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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 04:12:49 -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/t1259061274y2rnj8ym49gb7zs.htm/, Retrieved Tue, 24 Nov 2009 12:14:37 +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/t1259061274y2rnj8ym49gb7zs.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	-0.396681	-3.846	0.000109
2	-0.039667	-0.3846	0.350707
3	0.054195	0.5254	0.300258
4	-0.031524	-0.3056	0.380278
5	-0.012404	-0.1203	0.452265
6	-0.157049	-1.5226	0.065602
7	0.20201	1.9586	0.026564
8	-0.067427	-0.6537	0.257443
9	-0.093056	-0.9022	0.184625
10	-0.049325	-0.4782	0.316801
11	0.286735	2.78	0.003283
12	-0.389721	-3.7785	0.000138
13	0.113391	1.0994	0.137208
14	0.090013	0.8727	0.192523
15	0.101976	0.9887	0.162675
16	-0.194972	-1.8903	0.030897
17	-0.017026	-0.1651	0.434621
18	0.239969	2.3266	0.011068
19	-0.266483	-2.5837	0.005658
20	0.13954	1.3529	0.089668
21	-0.043033	-0.4172	0.338735
22	0.124909	1.211	0.114459
23	-0.11474	-1.1124	0.134393
24	-0.016316	-0.1582	0.437325
25	0.089159	0.8644	0.194776
26	-0.045826	-0.4443	0.328924
27	-0.087943	-0.8526	0.198014
28	0.101681	0.9858	0.163372
29	0.097257	0.9429	0.174065
30	-0.234353	-2.2721	0.012679
31	0.181216	1.757	0.041091
32	-0.066541	-0.6451	0.260205
33	0.039889	0.3867	0.349913
34	-0.048737	-0.4725	0.318825
35	0.032157	0.3118	0.377951
36	0.016287	0.1579	0.437435
37	-0.060565	-0.5872	0.27924
38	0.051773	0.502	0.308435
39	-0.037182	-0.3605	0.359644
40	-0.010152	-0.0984	0.460901
41	-0.094522	-0.9164	0.180894
42	0.138982	1.3475	0.090533
43	-0.080722	-0.7826	0.217907
44	0.069481	0.6736	0.251096
45	-0.008009	-0.0776	0.469138
46	0.045517	0.4413	0.330005
47	-0.072829	-0.7061	0.240936
48	-0.01381	-0.1339	0.446887
49	0.078656	0.7626	0.223808
50	-0.074849	-0.7257	0.234917
51	0.072338	0.7013	0.242411
52	0.001928	0.0187	0.492562
53	0.038697	0.3752	0.354187
54	-0.12918	-1.2524	0.106757
55	0.049874	0.4835	0.314916
56	-0.002344	-0.0227	0.490959
57	-0.024415	-0.2367	0.406697
58	-0.016619	-0.1611	0.43617
59	0.087867	0.8519	0.198217
60	-0.004258	-0.0413	0.483578

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.396681	-3.846	0.000109
2	-0.233815	-2.2669	0.012844
3	-0.072773	-0.7056	0.241103
4	-0.055067	-0.5339	0.297338
5	-0.049277	-0.4778	0.316964
6	-0.239896	-2.3259	0.011087
7	0.023374	0.2266	0.410605
8	-0.010045	-0.0974	0.461312
9	-0.11585	-1.1232	0.132105
10	-0.230292	-2.2328	0.013969
11	0.187069	1.8137	0.036457
12	-0.321316	-3.1153	0.001218
13	-0.138853	-1.3462	0.090733
14	-0.09238	-0.8957	0.186361
15	0.184727	1.791	0.038256
16	-0.222314	-2.1554	0.016842
17	-0.111995	-1.0858	0.140166
18	-0.035677	-0.3459	0.365094
19	-0.118386	-1.1478	0.126984
20	-0.028322	-0.2746	0.392116
21	-0.090677	-0.8791	0.190783
22	-0.083396	-0.8086	0.210408
23	0.079215	0.768	0.222202
24	-0.118072	-1.1448	0.127609
25	-0.126934	-1.2307	0.110759
26	-0.05305	-0.5143	0.304112
27	0.020596	0.1997	0.421079
28	-0.10536	-1.0215	0.154819
29	-0.009004	-0.0873	0.46531
30	-0.119703	-1.1606	0.124379
31	0.049641	0.4813	0.315716
32	-0.027325	-0.2649	0.395825
33	-0.059916	-0.5809	0.281347
34	0.017112	0.1659	0.434292
35	0.090293	0.8754	0.191788
36	-0.114627	-1.1113	0.134626
37	-0.014142	-0.1371	0.445617
38	0.060424	0.5858	0.279698
39	0.041314	0.4006	0.344829
40	-0.171233	-1.6602	0.050107
41	-0.05586	-0.5416	0.294692
42	-0.0398	-0.3859	0.35023
43	-0.051711	-0.5014	0.308647
44	0.004516	0.0438	0.482586
45	0.017193	0.1667	0.433986
46	0.027108	0.2628	0.396631
47	-0.021105	-0.2046	0.419156
48	-0.091188	-0.8841	0.18945
49	-0.088401	-0.8571	0.19679
50	0.073445	0.7121	0.23909
51	0.024507	0.2376	0.406352
52	-0.000574	-0.0056	0.497785
53	0.047857	0.464	0.321862
54	-0.00566	-0.0549	0.478176
55	-0.027638	-0.268	0.394659
56	-0.006417	-0.0622	0.47526
57	-0.061566	-0.5969	0.276003
58	0.020552	0.1993	0.421246
59	0.080572	0.7812	0.218332
60	-0.033119	-0.3211	0.374424

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259061274y2rnj8ym49gb7zs/11wgq1259061167.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259061274y2rnj8ym49gb7zs/11wgq1259061167.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259061274y2rnj8ym49gb7zs/2qhru1259061167.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259061274y2rnj8ym49gb7zs/2qhru1259061167.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 2 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 2 ; par4 = 1 ; 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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