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Tijdreeks A stap 20

*Unverified author*

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

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Mon, 02 Aug 2010 12:10:45 +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/02/t1280751111ba8xfjxohjntfi2.htm/, Retrieved Mon, 02 Aug 2010 14:11:52 +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/02/t1280751111ba8xfjxohjntfi2.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:

Bogaerts Yannik

Dataseries X:

» Textbox « » Textfile « » CSV «

442 441 440 438 458 457 442 432 433 433 434 436 439 439 441 436 460 453 435 421 412 408 402 409 410 410 416 410 437 431 411 398 394 395 389 404 397 401 402 383 406 400 377 372 362 365 361 372 355 365 367 341 370 366 333 320 298 306 293 313 293 304 304 286 320 313 283 272 251 262 247 268 251 257 261 242 274 272 243 234 217 231 209 226 208 214 222 194 230 226 197 188 175 190 165 176 159 169 170 141 170 164 132 123 113 125 101 99 87 90 89 66 102 97 65 54 33 49 30 34

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	0.967619	10.5997	0
2	0.939307	10.2896	0
3	0.913137	10.0029	0
4	0.883515	9.6784	0
5	0.857515	9.3936	0
6	0.828883	9.08	0
7	0.81004	8.8735	0
8	0.788732	8.6401	0
9	0.764192	8.3713	0
10	0.741756	8.1255	0
11	0.718653	7.8724	0
12	0.699305	7.6605	0
13	0.666803	7.3045	0
14	0.638773	6.9974	0
15	0.613482	6.7204	0
16	0.585413	6.4129	0
17	0.559231	6.1261	0
18	0.53069	5.8134	0
19	0.511731	5.6057	0
20	0.491403	5.3831	0
21	0.469651	5.1448	1e-06
22	0.451615	4.9472	1e-06
23	0.432866	4.7418	3e-06
24	0.416244	4.5597	6e-06
25	0.389345	4.2651	2e-05
26	0.364348	3.9912	5.7e-05
27	0.342277	3.7495	0.000137
28	0.317307	3.4759	0.000355
29	0.294326	3.2242	0.000814
30	0.269219	2.9491	0.001916
31	0.253	2.7715	0.003235
32	0.235543	2.5802	0.005539
33	0.215344	2.359	0.00997
34	0.198253	2.1718	0.015921
35	0.179505	1.9664	0.025782
36	0.162075	1.7754	0.03918
37	0.137242	1.5034	0.06768
38	0.112065	1.2276	0.110998
39	0.090118	0.9872	0.162768
40	0.066582	0.7294	0.233599
41	0.045449	0.4979	0.309743
42	0.022824	0.25	0.401497
43	0.008577	0.094	0.46265
44	-0.007068	-0.0774	0.469205
45	-0.02467	-0.2702	0.393719
46	-0.040495	-0.4436	0.329066
47	-0.057184	-0.6264	0.266115
48	-0.073089	-0.8007	0.212457
49	-0.093784	-1.0273	0.153161
50	-0.116797	-1.2794	0.101604
51	-0.137389	-1.505	0.067473
52	-0.158548	-1.7368	0.042493
53	-0.177579	-1.9453	0.02704
54	-0.197479	-2.1633	0.016251
55	-0.208523	-2.2843	0.012057
56	-0.219073	-2.3998	0.00897
57	-0.231452	-2.5354	0.006258
58	-0.24234	-2.6547	0.004507
59	-0.252426	-2.7652	0.003294
60	-0.264005	-2.892	0.002273

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.967619	10.5997	0
2	0.04741	0.5194	0.302235
3	0.022983	0.2518	0.400824
4	-0.063614	-0.6969	0.243619
5	0.036253	0.3971	0.345989
6	-0.052591	-0.5761	0.282813
7	0.141224	1.547	0.062245
8	-0.04201	-0.4602	0.323102
9	-0.048792	-0.5345	0.296997
10	-0.008235	-0.0902	0.464137
11	-0.003111	-0.0341	0.486435
12	0.039082	0.4281	0.334666
13	-0.201466	-2.207	0.01461
14	0.036976	0.405	0.343082
15	-0.002137	-0.0234	0.490681
16	-0.0153	-0.1676	0.43359
17	-0.019391	-0.2124	0.41607
18	-0.029162	-0.3195	0.374968
19	0.087975	0.9637	0.168563
20	-0.012929	-0.1416	0.443805
21	0.003753	0.0411	0.483637
22	0.003165	0.0347	0.4862
23	0.004388	0.0481	0.48087
24	-0.00389	-0.0426	0.483039
25	-0.116375	-1.2748	0.102417
26	-0.013667	-0.1497	0.440621
27	-0.005789	-0.0634	0.474771
28	-0.012794	-0.1401	0.444389
29	-0.015396	-0.1687	0.433176
30	-0.030379	-0.3328	0.369939
31	0.06166	0.6754	0.250345
32	-0.014404	-0.1578	0.437445
33	-0.016671	-0.1826	0.4277
34	-0.01858	-0.2035	0.41953
35	-0.015334	-0.168	0.433443
36	-0.016801	-0.184	0.427145
37	-0.066401	-0.7274	0.234202
38	-0.045777	-0.5015	0.308481
39	-0.01371	-0.1502	0.440436
40	0.006149	0.0674	0.473202
41	-0.00202	-0.0221	0.491189
42	-0.024796	-0.2716	0.393188
43	0.049722	0.5447	0.293492
44	-0.026961	-0.2953	0.384122
45	-0.000533	-0.0058	0.497677
46	-0.04128	-0.4522	0.32597
47	-0.002564	-0.0281	0.488821
48	-0.028792	-0.3154	0.376501
49	-0.024426	-0.2676	0.394744
50	-0.072118	-0.79	0.21554
51	-0.030624	-0.3355	0.36893
52	0.004953	0.0543	0.47841
53	-0.002399	-0.0263	0.489539
54	-0.020602	-0.2257	0.410915
55	0.05452	0.5972	0.275736
56	0.000531	0.0058	0.497686
57	-0.004232	-0.0464	0.481553
58	-0.029544	-0.3236	0.373389
59	0.020032	0.2194	0.413339
60	-0.058172	-0.6372	0.262592

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/02/t1280751111ba8xfjxohjntfi2/1g0eh1280751041.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/02/t1280751111ba8xfjxohjntfi2/1g0eh1280751041.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/02/t1280751111ba8xfjxohjntfi2/2g0eh1280751041.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/02/t1280751111ba8xfjxohjntfi2/2g0eh1280751041.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; 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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