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R Software Module: /rwasp_autocorrelation.wasp (opens new window with default values)

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Thu, 19 Aug 2010 09:40:21 +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/Aug/19/t1282210935c8ww5jcf3jq9nxe.htm/, Retrieved Thu, 19 Aug 2010 11:43:39 +0200

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/Aug/19/t1282210935c8ww5jcf3jq9nxe.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 «

239 238 237 235 255 254 239 229 230 230 231 233 239 236 231 235 253 257 236 226 226 221 217 219 225 226 225 229 242 252 233 232 225 218 209 211 220 225 215 222 238 246 226 230 222 214 208 203 208 212 199 200 223 225 203 207 195 198 193 189 184 188 180 186 215 212 191 190 180 190 189 181 174 179 165 185 211 209 183 178 170 182 195 188 175 176 162 193 211 207 179 176 167 175 190 173 159 159 147 181 196 199 171 170 156 164 178 155 138 142 113 148 156 158 141 139 119 120 125 102

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.004376	0.0477	0.481005
2	-0.240057	-2.6187	0.004987
3	-0.231426	-2.5246	0.00645
4	-0.134558	-1.4678	0.072392
5	0.000474	0.0052	0.497939
6	0.327098	3.5682	0.00026
7	-0.02967	-0.3237	0.373382
8	-0.135793	-1.4813	0.070582
9	-0.201318	-2.1961	0.015011
10	-0.280568	-3.0606	0.001365
11	0.074034	0.8076	0.210462
12	0.813905	8.8787	0
13	0.000307	0.0033	0.498669
14	-0.199889	-2.1805	0.015593
15	-0.177401	-1.9352	0.027668
16	-0.099122	-1.0813	0.140876
17	0.019707	0.215	0.415075
18	0.250855	2.7365	0.003581
19	-0.089815	-0.9798	0.164594
20	-0.094447	-1.0303	0.152481
21	-0.159261	-1.7373	0.042458
22	-0.252971	-2.7596	0.003352
23	0.10294	1.1229	0.13186
24	0.613536	6.6929	0
25	-0.027791	-0.3032	0.381145
26	-0.162328	-1.7708	0.039578
27	-0.105074	-1.1462	0.127002
28	-0.048524	-0.5293	0.29878
29	0.020375	0.2223	0.412244
30	0.184992	2.018	0.022919
31	-0.157484	-1.7179	0.044204
32	-0.04163	-0.4541	0.325281
33	-0.111007	-1.2109	0.114159
34	-0.200879	-2.1913	0.015188
35	0.123224	1.3442	0.090719
36	0.437462	4.7721	3e-06
37	-0.047986	-0.5235	0.300811
38	-0.138418	-1.51	0.066852
39	-0.032443	-0.3539	0.362017
40	-0.021887	-0.2388	0.405852
41	0.032625	0.3559	0.361272
42	0.118346	1.291	0.099603
43	-0.202301	-2.2068	0.014622
44	-0.006591	-0.0719	0.471402
45	-0.077869	-0.8494	0.198669
46	-0.125687	-1.3711	0.086464
47	0.126453	1.3794	0.085174
48	0.313779	3.4229	0.000425

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.004376	0.0477	0.481005
2	-0.240081	-2.619	0.004983
3	-0.243089	-2.6518	0.004549
4	-0.229018	-2.4983	0.006922
5	-0.169389	-1.8478	0.033556
6	0.187057	2.0406	0.021754
7	-0.130265	-1.421	0.078963
8	-0.085548	-0.9332	0.176297
9	-0.203357	-2.2184	0.014214
10	-0.440157	-4.8015	2e-06
11	-0.258698	-2.8221	0.002797
12	0.67996	7.4175	0
13	0.055516	0.6056	0.272966
14	0.019975	0.2179	0.413941
15	0.187686	2.0474	0.02141
16	0.186391	2.0333	0.022124
17	0.034646	0.3779	0.353075
18	-0.1428	-1.5578	0.060972
19	-0.149011	-1.6255	0.053349
20	0.01619	0.1766	0.430056
21	-0.003821	-0.0417	0.483411
22	0.02908	0.3172	0.375815
23	-4.3e-05	-5e-04	0.499813
24	-0.096657	-1.0544	0.146918
25	-0.05035	-0.5493	0.29193
26	-0.051884	-0.566	0.286234
27	-0.031126	-0.3395	0.3674
28	-0.018998	-0.2072	0.418086
29	-0.10291	-1.1226	0.131931
30	0.04554	0.4968	0.31013
31	-0.067476	-0.7361	0.231567
32	0.002512	0.0274	0.489094
33	0.027543	0.3005	0.382176
34	-0.002783	-0.0304	0.487915
35	0.071852	0.7838	0.217354
36	-0.031594	-0.3446	0.365485
37	0.042324	0.4617	0.322569
38	-0.008392	-0.0915	0.463605
39	-0.007135	-0.0778	0.469047
40	-0.02952	-0.322	0.374
41	-0.04508	-0.4918	0.311895
42	0.003614	0.0394	0.48431
43	-0.061504	-0.6709	0.251782
44	-0.050852	-0.5547	0.290061
45	-0.043421	-0.4737	0.318301
46	0.039936	0.4356	0.331941
47	0.013674	0.1492	0.440836
48	-0.004886	-0.0533	0.47879

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282210935c8ww5jcf3jq9nxe/1jbrr1282210817.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282210935c8ww5jcf3jq9nxe/1jbrr1282210817.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282210935c8ww5jcf3jq9nxe/2jbrr1282210817.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282210935c8ww5jcf3jq9nxe/2jbrr1282210817.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 1 ; 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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