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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, 10 Dec 2009 10:50:50 -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/Dec/10/t1260467557hn2qy9yizswrbf7.htm/, Retrieved Thu, 10 Dec 2009 18:52:40 +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/Dec/10/t1260467557hn2qy9yizswrbf7.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 «

99.026 101.851 99.958 97.875 97.927 95.149 94.551 93.999 93.297 89.901 89.742 87.096 86.863 86.718 80.020 63.483 51.289 44.071 43.654 66.115 84.518 83.395 78.307 80.049 78.346 78.317 75.918 73.739 74.530 74.179 76.974 75.408 73.336 69.210 67.286 64.606 64.159 64.423 66.411 64.270 56.521 50.599 54.751 62.227 63.932 65.391 75.744 74.590 76.035 74.427 73.354 73.081 75.309 75.463 75.910 76.151 76.882 78.632 80.137 82.490 79.896 81.303 79.344 81.355 82.328 79.669 77.249 75.101 72.520 72.438 72.653 71.429 69.189 66.451 63.354 61.379 61.880 62.274 62.429 63.905 63.917 64.295 61.930 60.440 59.353 58.695 60.569 60.386 60.938 61.795 63.304 64.270 63.492 61.333 59.341 58.412 58.725 59.277 58.562 57.858 58.790 58.243 57.044 57.339 59.429 60.575 61.950 61.712

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	0 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.915362	9.5127	0
2	0.768957	7.9912	0
3	0.627354	6.5197	0
4	0.515238	5.3545	0
5	0.433857	4.5088	8e-06
6	0.381472	3.9644	6.6e-05
7	0.331375	3.4438	0.000409
8	0.277566	2.8845	0.002366
9	0.22364	2.3241	0.010995
10	0.170838	1.7754	0.039325
11	0.115139	1.1966	0.117049
12	0.06113	0.6353	0.263294
13	0.008551	0.0889	0.464678
14	-0.038277	-0.3978	0.345785
15	-0.05804	-0.6032	0.27383
16	-0.040689	-0.4229	0.336622
17	0.00228	0.0237	0.490571
18	0.056753	0.5898	0.278282
19	0.097531	1.0136	0.156527
20	0.092233	0.9585	0.169972
21	0.064827	0.6737	0.25097
22	0.060359	0.6273	0.265904
23	0.070957	0.7374	0.231238
24	0.064645	0.6718	0.251571
25	0.044481	0.4623	0.322414
26	0.010627	0.1104	0.456132
27	-0.033702	-0.3502	0.363421
28	-0.082152	-0.8537	0.197568
29	-0.12089	-1.2563	0.105854
30	-0.149782	-1.5566	0.061248
31	-0.168572	-1.7519	0.041319
32	-0.17264	-1.7941	0.037795
33	-0.172476	-1.7924	0.037932
34	-0.172621	-1.7939	0.037811
35	-0.173046	-1.7983	0.037458
36	-0.168986	-1.7562	0.040948

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.915362	9.5127	0
2	-0.425203	-4.4188	1.2e-05
3	0.100938	1.049	0.148265
4	0.043404	0.4511	0.326422
5	0.027897	0.2899	0.386217
6	0.063363	0.6585	0.255812
7	-0.112781	-1.172	0.121878
8	0.003628	0.0377	0.484996
9	-0.009326	-0.0969	0.461486
10	-0.038415	-0.3992	0.34526
11	-0.061296	-0.637	0.262733
12	-0.027823	-0.2891	0.386511
13	-0.050927	-0.5292	0.298859
14	-0.009175	-0.0953	0.462108
15	0.124811	1.2971	0.098685
16	0.101813	1.0581	0.146191
17	0.0618	0.6422	0.261037
18	0.06786	0.7052	0.241097
19	-0.054585	-0.5673	0.285857
20	-0.180906	-1.88	0.031399
21	0.080883	0.8406	0.201226
22	0.167985	1.7458	0.041849
23	-0.088938	-0.9243	0.178702
24	-0.190963	-1.9845	0.024866
25	-0.014624	-0.152	0.439745
26	-0.053372	-0.5547	0.290136
27	-0.043087	-0.4478	0.327606
28	-0.092933	-0.9658	0.168155
29	0.009501	0.0987	0.460763
30	0.034105	0.3544	0.361852
31	0.028398	0.2951	0.384236
32	0.086896	0.9031	0.184254
33	-0.024311	-0.2526	0.40051
34	-0.029374	-0.3053	0.380377
35	-0.058116	-0.604	0.273568
36	0.051327	0.5334	0.297425

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/10/t1260467557hn2qy9yizswrbf7/1kahi1260467448.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/10/t1260467557hn2qy9yizswrbf7/1kahi1260467448.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/10/t1260467557hn2qy9yizswrbf7/2bgif1260467448.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/10/t1260467557hn2qy9yizswrbf7/2bgif1260467448.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 36 ; 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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