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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 03:04:18 -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/t12590570981v8tjxgwpj70ae3.htm/, Retrieved Tue, 24 Nov 2009 11:05:00 +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/t12590570981v8tjxgwpj70ae3.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 «

95.1 97 112.7 102.9 97.4 111.4 87.4 96.8 114.1 110.3 103.9 101.6 94.6 95.9 104.7 102.8 98.1 113.9 80.9 95.7 113.2 105.9 108.8 102.3 99 100.7 115.5 100.7 109.9 114.6 85.4 100.5 114.8 116.5 112.9 102 106 105.3 118.8 106.1 109.3 117.2 92.5 104.2 112.5 122.4 113.3 100 110.7 112.8 109.8 117.3 109.1 115.9 96.0

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	-0.653552	-4.2355	6.1e-05
2	0.088874	0.576	0.283855
3	0.174268	1.1294	0.132572
4	-0.091083	-0.5903	0.27908
5	-0.130821	-0.8478	0.200672
6	0.246167	1.5953	0.059066
7	-0.137715	-0.8925	0.188606
8	-0.07929	-0.5139	0.305023
9	0.193181	1.252	0.108757
10	-0.134311	-0.8704	0.194505
11	0.033782	0.2189	0.413882
12	-0.017779	-0.1152	0.454409
13	0.058299	0.3778	0.353734
14	-0.112316	-0.7279	0.235359
15	0.116093	0.7524	0.228012
16	-0.085959	-0.5571	0.290216
17	0.033289	0.2157	0.415119
18	0.055447	0.3593	0.360572
19	-0.105337	-0.6827	0.249284
20	0.023704	0.1536	0.439323
21	0.128536	0.833	0.204777
22	-0.271415	-1.759	0.042933
23	0.332688	2.1561	0.018427
24	-0.254968	-1.6524	0.052957
25	0.055097	0.3571	0.361415
26	0.080321	0.5205	0.302711
27	-0.011949	-0.0774	0.46932
28	-0.124532	-0.8071	0.21209
29	0.144434	0.936	0.177302
30	-0.046754	-0.303	0.381693
31	-0.084624	-0.5484	0.293152
32	0.148079	0.9597	0.171359
33	-0.096991	-0.6286	0.266517
34	0.044306	0.2871	0.38771
35	-0.055485	-0.3596	0.36048
36	0.09872	0.6398	0.262896

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.653552	-4.2355	6.1e-05
2	-0.590459	-3.8266	0.000213
3	-0.319578	-2.0711	0.022265
4	-0.011697	-0.0758	0.469967
5	-0.174106	-1.1283	0.132791
6	-0.039225	-0.2542	0.400289
7	0.093041	0.603	0.274883
8	-0.049537	-0.321	0.374887
9	-0.000831	-0.0054	0.497863
10	-0.015944	-0.1033	0.459097
11	0.102249	0.6626	0.255589
12	-0.045232	-0.2931	0.385429
13	-0.035652	-0.2311	0.409197
14	-0.100498	-0.6513	0.259199
15	-0.06991	-0.4531	0.326415
16	-0.1373	-0.8898	0.18932
17	-0.134533	-0.8719	0.194117
18	0.087613	0.5678	0.286597
19	0.046323	0.3002	0.38275
20	-0.138889	-0.9001	0.186598
21	0.067006	0.4343	0.333164
22	-0.246091	-1.5949	0.059122
23	0.107836	0.6989	0.244246
24	-0.077149	-0.5	0.309848
25	-0.135752	-0.8798	0.191994
26	-0.118745	-0.7696	0.222936
27	-0.005399	-0.035	0.486127
28	0.033402	0.2165	0.414836
29	-0.070288	-0.4555	0.325542
30	-0.039344	-0.255	0.399991
31	-0.063185	-0.4095	0.342131
32	-0.076417	-0.4952	0.311507
33	-0.040053	-0.2596	0.398232
34	0.05596	0.3627	0.359339
35	0.048106	0.3118	0.378381
36	-0.069224	-0.4486	0.328006

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/24/t12590570981v8tjxgwpj70ae3/1gt921259057056.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t12590570981v8tjxgwpj70ae3/1gt921259057056.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t12590570981v8tjxgwpj70ae3/2l2vr1259057056.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t12590570981v8tjxgwpj70ae3/2l2vr1259057056.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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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