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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, 14 Dec 2010 12:29:39 +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/14/t1292329950e4u1lyupx09qmac.htm/, Retrieved Tue, 14 Dec 2010 13:32:32 +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/14/t1292329950e4u1lyupx09qmac.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 «

19876 45335 48674 156392 100837 101605 532850 294189 80763 105995 25045 90474 48481 50730 68694 207716 99132 104012 422632 364974 82687 66834 28408 97073 40284 24421 116346 72120 108751 91738 402216 390070 106045 110070 70668 167841 28607 95371 30605 131063 81214 85451 455196 454570 63114 74287 42350 113375

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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.346923	2.4036	0.010074
2	-0.125871	-0.8721	0.193759
3	-0.124839	-0.8649	0.195696
4	-0.172303	-1.1938	0.119221
5	-0.248	-1.7182	0.046103
6	-0.35013	-2.4258	0.009542
7	-0.20723	-1.4357	0.078782
8	-0.082669	-0.5727	0.284744
9	-0.056331	-0.3903	0.34903
10	-0.074847	-0.5186	0.303227
11	0.236089	1.6357	0.054225
12	0.659897	4.5719	1.7e-05
13	0.305827	2.1188	0.019653
14	-0.090201	-0.6249	0.267489
15	-0.088017	-0.6098	0.272434
16	-0.082664	-0.5727	0.284756
17	-0.147864	-1.0244	0.155383
18	-0.262547	-1.819	0.037578
19	-0.163064	-1.1297	0.1321
20	-0.077419	-0.5364	0.297089
21	-0.098701	-0.6838	0.248688
22	-0.051802	-0.3589	0.360625
23	0.126178	0.8742	0.193184
24	0.459397	3.1828	0.00128
25	0.238893	1.6551	0.052215
26	-0.058977	-0.4086	0.342324
27	-0.018182	-0.126	0.450142
28	-0.034074	-0.2361	0.407191
29	-0.102411	-0.7095	0.240715
30	-0.162355	-1.1248	0.133128
31	-0.10308	-0.7142	0.239295
32	-0.0643	-0.4455	0.328988
33	-0.029867	-0.2069	0.418472
34	-0.022	-0.1524	0.439746
35	0.04503	0.312	0.378203
36	0.266528	1.8466	0.03549
37	0.152545	1.0569	0.147933
38	-0.04654	-0.3224	0.37426
39	-0.036889	-0.2556	0.399686
40	-0.056337	-0.3903	0.349014
41	-0.067461	-0.4674	0.321169
42	-0.067816	-0.4698	0.320297
43	-0.030722	-0.2128	0.416174
44	0.026927	0.1866	0.426397
45	0.021887	0.1516	0.440053
46	0.016004	0.1109	0.456087
47	0.003384	0.0234	0.490697
48	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.346923	2.4036	0.010074
2	-0.279916	-1.9393	0.029176
3	0.034737	0.2407	0.405421
4	-0.203623	-1.4107	0.082384
5	-0.162762	-1.1277	0.132536
6	-0.334597	-2.3182	0.012374
7	-0.105449	-0.7306	0.234296
8	-0.266452	-1.846	0.03553
9	-0.237644	-1.6464	0.053102
10	-0.455703	-3.1572	0.001376
11	-0.023181	-0.1606	0.43654
12	0.320979	2.2238	0.015451
13	-0.156176	-1.082	0.142325
14	-0.11688	-0.8098	0.211035
15	-0.012989	-0.09	0.464335
16	0.02482	0.172	0.432097
17	0.071576	0.4959	0.311117
18	0.010891	0.0755	0.470083
19	0.066799	0.4628	0.322801
20	-0.055866	-0.387	0.350215
21	-0.050724	-0.3514	0.363402
22	0.063285	0.4385	0.331513
23	-0.095019	-0.6583	0.256742
24	0.064935	0.4499	0.32741
25	-0.154621	-1.0712	0.144708
26	-0.009053	-0.0627	0.475125
27	-0.022078	-0.153	0.439535
28	-0.083062	-0.5755	0.283831
29	-0.088742	-0.6148	0.270788
30	0.020389	0.1413	0.444127
31	-0.050843	-0.3523	0.363096
32	-0.015583	-0.108	0.457237
33	0.147019	1.0186	0.156756
34	0.034627	0.2399	0.405713
35	0.018583	0.1287	0.449047
36	0.032613	0.226	0.4111
37	0.079092	0.548	0.293127
38	0.078408	0.5432	0.294743
39	-0.041282	-0.286	0.388051
40	-0.052861	-0.3662	0.357901
41	-0.018915	-0.131	0.448142
42	-0.021996	-0.1524	0.439757
43	-0.016964	-0.1175	0.453464
44	0.057123	0.3958	0.347017
45	-0.010874	-0.0753	0.47013
46	0.021585	0.1495	0.440875
47	0.025386	0.1759	0.430565
48	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/14/t1292329950e4u1lyupx09qmac/1ilzz1292329777.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/14/t1292329950e4u1lyupx09qmac/1ilzz1292329777.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/14/t1292329950e4u1lyupx09qmac/2ilzz1292329777.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/14/t1292329950e4u1lyupx09qmac/2ilzz1292329777.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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