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R Software Module: /rwasp_autocorrelation.wasp (opens new window with default values)

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Tue, 16 Nov 2010 12:22:30 +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/Nov/16/t12899102343v96lrip4s0q697.htm/, Retrieved Tue, 16 Nov 2010 13:23:57 +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/Nov/16/t12899102343v96lrip4s0q697.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:

KDGP2W12

Dataseries X:

» Textbox « » Textfile « » CSV «

98.1 98.0 98.3 98.5 98.7 99.3 99.5 99.8 100.3 99.3 99.6 99.3 99.4 99.7 100.0 99.3 100.3 100.8 101.4 101.1 100.6 99.5 99.1 98.8 99.1 98.8 98.5 99.0 99.0 100.6 101.0 101.8 101.8 101.8 101.8 102.4 103.0 103.3 103.6 104.1 104.5 105.6 105.9 106.0 106.3 107.3 107.1 107.3 107.7 108.0 108.9 108.5 109.0 108.9 109.0 108.9 110.3 109.4 108.6 108.0 108.4 108.0 108.0 107.6 107.5 107.9 108.0 107.5 106.8 106.7 107.2 107.8 106.6 106.3 105.7 105.9 106.5 107.2 108.3

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
R Framework error message	Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.967796	8.602	0
2	0.935734	8.317	0
3	0.903618	8.0315	0
4	0.87634	7.7891	0
5	0.848343	7.5402	0
6	0.819601	7.2848	0
7	0.786534	6.9909	0
8	0.751022	6.6752	0
9	0.720377	6.4029	0
10	0.686705	6.1036	0
11	0.652592	5.8004	0
12	0.609746	5.4195	0
13	0.5637	5.0103	2e-06
14	0.517509	4.5997	8e-06
15	0.473605	4.2095	3.4e-05
16	0.423379	3.7631	0.00016
17	0.378386	3.3632	0.000595
18	0.336582	2.9916	0.00185
19	0.299643	2.6633	0.004687
20	0.263671	2.3436	0.010808
21	0.226476	2.013	0.023763
22	0.178614	1.5876	0.058191
23	0.127121	1.1299	0.130973
24	0.078815	0.7005	0.242831
25	0.032331	0.2874	0.387292
26	-0.01762	-0.1566	0.437975
27	-0.069542	-0.6181	0.269143
28	-0.117297	-1.0426	0.150165
29	-0.165461	-1.4707	0.072679
30	-0.202663	-1.8013	0.037735
31	-0.235343	-2.0918	0.019836
32	-0.263099	-2.3385	0.010946
33	-0.290146	-2.5789	0.005884
34	-0.318514	-2.831	0.002941
35	-0.344224	-3.0595	0.001514
36	-0.366144	-3.2544	0.000837
37	-0.387471	-3.4439	0.00046
38	-0.408104	-3.6273	0.000253
39	-0.42535	-3.7806	0.000151
40	-0.439015	-3.902	1e-04
41	-0.45159	-4.0138	6.7e-05
42	-0.456186	-4.0547	5.8e-05
43	-0.461452	-4.1015	4.9e-05
44	-0.46298	-4.1151	4.7e-05
45	-0.460957	-4.0971	5e-05
46	-0.452201	-4.0193	6.6e-05
47	-0.44677	-3.971	7.8e-05
48	-0.442081	-3.9293	9.1e-05

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.967796	8.602	0
2	-0.014125	-0.1255	0.450206
3	-0.017421	-0.1548	0.438672
4	0.059523	0.5291	0.299126
5	-0.025788	-0.2292	0.409649
6	-0.027256	-0.2423	0.404603
7	-0.078771	-0.7001	0.24295
8	-0.059265	-0.5268	0.299918
9	0.055928	0.4971	0.310251
10	-0.075321	-0.6695	0.252574
11	-0.031873	-0.2833	0.388845
12	-0.148406	-1.3191	0.09548
13	-0.085319	-0.7583	0.225253
14	-0.030903	-0.2747	0.392143
15	-0.022642	-0.2012	0.420511
16	-0.142112	-1.2631	0.105131
17	0.058061	0.5161	0.303628
18	0.031341	0.2786	0.390653
19	0.054357	0.4831	0.315169
20	-0.010914	-0.097	0.461483
21	-0.037469	-0.333	0.369998
22	-0.182404	-1.6212	0.054476
23	-0.087901	-0.7813	0.218485
24	-0.019421	-0.1726	0.431696
25	-0.025669	-0.2281	0.41006
26	-0.129593	-1.1518	0.126429
27	-0.054427	-0.4838	0.314947
28	0.019874	0.1766	0.430119
29	-0.079347	-0.7053	0.241364
30	0.075075	0.6673	0.253269
31	0.051352	0.4564	0.324668
32	0.049971	0.4442	0.329072
33	0.057456	0.5107	0.305499
34	-0.030007	-0.2667	0.395195
35	0.028331	0.2518	0.40092
36	0.02815	0.2502	0.401541
37	-0.00946	-0.0841	0.466604
38	-0.012753	-0.1134	0.455018
39	-0.041661	-0.3703	0.356078
40	-0.008325	-0.074	0.470602
41	-0.047627	-0.4233	0.336607
42	0.060242	0.5354	0.296925
43	-0.05068	-0.4505	0.32681
44	0.051143	0.4546	0.325332
45	0.018722	0.1664	0.434133
46	0.112108	0.9964	0.16104
47	-0.035823	-0.3184	0.375512
48	0.012169	0.1082	0.457071

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/16/t12899102343v96lrip4s0q697/1cmtt1289910148.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/16/t12899102343v96lrip4s0q697/1cmtt1289910148.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/16/t12899102343v96lrip4s0q697/2cmtt1289910148.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/16/t12899102343v96lrip4s0q697/2cmtt1289910148.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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