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ws4

*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, 24 Nov 2009 03:25:36 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/24/t1259058391x0xhtr2ql3x7vty.htm/, Retrieved Tue, 24 Nov 2009 11:26:33 +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/2009/Nov/24/t1259058391x0xhtr2ql3x7vty.htm/},
    year = {2009},
}
@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 = {2009},
    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 «

395.3 395.1 403.5 403.3 405.7 406.7 407.2 412.4 415.9 414 411.8 409.9 412.4 415.9 416.3 417.2 421.8 421.4 415.1 412.4 411.8 408.8 404.5 402.5 409.4 410.7 413.4 415.2 417.7 417.8 417.9 418.4 418.2 416.6 418.9 421 423.5 432.3 432.3 428.6 426.7 427.3 428.5 437 442 444.9 441.4 440.3 447.1 455.3 478.6 486.5 487.8 485.9 483.8 488.4 494 493.6 487.3 482.1 484.2 496.8 501.1 499.8 495.5 498.1 503.8 516.2 526.1 527.1 525.1 528.9 540.1 549 556 568.9 589.1 590.3 603.3 638.8 643 656.7 656.1 654.1 659.9 662.1 669.2 673.1 678.3 677.4 678.5 672.4 665.3 667.9 672.1 662.5 682.3 692.1 702.7 721.4 733.2 747.7 737.6 729.3 706.1 674.3 659 645.7

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	0.511455	5.2905	0
2	0.324057	3.3521	0.000555
3	0.163856	1.6949	0.046498
4	-0.056721	-0.5867	0.279312
5	-0.017145	-0.1774	0.429784
6	-0.092105	-0.9527	0.171434
7	-0.056982	-0.5894	0.278408
8	-0.147196	-1.5226	0.065404
9	-0.143409	-1.4834	0.070449
10	-0.026076	-0.2697	0.393943
11	0.072977	0.7549	0.225989
12	0.14349	1.4843	0.070339
13	0.091955	0.9512	0.171825
14	0.014726	0.1523	0.43961
15	0.00963	0.0996	0.46042
16	-0.097288	-1.0064	0.158258
17	0.060612	0.627	0.266006
18	0.106282	1.0994	0.137033
19	-0.000603	-0.0062	0.497517
20	0.066416	0.687	0.24678
21	0.011132	0.1151	0.454271
22	0.071717	0.7418	0.229903
23	0.014777	0.1529	0.4394
24	0.020353	0.2105	0.416827
25	-0.042642	-0.4411	0.330017
26	-0.172278	-1.7821	0.038788
27	-0.168199	-1.7399	0.042379
28	-0.124535	-1.2882	0.100228
29	-0.048278	-0.4994	0.309264
30	-0.083202	-0.8606	0.195679
31	-0.049528	-0.5123	0.304741
32	-0.093667	-0.9689	0.167389
33	-0.080361	-0.8313	0.203839
34	-0.051137	-0.529	0.298961
35	0.002004	0.0207	0.491752
36	0.014311	0.148	0.441299
37	-0.050926	-0.5268	0.299718
38	-0.057773	-0.5976	0.275682
39	-0.096429	-0.9975	0.160394
40	-0.084934	-0.8786	0.190804
41	-0.044184	-0.457	0.324283
42	-0.032533	-0.3365	0.368566
43	-0.036853	-0.3812	0.3519
44	-0.033785	-0.3495	0.363712
45	-0.031728	-0.3282	0.371702
46	0.027733	0.2869	0.387383
47	0.03992	0.4129	0.340241
48	0.078731	0.8144	0.208612
49	0.052326	0.5413	0.294724
50	0.019775	0.2046	0.419154
51	0.040519	0.4191	0.337982
52	-0.022382	-0.2315	0.408677
53	-0.041314	-0.4274	0.334991
54	-0.135878	-1.4055	0.08138
55	-0.147757	-1.5284	0.064681
56	-0.136453	-1.4115	0.080502
57	-0.137984	-1.4273	0.0782
58	-0.079284	-0.8201	0.206987
59	-0.01558	-0.1612	0.436137
60	-0.033772	-0.3493	0.36376

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.511455	5.2905	0
2	0.084602	0.8751	0.191733
3	-0.042465	-0.4393	0.330677
4	-0.19973	-2.066	0.020621
5	0.105282	1.089	0.13929
6	-0.081511	-0.8432	0.20051
7	0.038231	0.3955	0.346642
8	-0.193197	-1.9984	0.024103
9	0.022015	0.2277	0.410145
10	0.099979	1.0342	0.151689
11	0.160088	1.656	0.05033
12	-0.013901	-0.1438	0.442966
13	-0.077516	-0.8018	0.212215
14	-0.092011	-0.9518	0.17168
15	0.095593	0.9888	0.162491
16	-0.130076	-1.3455	0.090652
17	0.222757	2.3042	0.011571
18	0.009612	0.0994	0.460492
19	-0.078403	-0.811	0.209581
20	0.047384	0.4901	0.312517
21	0.061206	0.6331	0.264004
22	0.036866	0.3813	0.351851
23	-0.1307	-1.352	0.089617
24	0.00352	0.0364	0.485512
25	-0.084581	-0.8749	0.191792
26	-0.031177	-0.3225	0.373854
27	-0.056488	-0.5843	0.280118
28	0.081648	0.8446	0.200117
29	-0.034597	-0.3579	0.360572
30	-0.11563	-1.1961	0.117153
31	0.019074	0.1973	0.421983
32	-0.119299	-1.234	0.109947
33	0.047349	0.4898	0.312646
34	-0.046268	-0.4786	0.316601
35	-0.009164	-0.0948	0.46233
36	-0.000827	-0.0086	0.496597
37	-0.024896	-0.2575	0.398634
38	-0.007248	-0.075	0.470188
39	-0.098114	-1.0149	0.156222
40	-0.034149	-0.3532	0.362301
41	0.033157	0.343	0.366145
42	-0.050545	-0.5228	0.301084
43	0.023284	0.2409	0.405064
44	0.034217	0.3539	0.362041
45	0.023293	0.2409	0.405029
46	-0.032161	-0.3327	0.370016
47	0.066427	0.6871	0.246745
48	0.045595	0.4716	0.319074
49	-0.039157	-0.405	0.343128
50	0.03401	0.3518	0.362838
51	0.022681	0.2346	0.407477
52	-0.013723	-0.142	0.443692
53	-0.148893	-1.5402	0.063236
54	-0.063205	-0.6538	0.257322
55	-0.013996	-0.1448	0.442579
56	-0.017757	-0.1837	0.427305
57	-0.030366	-0.3141	0.377026
58	-0.083732	-0.8661	0.194179
59	0.072199	0.7468	0.228403
60	-0.115575	-1.1955	0.117264

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259058391x0xhtr2ql3x7vty/134rm1259058335.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259058391x0xhtr2ql3x7vty/134rm1259058335.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259058391x0xhtr2ql3x7vty/2kb6o1259058335.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259058391x0xhtr2ql3x7vty/2kb6o1259058335.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; 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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