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ACF-D=1

*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, 21 Dec 2010 20:02:05 +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/Dec/21/t12929616225wbcm3gizso9xjm.htm/, Retrieved Tue, 21 Dec 2010 21:00:22 +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/Dec/21/t12929616225wbcm3gizso9xjm.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

8.1 9.9 11.5 23.4 25.4 27.9 26.1 18.8 14.1 11.5 15.8 12.4 4.5 -2.2 -4.2 -9.4 -14.5 -17.9 -15.1 -15.2 -15.7 -18 -18.1 -13.5 -9.9 -4.8 -1.7 -0.1 2.2 10.2 7.6 10.8 3.8 11 10.8 20.1 14.9 13 10.9 9.6 4 -1.1 -7.7 -8.9 -8 -7.1 -5.3 -2.5 -2.4 -2.9 -4.8 -7.2 1.7 2.2 13.4 12.3 13.7 4.4 -2.5

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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.938672	6.4352	0
2	0.833382	5.7134	0
3	0.675019	4.6277	1.5e-05
4	0.529748	3.6318	0.000347
5	0.365513	2.5058	0.007869
6	0.204745	1.4037	0.083497
7	0.035805	0.2455	0.403583
8	-0.112122	-0.7687	0.222968
9	-0.249678	-1.7117	0.046772
10	-0.37147	-2.5467	0.007105
11	-0.481344	-3.2999	0.000925
12	-0.561506	-3.8495	0.000178
13	-0.591219	-4.0532	9.4e-05
14	-0.580376	-3.9789	0.000119
15	-0.53014	-3.6345	0.000344
16	-0.474198	-3.2509	0.001065
17	-0.392332	-2.6897	0.004934
18	-0.307174	-2.1059	0.020292
19	-0.198649	-1.3619	0.089866
20	-0.106482	-0.73	0.234505
21	-0.012717	-0.0872	0.465447
22	0.058167	0.3988	0.345932
23	0.137801	0.9447	0.174818
24	0.199609	1.3684	0.088839
25	0.252701	1.7324	0.044878
26	0.273369	1.8741	0.033568
27	0.271444	1.8609	0.034508
28	0.246989	1.6933	0.048512
29	0.205044	1.4057	0.083193
30	0.15333	1.0512	0.149276
31	0.094704	0.6493	0.259667
32	0.040198	0.2756	0.392039
33	-0.009292	-0.0637	0.474738
34	-0.04904	-0.3362	0.369109
35	-0.086007	-0.5896	0.27913
36	-0.119454	-0.8189	0.208479
37	-0.150153	-1.0294	0.154281
38	-0.162924	-1.117	0.134846
39	-0.158981	-1.0899	0.140653
40	-0.128795	-0.883	0.190872
41	-0.092316	-0.6329	0.264937
42	-0.052911	-0.3627	0.359212
43	-0.025824	-0.177	0.430119
44	-0.008906	-0.0611	0.475788
45	-0.002292	-0.0157	0.493764
46	6.5e-05	4e-04	0.499824
47	NA	NA	NA
48	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.938672	6.4352	0
2	-0.401385	-2.7518	0.004197
3	-0.44592	-3.0571	0.00184
4	0.336043	2.3038	0.012852
5	-0.34496	-2.3649	0.011107
6	-0.280648	-1.924	0.030209
7	0.142683	0.9782	0.166496
8	-0.028121	-0.1928	0.423978
9	-0.303194	-2.0786	0.02157
10	-0.153008	-1.049	0.149778
11	0.12401	0.8502	0.199771
12	0.005573	0.0382	0.484842
13	0.168711	1.1566	0.126635
14	-0.119576	-0.8198	0.208242
15	0.022225	0.1524	0.439776
16	-0.073243	-0.5021	0.308961
17	0.10636	0.7292	0.234759
18	-0.075434	-0.5172	0.303738
19	-0.019714	-0.1352	0.446534
20	-0.077919	-0.5342	0.297866
21	0.01084	0.0743	0.470538
22	-0.046445	-0.3184	0.375792
23	0.052872	0.3625	0.359312
24	0.013655	0.0936	0.462906
25	-0.092949	-0.6372	0.263535
26	0.049542	0.3396	0.367818
27	-0.153268	-1.0508	0.149372
28	-0.050771	-0.3481	0.364671
29	-0.022685	-0.1555	0.43854
30	0.081277	0.5572	0.290014
31	0.044897	0.3078	0.379797
32	-0.145598	-0.9982	0.161655
33	0.08211	0.5629	0.288083
34	-0.009241	-0.0634	0.474878
35	0.027617	0.1893	0.425322
36	-0.172452	-1.1823	0.121522
37	0.125063	0.8574	0.19779
38	0.103353	0.7085	0.241052
39	-0.042605	-0.2921	0.385753
40	0.050199	0.3441	0.366135
41	-0.087588	-0.6005	0.275538
42	-0.121739	-0.8346	0.204082
43	-0.062716	-0.43	0.334595
44	-0.044568	-0.3055	0.380652
45	-0.075662	-0.5187	0.303197
46	0.095443	0.6543	0.258046
47	NA	NA	NA
48	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/21/t12929616225wbcm3gizso9xjm/11xxr1292961721.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t12929616225wbcm3gizso9xjm/11xxr1292961721.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t12929616225wbcm3gizso9xjm/21xxr1292961721.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t12929616225wbcm3gizso9xjm/21xxr1292961721.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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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