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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: Tue, 24 Nov 2009 07:35:03 -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/Nov/24/t1259073333zpkh82zhy9ir675.htm/, Retrieved Tue, 24 Nov 2009 15:35:36 +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/Nov/24/t1259073333zpkh82zhy9ir675.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 «

115.47 103.34 102.6 100.69 105.67 123.61 113.08 106.46 123.38 109.87 95.74 123.06 123.39 120.28 115.33 110.4 114.49 132.03 123.16 118.82 128.32 112.24 104.53 132.57 122.52 131.8 124.55 120.96 122.6 145.52 118.57 134.25 136.7 121.37 111.63 134.42 137.65 137.86 119.77 130.69 128.28 147.45 128.42 136.9 143.95 135.64 122.48 136.83 153.04 142.71 123.46 144.37 146.15 147.61 158.51 147.4 165.05 154.64 126.2 157.36 154.15 123.21 113.07 110.45 113.57 122.44 114.93 111.85 126.04 121.34

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	-0.606602	-4.0692	9.4e-05
2	0.102146	0.6852	0.248362
3	0.270546	1.8149	0.038105
4	-0.243376	-1.6326	0.054764
5	0.104881	0.7036	0.242665
6	0.13473	0.9038	0.185458
7	-0.257808	-1.7294	0.045293
8	0.190412	1.2773	0.10402
9	-0.094309	-0.6326	0.265085
10	0.018262	0.1225	0.451521
11	0.048345	0.3243	0.373604
12	-0.152868	-1.0255	0.155311
13	0.119528	0.8018	0.213437
14	-0.077746	-0.5215	0.302276
15	0.109982	0.7378	0.232239
16	-0.178959	-1.2005	0.118115
17	0.137114	0.9198	0.181293
18	-0.052235	-0.3504	0.363836
19	-0.059764	-0.4009	0.345193
20	0.143978	0.9658	0.169646
21	-0.089885	-0.603	0.27478
22	-0.170604	-1.1444	0.129245
23	0.387562	2.5998	0.006285
24	-0.353594	-2.372	0.011015
25	0.153481	1.0296	0.154355
26	0.040207	0.2697	0.394306
27	-0.104526	-0.7012	0.2434
28	0.057936	0.3886	0.349684
29	0.037208	0.2496	0.402017
30	-0.102485	-0.6875	0.247652
31	0.082507	0.5535	0.291339
32	-0.080274	-0.5385	0.296445
33	0.034496	0.2314	0.409024
34	0.03183	0.2135	0.415942
35	-0.128568	-0.8625	0.196504
36	0.119082	0.7988	0.214294
37	-0.095866	-0.6431	0.261715
38	0.051517	0.3456	0.365631
39	-0.03765	-0.2526	0.400879
40	0.016208	0.1087	0.45695
41	-0.016378	-0.1099	0.456502
42	0.010998	0.0738	0.470758
43	-0.002606	-0.0175	0.493064
44	0.003146	0.0211	0.491628
45	NA	NA	NA
46	NA	NA	NA
47	NA	NA	NA
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	-0.606602	-4.0692	9.4e-05
2	-0.420579	-2.8213	0.003546
3	0.19884	1.3339	0.094481
4	0.226572	1.5199	0.067767
5	0.117756	0.7899	0.216855
6	0.207405	1.3913	0.085486
7	-0.081436	-0.5463	0.293783
8	-0.153829	-1.0319	0.153813
9	-0.262946	-1.7639	0.042269
10	-0.044911	-0.3013	0.382299
11	0.154291	1.035	0.153097
12	-0.013539	-0.0908	0.464019
13	-0.040797	-0.2737	0.392795
14	-0.16316	-1.0945	0.139778
15	0.212944	1.4285	0.08003
16	-0.047115	-0.3161	0.376709
17	-0.008201	-0.055	0.478186
18	-0.036941	-0.2478	0.402705
19	-0.140932	-0.9454	0.174752
20	0.045254	0.3036	0.381426
21	0.101321	0.6797	0.250094
22	-0.181114	-1.2149	0.115361
23	0.079149	0.5309	0.299033
24	0.009048	0.0607	0.475934
25	0.070773	0.4748	0.318627
26	-0.052567	-0.3526	0.363006
27	0.155255	1.0415	0.151608
28	-0.048696	-0.3267	0.372718
29	-0.13528	-0.9075	0.184492
30	-0.143539	-0.9629	0.170374
31	-0.040729	-0.2732	0.392967
32	-0.014234	-0.0955	0.462177
33	-0.057204	-0.3837	0.351491
34	0.045864	0.3077	0.379878
35	-0.001982	-0.0133	0.494724
36	0.034004	0.2281	0.4103
37	-0.047612	-0.3194	0.375455
38	-0.101994	-0.6842	0.24868
39	0.039771	0.2668	0.395424
40	-0.079028	-0.5301	0.299311
41	0.02398	0.1609	0.436462
42	0.003401	0.0228	0.49095
43	-0.006851	-0.046	0.481772
44	-0.085507	-0.5736	0.284548
45	NA	NA	NA
46	NA	NA	NA
47	NA	NA	NA
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/2009/Nov/24/t1259073333zpkh82zhy9ir675/1b1yg1259073302.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259073333zpkh82zhy9ir675/1b1yg1259073302.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259073333zpkh82zhy9ir675/2dve81259073302.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259073333zpkh82zhy9ir675/2dve81259073302.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 2 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 2 ; 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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