 6.5 6.8 6.8 6.4 6.1 5.8 6.1 7.2 7.3 6.9 6.1 5.8 6.2 7.1 7.7 7.9 7.7 7.4 7.5 8 8.1 8

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	0.848975	6.6307	0
2	0.60898	4.7563	6e-06
3	0.422227	3.2977	0.000815
4	0.375606	2.9336	0.002358
5	0.423364	3.3066	0.000793
6	0.445943	3.4829	0.000462
7	0.359206	2.8055	0.003366
8	0.215075	1.6798	0.049057
9	0.106131	0.8289	0.205194
10	0.108567	0.8479	0.199893
11	0.175852	1.3734	0.08732
12	0.230093	1.7971	0.038636
13	0.181496	1.4175	0.080708
14	0.085247	0.6658	0.254025
15	-0.014365	-0.1122	0.455518
16	-0.079779	-0.6231	0.267773
17	-0.116701	-0.9115	0.182819
18	-0.144341	-1.1273	0.132006
19	-0.177061	-1.3829	0.08587
20	-0.225148	-1.7585	0.041842
21	-0.27119	-2.1181	0.019126
22	-0.308821	-2.412	0.009445
23	-0.325246	-2.5403	0.00682
24	-0.318818	-2.49	0.007756
25	-0.306422	-2.3932	0.009897
26	-0.269955	-2.1084	0.019555
27	-0.241171	-1.8836	0.032194
28	-0.236938	-1.8505	0.03454
29	-0.275806	-2.1541	0.017595
30	-0.325721	-2.544	0.006755
31	-0.350458	-2.7372	0.004054
32	-0.356762	-2.7864	0.003547
33	-0.323198	-2.5243	0.007106
34	-0.259805	-2.0291	0.023407
35	-0.211302	-1.6503	0.052009
36	-0.180143	-1.407	0.082256
37	-0.15675	-1.2243	0.112782
38	-0.110503	-0.8631	0.195743
39	-0.048429	-0.3782	0.353283
40	0.012919	0.1009	0.459981
41	0.035896	0.2804	0.390077
42	0.02156	0.1684	0.433419
43	-0.016848	-0.1316	0.447871
44	-0.053211	-0.4156	0.339584
45	-0.049176	-0.3841	0.351128
46	-0.009544	-0.0745	0.470411
47	0.008024	0.0627	0.475117
48	0.004306	0.0336	0.486641

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.848975	6.6307	0
2	-0.400289	-3.1264	0.001355
3	0.162475	1.269	0.104636
4	0.305093	2.3829	0.010155
5	0.097311	0.76	0.225085
6	-0.124597	-0.9731	0.167166
7	-0.196909	-1.5379	0.064621
8	0.027325	0.2134	0.415857
9	0.052896	0.4131	0.34048
10	0.12728	0.9941	0.162054
11	-0.031845	-0.2487	0.402206
12	0.016527	0.1291	0.448859
13	-0.153161	-1.1962	0.118118
14	0.094531	0.7383	0.231578
15	-0.136885	-1.0691	0.144617
16	-0.186517	-1.4567	0.075158
17	-0.117334	-0.9164	0.181532
18	0.005965	0.0466	0.481498
19	0.062534	0.4884	0.313508
20	-0.125229	-0.9781	0.165952
21	-0.033388	-0.2608	0.397575
22	-0.103056	-0.8049	0.212004
23	0.051452	0.4019	0.344599
24	-0.027372	-0.2138	0.415716
25	-0.047345	-0.3698	0.356415
26	0.089143	0.6962	0.244464
27	-0.012665	-0.0989	0.460764
28	0.00749	0.0585	0.476771
29	-0.179508	-1.402	0.082992
30	-0.029169	-0.2278	0.410276
31	-0.041001	-0.3202	0.374945
32	-0.10649	-0.8317	0.204407
33	0.109074	0.8519	0.198802
34	0.14667	1.1455	0.128233
35	-0.012911	-0.1008	0.460005
36	0.012361	0.0965	0.461703
37	0.063884	0.4989	0.309806
38	0.013296	0.1038	0.458817
39	-0.047177	-0.3685	0.3569
40	-0.045704	-0.357	0.361178
41	-0.041856	-0.3269	0.372428
42	-0.008839	-0.069	0.472594
43	-0.052927	-0.4134	0.340392
44	-0.026061	-0.2035	0.419694
45	-0.005799	-0.0453	0.48201
46	-0.011821	-0.0923	0.463372
47	-0.163869	-1.2799	0.10272
48	0.041108	0.3211	0.374631

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259855865p38h02seubi8lz8/1atsc1259855374.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259855865p38h02seubi8lz8/1atsc1259855374.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259855865p38h02seubi8lz8/24vxe1259855374.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259855865p38h02seubi8lz8/24vxe1259855374.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = MA ; 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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