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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, 12 Jan 2010 05:35:39 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jan/12/t1263299796tmjrhwbnjm57xam.htm/, Retrieved Tue, 12 Jan 2010 13:36:38 +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/Jan/12/t1263299796tmjrhwbnjm57xam.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 «

277 260.6 291.6 275.4 275.3 231.7 238.8 274.2 277.8 299.1 286.6 232.3 294.1 267.5 309.7 280.7 287.3 235.7 256.4 289 290.8 321.9 291.8 241.4 295.5 258.2 306.1 281.5 283.1 237.4 274.8 299.3 300.4 340.9 318.8 265.7 322.7 281.6 323.5 312.6 310.8 262.8 273.8 320 310.3 342.2 320.1 265.6 327 300.7 346.4 317.3 326.2 270.7 278.2 324.6 321.8 343.5 354 278.2 330.2 307.3 375.9 335.3 339.3 280.3 293.7 341.2 345.1 368.7 369.4 288.4 341 319.1 374.2 344.5 337.3 281 282.2 321 325.4 366.3 380.3 300.7 359.3 327.6 383.6 352.4 329.4 294.5 333.5 334.3 358 396.1 387 307.2 363.9 344.7 397.6 376.8 337.1 299.3 323.1 329.1 347 462 436.5 360.4 415.5 382.1 432.2 424.3 386.7 354.5 375.8 368 402.4 426.5 433.3 338.5 416.8 381.1 445.7 412.4 394 348.2 380.1 373.7 393.6 434.2 430.7 344.5 411.9 370.5 437.3 411.3 385.5 341.3 384.2 373.2 415.8 448.6 454.3 350.3 419.1 398 456.1 430.1 399.8 362.7 384. etc...

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	0.469686	5.9781	0
2	0.44758	5.6968	0
3	0.188679	2.4015	0.00873
4	0.154653	1.9684	0.025364
5	0.069534	0.885	0.188728
6	0.075097	0.9558	0.17029
7	0.083196	1.0589	0.145608
8	0.010719	0.1364	0.445827
9	-0.084608	-1.0769	0.141566
10	-0.269639	-3.4319	0.00038
11	-0.273711	-3.4838	0.000318
12	-0.598896	-7.6227	0
13	-0.226915	-2.8882	0.002203
14	-0.220484	-2.8063	0.002813
15	0.033359	0.4246	0.335851
16	-0.042841	-0.5453	0.293157
17	-0.045377	-0.5776	0.282183
18	-0.045047	-0.5733	0.283602
19	-0.068869	-0.8766	0.19101
20	-0.07541	-0.9598	0.169291
21	0.003855	0.0491	0.480465
22	0.094425	1.2018	0.115591
23	0.073661	0.9376	0.174934
24	0.169296	2.1548	0.016328
25	-0.009364	-0.1192	0.452638
26	0.024755	0.3151	0.376553
27	-0.151799	-1.9321	0.027547
28	-0.086033	-1.095	0.137566
29	-0.001914	-0.0244	0.490298
30	-0.023993	-0.3054	0.380236
31	0.030546	0.3888	0.348973
32	0.026585	0.3384	0.36776
33	-0.003278	-0.0417	0.483385
34	-0.039325	-0.5005	0.308691
35	-0.046566	-0.5927	0.277109
36	-0.056838	-0.7234	0.235228
37	0.022324	0.2841	0.388333
38	-0.022053	-0.2807	0.389655
39	0.071157	0.9057	0.183225
40	0.082652	1.052	0.147185
41	-0.016763	-0.2134	0.41566
42	0.00389	0.0495	0.480288
43	-0.060494	-0.77	0.221222
44	-0.000921	-0.0117	0.495332
45	-0.014342	-0.1825	0.427694
46	0.016039	0.2041	0.419251
47	0.04958	0.6311	0.264448
48	0.020384	0.2594	0.397811
49	-0.002364	-0.0301	0.488018
50	0.009463	0.1204	0.45214
51	-0.043672	-0.5559	0.28954
52	-0.064479	-0.8207	0.206515
53	0.0192	0.2444	0.403626
54	-0.034578	-0.4401	0.330224
55	0.088101	1.1213	0.1319
56	-0.022906	-0.2915	0.385506
57	-0.021502	-0.2737	0.392342
58	-0.052823	-0.6723	0.251167
59	-0.084515	-1.0757	0.141831
60	-0.074564	-0.949	0.172005

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.469686	5.9781	0
2	0.291219	3.7066	0.000144
3	-0.136135	-1.7327	0.042525
4	-0.003324	-0.0423	0.483154
5	0.014595	0.1858	0.426432
6	0.028777	0.3663	0.35732
7	0.058469	0.7442	0.22892
8	-0.089199	-1.1353	0.128959
9	-0.155735	-1.9822	0.024575
10	-0.254355	-3.2374	0.000732
11	-0.053987	-0.6871	0.246489
12	-0.482373	-6.1396	0
13	0.363635	4.6283	4e-06
14	0.191078	2.432	0.008052
15	0.144774	1.8427	0.033602
16	-0.061075	-0.7774	0.219041
17	-0.172247	-2.1923	0.014891
18	0.070108	0.8923	0.186771
19	0.021226	0.2702	0.393688
20	-0.151943	-1.9339	0.027433
21	-0.075517	-0.9612	0.168948
22	-0.096559	-1.229	0.110428
23	-0.036915	-0.4699	0.319545
24	-0.187156	-2.3821	0.009187
25	0.152159	1.9367	0.027263
26	0.155205	1.9754	0.024958
27	0.071623	0.9116	0.181662
28	-0.150184	-1.9115	0.028851
29	0.017771	0.2262	0.41067
30	-0.035932	-0.4573	0.324021
31	0.082486	1.0499	0.147668
32	-0.07648	-0.9734	0.165895
33	-0.092399	-1.176	0.120651
34	-0.032572	-0.4146	0.339499
35	-0.034851	-0.4436	0.328969
36	-0.105815	-1.3468	0.089962
37	0.03363	0.428	0.334595
38	0.069975	0.8906	0.187222
39	0.062625	0.7971	0.213284
40	0.03839	0.4886	0.312882
41	-0.061624	-0.7843	0.216991
42	-0.055739	-0.7094	0.239536
43	0.067585	0.8602	0.19547
44	-0.011087	-0.1411	0.443978
45	-0.050661	-0.6448	0.25998
46	-0.03006	-0.3826	0.35126
47	-0.000513	-0.0065	0.497401
48	-0.12765	-1.6247	0.053084
49	0.025313	0.3222	0.373866
50	0.022245	0.2831	0.388719
51	0.006712	0.0854	0.466013
52	0.052832	0.6724	0.251131
53	0.031742	0.404	0.343368
54	-0.146532	-1.865	0.031992
55	0.133045	1.6934	0.046152
56	-0.002661	-0.0339	0.486514
57	-0.138739	-1.7659	0.039652
58	-0.061301	-0.7802	0.218197
59	-0.032455	-0.4131	0.340046
60	-0.139647	-1.7774	0.038688

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/12/t1263299796tmjrhwbnjm57xam/1gjo71263299737.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/12/t1263299796tmjrhwbnjm57xam/1gjo71263299737.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/12/t1263299796tmjrhwbnjm57xam/2usrr1263299737.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/12/t1263299796tmjrhwbnjm57xam/2usrr1263299737.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 0.6 ; par3 = 0 ; par4 = 2 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 0.6 ; par3 = 0 ; par4 = 2 ; par5 = 12 ; par6 = MA ; 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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