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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: Thu, 26 Nov 2009 16:50:07 -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/27/t1259279659uy2eo9tnofcref4.htm/, Retrieved Fri, 27 Nov 2009 00:54:21 +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/27/t1259279659uy2eo9tnofcref4.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 «

6802.96 7132.68 7073.29 7264.5 7105.33 7218.71 7225.72 7354.25 7745.46 8070.26 8366.33 8667.51 8854.34 9218.1 9332.9 9358.31 9248.66 9401.2 9652.04 9957.38 10110.63 10169.26 10343.78 10750.21 11337.5 11786.96 12083.04 12007.74 11745.93 11051.51 11445.9 11924.88 12247.63 12690.91 12910.7 13202.12 13654.67 13862.82 13523.93 14211.17 14510.35 14289.23 14111.82 13086.59 13351.54 13747.69 12855.61 12926.93 12121.95 11731.65 11639.51 12163.78 12029.53 11234.18 9852.13 9709.04 9332.75 7108.6 6691.49 6143.05

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	0.926813	7.1791	0
2	0.849126	6.5773	0
3	0.766604	5.9381	0
4	0.703778	5.4514	0
5	0.636095	4.9272	3e-06
6	0.559575	4.3344	2.8e-05
7	0.495204	3.8358	0.000151
8	0.439195	3.402	0.000598
9	0.382363	2.9618	0.002189
10	0.316609	2.4524	0.008557
11	0.252519	1.956	0.027562
12	0.184367	1.4281	0.079224
13	0.126538	0.9802	0.165471
14	0.070118	0.5431	0.294525
15	0.018042	0.1398	0.444663
16	-0.040815	-0.3162	0.376491
17	-0.107632	-0.8337	0.203875
18	-0.156577	-1.2128	0.114972
19	-0.192933	-1.4945	0.070149
20	-0.222739	-1.7253	0.044808
21	-0.251999	-1.952	0.027806
22	-0.285936	-2.2149	0.015289
23	-0.307662	-2.3831	0.010174
24	-0.321315	-2.4889	0.007803
25	-0.328783	-2.5467	0.006728
26	-0.335169	-2.5962	0.005918
27	-0.338742	-2.6239	0.005504
28	-0.347341	-2.6905	0.004614
29	-0.364336	-2.8221	0.003231
30	-0.393428	-3.0475	0.001714
31	-0.420706	-3.2588	0.000922
32	-0.429498	-3.3269	0.000752
33	-0.426814	-3.3061	8e-04
34	-0.410992	-3.1835	0.001153
35	-0.390386	-3.0239	0.001834
36	-0.365195	-2.8288	0.003172

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.926813	7.1791	0
2	-0.069897	-0.5414	0.295111
3	-0.07556	-0.5853	0.280276
4	0.096226	0.7454	0.22948
5	-0.08019	-0.6212	0.268427
6	-0.113315	-0.8777	0.191794
7	0.067186	0.5204	0.302343
8	0.005927	0.0459	0.481767
9	-0.078257	-0.6062	0.273343
10	-0.079154	-0.6131	0.271056
11	-0.017047	-0.132	0.447694
12	-0.101229	-0.7841	0.218028
13	0.008925	0.0691	0.472557
14	-0.019891	-0.1541	0.439033
15	-0.037532	-0.2907	0.386133
16	-0.102188	-0.7915	0.215872
17	-0.115034	-0.891	0.188231
18	0.067558	0.5233	0.301346
19	0.022131	0.1714	0.432233
20	-0.035298	-0.2734	0.392736
21	-0.004053	-0.0314	0.487531
22	-0.084416	-0.6539	0.257843
23	0.002763	0.0214	0.491497
24	0.015694	0.1216	0.451825
25	0.014869	0.1152	0.454346
26	-0.013338	-0.1033	0.459029
27	-0.01781	-0.138	0.44537
28	-0.095908	-0.7429	0.23022
29	-0.128182	-0.9929	0.162374
30	-0.120584	-0.934	0.177013
31	-0.035737	-0.2768	0.391437
32	0.0792	0.6135	0.270938
33	0.015145	0.1173	0.453503
34	0.0107	0.0829	0.46711
35	0.016636	0.1289	0.448948
36	-0.01445	-0.1119	0.455627

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259279659uy2eo9tnofcref4/16k3j1259279406.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259279659uy2eo9tnofcref4/16k3j1259279406.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259279659uy2eo9tnofcref4/2zlum1259279406.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259279659uy2eo9tnofcref4/2zlum1259279406.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; 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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