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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: Tue, 17 Aug 2010 10:49:33 +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/17/t12820423825id32sop13khdup.htm/, Retrieved Tue, 17 Aug 2010 12:53:05 +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/17/t12820423825id32sop13khdup.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:

DeGroodtOlivierStap20

Dataseries X:

» Textbox « » Textfile « » CSV «

356 355 354 352 372 371 356 346 347 347 348 350 353 351 348 351 370 370 351 335 330 328 332 334 343 334 336 343 365 364 351 326 320 312 315 316 319 311 315 322 336 339 317 295 291 283 285 289 296 283 285 289 306 306 283 258 255 248 244 249 258 252 246 249 267 284 261 235 229 218 218 229 237 231 229 233 245 256 224 194 192 178 170 187 192 182 178 186 204 224 194 173 178 168 152 163 172 170 156 155 178 194 164 135 139 135 109 121 131 135 119 121 151 169 135 105 112 105 82 81

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	0.961322	10.5308	0
2	0.915514	10.029	0
3	0.884678	9.6912	0
4	0.860316	9.4243	0
5	0.82901	9.0814	0
6	0.805622	8.8251	0
7	0.794633	8.7048	0
8	0.783347	8.5811	0
9	0.763678	8.3657	0
10	0.747811	8.1919	0
11	0.744234	8.1527	0
12	0.733731	8.0376	0
13	0.69788	7.6449	0
14	0.651964	7.1419	0
15	0.619479	6.7861	0
16	0.591867	6.4836	0
17	0.559951	6.134	0
18	0.53518	5.8626	0
19	0.520693	5.7039	0
20	0.506633	5.5499	0
21	0.487382	5.339	0
22	0.47243	5.1752	0
23	0.466939	5.1151	1e-06
24	0.456986	5.006	1e-06
25	0.424917	4.6547	4e-06
26	0.383726	4.2035	2.5e-05
27	0.350854	3.8434	9.8e-05
28	0.323081	3.5392	0.000286
29	0.291779	3.1963	0.00089
30	0.266236	2.9165	0.002113
31	0.249682	2.7351	0.003591
32	0.233341	2.5561	0.005916
33	0.213906	2.3432	0.010382
34	0.197437	2.1628	0.01627
35	0.187851	2.0578	0.020888
36	0.176124	1.9293	0.028024
37	0.14725	1.613	0.054681
38	0.108151	1.1847	0.119232
39	0.074461	0.8157	0.20815
40	0.045544	0.4989	0.309378
41	0.015428	0.169	0.433039
42	-0.007618	-0.0835	0.466814
43	-0.019821	-0.2171	0.414237
44	-0.031324	-0.3431	0.366049
45	-0.04544	-0.4978	0.309777
46	-0.056144	-0.615	0.269852
47	-0.061033	-0.6686	0.252523
48	-0.068439	-0.7497	0.227449

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.961322	10.5308	0
2	-0.113712	-1.2457	0.107659
3	0.184431	2.0203	0.022787
4	0.030105	0.3298	0.371068
5	-0.083663	-0.9165	0.180625
6	0.137222	1.5032	0.067709
7	0.105233	1.1528	0.125649
8	-0.007991	-0.0875	0.465195
9	-0.043749	-0.4792	0.316319
10	0.064073	0.7019	0.242055
11	0.120038	1.315	0.095516
12	-0.092114	-1.0091	0.157489
13	-0.265393	-2.9072	0.002172
14	-0.141856	-1.554	0.061414
15	0.064735	0.7091	0.239806
16	-0.003006	-0.0329	0.486894
17	-0.024959	-0.2734	0.392501
18	0.039706	0.435	0.332186
19	-0.003783	-0.0414	0.483506
20	0.02679	0.2935	0.384835
21	0.031372	0.3437	0.365849
22	0.03488	0.3821	0.351533
23	0.041773	0.4576	0.324032
24	-0.020927	-0.2292	0.409535
25	-0.157121	-1.7212	0.043898
26	-0.079736	-0.8735	0.192078
27	-0.012361	-0.1354	0.446257
28	-0.010659	-0.1168	0.45362
29	-0.03607	-0.3951	0.346725
30	-0.004636	-0.0508	0.479789
31	-0.026379	-0.289	0.386552
32	0.000329	0.0036	0.498567
33	0.036403	0.3988	0.345383
34	-0.003952	-0.0433	0.482768
35	-0.000911	-0.01	0.496026
36	0.009061	0.0993	0.46055
37	-0.088042	-0.9644	0.16838
38	-0.067989	-0.7448	0.228931
39	-0.026055	-0.2854	0.387909
40	-0.027034	-0.2961	0.383815
41	-0.019846	-0.2174	0.414132
42	0.026813	0.2937	0.384739
43	0.018854	0.2065	0.41836
44	-0.007251	-0.0794	0.468411
45	0.030702	0.3363	0.368608
46	0.01571	0.1721	0.431828
47	0.004898	0.0537	0.478649
48	0.000303	0.0033	0.498677

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/17/t12820423825id32sop13khdup/1grxd1282042171.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/17/t12820423825id32sop13khdup/1grxd1282042171.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/17/t12820423825id32sop13khdup/2grxd1282042171.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/17/t12820423825id32sop13khdup/2grxd1282042171.ps (open in new window)

Parameters (Session):

par1 = grey ;

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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