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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: Wed, 25 Nov 2009 10:25:52 -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/25/t1259170043nd4b2hzkyevxc28.htm/, Retrieved Wed, 25 Nov 2009 18:27:25 +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/25/t1259170043nd4b2hzkyevxc28.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:

ws8 ACF Y[t] (d=1,D=1,Lambda=1)

Dataseries X:

» Textbox « » Textfile « » CSV «

8.00 8.10 7.70 7.50 7.60 7.80 7.80 7.80 7.50 7.50 7.10 7.50 7.50 7.60 7.70 7.70 7.90 8.10 8.20 8.20 8.20 7.90 7.30 6.90 6.60 6.70 6.90 7.00 7.10 7.20 7.10 6.90 7.00 6.80 6.40 6.70 6.60 6.40 6.30 6.20 6.50 6.80 6.80 6.40 6.10 5.80 6.10 7.20 7.30 6.90 6.10 5.80 6.20 7.10 7.70 7.90 7.70 7.40 7.50 8.00

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	0.879174	6.0911	0
2	0.634572	4.3964	3e-05
3	0.395288	2.7386	0.004316
4	0.254834	1.7655	0.041917
5	0.211283	1.4638	0.074882
6	0.212549	1.4726	0.073696
7	0.18997	1.3162	0.097187
8	0.132175	0.9157	0.182192
9	0.058723	0.4068	0.342965
10	-0.000261	-0.0018	0.499283
11	-0.046885	-0.3248	0.373361
12	-0.093554	-0.6482	0.259984
13	-0.127819	-0.8856	0.190135
14	-0.146113	-1.0123	0.158235
15	-0.154762	-1.0722	0.144491
16	-0.165429	-1.1461	0.128712
17	-0.166384	-1.1527	0.127362
18	-0.142328	-0.9861	0.16452
19	-0.108604	-0.7524	0.227733
20	-0.093453	-0.6475	0.260208
21	-0.128795	-0.8923	0.188337
22	-0.22405	-1.5523	0.063584
23	-0.337452	-2.3379	0.011803
24	-0.399935	-2.7708	0.003965
25	-0.383461	-2.6567	0.005341
26	-0.312748	-2.1668	0.017623
27	-0.248653	-1.7227	0.045689
28	-0.218316	-1.5125	0.068477
29	-0.207113	-1.4349	0.078897
30	-0.201025	-1.3927	0.085058
31	-0.169073	-1.1714	0.123616
32	-0.118705	-0.8224	0.207454
33	-0.062618	-0.4338	0.333178
34	-0.009536	-0.0661	0.473799
35	0.054716	0.3791	0.353148
36	0.119148	0.8255	0.206591

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.879174	6.0911	0
2	-0.609431	-4.2223	5.4e-05
3	0.232495	1.6108	0.056893
4	0.226563	1.5697	0.06153
5	-0.062512	-0.4331	0.333443
6	-0.034229	-0.2371	0.406775
7	-0.125694	-0.8708	0.194091
8	0.069306	0.4802	0.316645
9	-0.019365	-0.1342	0.446916
10	-0.03919	-0.2715	0.393579
11	-0.132216	-0.916	0.182119
12	-0.070204	-0.4864	0.314453
13	0.149476	1.0356	0.152789
14	-0.090366	-0.6261	0.267115
15	-0.098465	-0.6822	0.2492
16	-0.044069	-0.3053	0.380722
17	0.149949	1.0389	0.152033
18	0.106559	0.7383	0.231975
19	-0.211655	-1.4664	0.074532
20	-0.117454	-0.8137	0.209905
21	-0.141089	-0.9775	0.166613
22	-0.099562	-0.6898	0.246825
23	-0.010817	-0.0749	0.470286
24	-0.006439	-0.0446	0.482302
25	-0.046822	-0.3244	0.373526
26	-0.022982	-0.1592	0.437081
27	-0.049797	-0.345	0.365799
28	0.034024	0.2357	0.407324
29	0.065354	0.4528	0.326371
30	-0.12977	-0.8991	0.186552
31	0.141951	0.9835	0.165155
32	-0.062815	-0.4352	0.332686
33	0.049603	0.3437	0.366302
34	0.047251	0.3274	0.372408
35	0.076531	0.5302	0.299201
36	-0.039415	-0.2731	0.392983

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/25/t1259170043nd4b2hzkyevxc28/1yppd1259169950.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/25/t1259170043nd4b2hzkyevxc28/1yppd1259169950.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/25/t1259170043nd4b2hzkyevxc28/2apgq1259169950.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/25/t1259170043nd4b2hzkyevxc28/2apgq1259169950.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 0 ; 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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