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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, 21 Dec 2010 20:16:07 +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/21/t12929626175ct92malxh0iyst.htm/, Retrieved Tue, 21 Dec 2010 21:16:59 +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/21/t12929626175ct92malxh0iyst.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 «

320 324 343 295 301 367 196 182 342 361 333 330 345 323 365 323 316 358 235 169 430 409 407 341 326 374 364 349 300 385 304 196 443 414 325 388 356 386 444 387 327 448 225 182 460 411 342 361 377 331 428 340 352 461 221 198 422 329 320 375 364 351 380 319 322 386 221 187 343 342 365 313 356 337 389 326 343 357 220 218 391 425 332 298 360 336 325 393 301 426 265 210 429 440 357 431 442 422 544 420 396 482 261 211 448 468 464 425

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	0.193311	2.0089	0.023519
2	-0.165442	-1.7193	0.04421
3	0.201636	2.0955	0.019234
4	-0.018549	-0.1928	0.423751
5	-0.024524	-0.2549	0.399659
6	0.154874	1.6095	0.055213
7	-0.046325	-0.4814	0.315595
8	0.047628	0.495	0.310815
9	0.166033	1.7255	0.043652
10	-0.239619	-2.4902	0.007145
11	0.09946	1.0336	0.151813
12	0.639853	6.6496	0
13	0.029042	0.3018	0.381688
14	-0.238687	-2.4805	0.007331
15	0.058966	0.6128	0.27065
16	-0.077482	-0.8052	0.211232
17	-0.07474	-0.7767	0.21951
18	0.00837	0.087	0.465421
19	-0.124159	-1.2903	0.099852
20	-0.070897	-0.7368	0.231427
21	0.01038	0.1079	0.45715
22	-0.276914	-2.8778	0.002414
23	0.001324	0.0138	0.494523
24	0.481694	5.0059	1e-06
25	0.013691	0.1423	0.443561
26	-0.249601	-2.5939	0.005402
27	-0.006998	-0.0727	0.471079
28	-0.074616	-0.7754	0.219889
29	-0.172128	-1.7888	0.038225
30	-0.045396	-0.4718	0.319023
31	-0.121286	-1.2604	0.105114
32	-0.134122	-1.3938	0.083114
33	-0.017343	-0.1802	0.428654
34	-0.242641	-2.5216	0.006571
35	-0.028389	-0.295	0.384271
36	0.41988	4.3635	1.5e-05
37	0.002401	0.025	0.490069
38	-0.255404	-2.6542	0.004575
39	0.024831	0.2581	0.398427
40	-0.048281	-0.5017	0.308433
41	-0.140105	-1.456	0.074145
42	0.012947	0.1346	0.446608
43	-0.065907	-0.6849	0.247431
44	-0.080848	-0.8402	0.201327
45	0.05315	0.5524	0.290923
46	-0.175662	-1.8255	0.035342
47	-0.006255	-0.065	0.474146
48	0.404923	4.2081	2.7e-05

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.193311	2.0089	0.023519
2	-0.210684	-2.1895	0.015357
3	0.305557	3.1754	0.000975
4	-0.221188	-2.2987	0.011725
5	0.196646	2.0436	0.021713
6	-0.023514	-0.2444	0.403706
7	-0.016754	-0.1741	0.43105
8	0.12833	1.3336	0.092562
9	0.019112	0.1986	0.421468
10	-0.261442	-2.717	0.003837
11	0.391937	4.0731	4.4e-05
12	0.432595	4.4957	9e-06
13	-0.198944	-2.0675	0.020539
14	-0.21588	-2.2435	0.013453
15	-0.065165	-0.6772	0.24986
16	0.049671	0.5162	0.303387
17	-0.085201	-0.8854	0.188944
18	-0.16891	-1.7554	0.041017
19	0.006812	0.0708	0.471847
20	-0.248549	-2.583	0.005566
21	0.029726	0.3089	0.378988
22	-0.026646	-0.2769	0.391188
23	0.055072	0.5723	0.284144
24	0.12718	1.3217	0.094531
25	0.030335	0.3153	0.376589
26	-0.009261	-0.0962	0.461754
27	-0.039986	-0.4155	0.339283
28	0.025866	0.2688	0.394296
29	-0.187104	-1.9444	0.027221
30	0.032903	0.3419	0.366532
31	-0.068277	-0.7096	0.239753
32	-0.107369	-1.1158	0.13349
33	-0.04112	-0.4273	0.334993
34	-0.026227	-0.2726	0.392857
35	0.056218	0.5842	0.28014
36	0.004247	0.0441	0.482437
37	-0.020293	-0.2109	0.416684
38	0.003335	0.0347	0.486207
39	0.028929	0.3006	0.382133
40	0.020923	0.2174	0.414137
41	0.027366	0.2844	0.388324
42	0.007989	0.083	0.466991
43	-0.007553	-0.0785	0.468789
44	0.033651	0.3497	0.363618
45	0.03087	0.3208	0.374487
46	0.001076	0.0112	0.495549
47	-0.089458	-0.9297	0.177308
48	0.01057	0.1098	0.456367

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/21/t12929626175ct92malxh0iyst/12dmy1292962565.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t12929626175ct92malxh0iyst/12dmy1292962565.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t12929626175ct92malxh0iyst/22dmy1292962565.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t12929626175ct92malxh0iyst/22dmy1292962565.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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