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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 03:14:44 -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/t1259058067wwy8oczc30xpc5v.htm/, Retrieved Tue, 24 Nov 2009 11:21:10 +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/t1259058067wwy8oczc30xpc5v.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	0.985026	10.2367	0
2	0.965318	10.0319	0
3	0.942517	9.7949	0
4	0.915065	9.5096	0
5	0.885272	9.2	0
6	0.854239	8.8775	0
7	0.822153	8.5441	0
8	0.7917	8.2276	0
9	0.763	7.9293	0
10	0.736249	7.6513	0
11	0.709958	7.3781	0
12	0.683518	7.1033	0
13	0.657948	6.8376	0
14	0.630712	6.5546	0
15	0.603339	6.2701	0
16	0.575749	5.9834	0
17	0.54792	5.6941	0
18	0.518578	5.3892	0
19	0.487626	5.0676	1e-06
20	0.455794	4.7368	3e-06
21	0.423495	4.4011	1.3e-05
22	0.390698	4.0603	4.7e-05
23	0.357255	3.7127	0.000163
24	0.323212	3.3589	0.000541
25	0.289719	3.0108	0.001622
26	0.255851	2.6589	0.004516
27	0.222616	2.3135	0.011294
28	0.191347	1.9885	0.024641
29	0.160925	1.6724	0.048672
30	0.133849	1.391	0.083542
31	0.108115	1.1236	0.131844
32	0.082398	0.8563	0.196863
33	0.058796	0.611	0.271233
34	0.036401	0.3783	0.352978
35	0.014828	0.1541	0.438909
36	-0.006041	-0.0628	0.475028
37	-0.025995	-0.2701	0.393782
38	-0.044801	-0.4656	0.321227
39	-0.063799	-0.663	0.254366
40	-0.082817	-0.8607	0.195667
41	-0.100866	-1.0482	0.148437
42	-0.117687	-1.223	0.111989
43	-0.133947	-1.392	0.083389
44	-0.149249	-1.551	0.061908
45	-0.164615	-1.7107	0.045001
46	-0.179951	-1.8701	0.032088
47	-0.195627	-2.033	0.022252
48	-0.210658	-2.1892	0.015366
49	-0.225576	-2.3443	0.010447
50	-0.240824	-2.5027	0.006911
51	-0.254929	-2.6493	0.004638
52	-0.268814	-2.7936	0.003084
53	-0.282116	-2.9318	0.002057
54	-0.295114	-3.0669	0.001367
55	-0.307961	-3.2004	0.000901
56	-0.319959	-3.3251	0.000604
57	-0.330759	-3.4373	0.000418
58	-0.340233	-3.5358	3e-04
59	-0.347705	-3.6135	0.00023
60	-0.354931	-3.6886	0.000177

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.985026	10.2367	0
2	-0.166766	-1.7331	0.042968
3	-0.091679	-0.9528	0.171422
4	-0.145774	-1.5149	0.066356
5	-0.048709	-0.5062	0.306874
6	-0.021972	-0.2283	0.409907
7	-0.020131	-0.2092	0.417339
8	0.063689	0.6619	0.254732
9	0.03953	0.4108	0.341015
10	0.037105	0.3856	0.350273
11	-0.038445	-0.3995	0.345144
12	-0.051669	-0.537	0.296199
13	-0.006139	-0.0638	0.474625
14	-0.091126	-0.947	0.172874
15	-0.003826	-0.0398	0.484179
16	-0.015689	-0.163	0.435394
17	0.004132	0.0429	0.482914
18	-0.058678	-0.6098	0.271638
19	-0.0634	-0.6589	0.255691
20	-0.032646	-0.3393	0.367534
21	-0.026435	-0.2747	0.392028
22	-0.022507	-0.2339	0.407752
23	-0.038946	-0.4047	0.343235
24	-0.0305	-0.317	0.375939
25	0.005649	0.0587	0.476646
26	-0.050721	-0.5271	0.2996
27	-0.004584	-0.0476	0.481044
28	0.027152	0.2822	0.389177
29	-0.010246	-0.1065	0.457701
30	0.074808	0.7774	0.219304
31	-0.023827	-0.2476	0.402451
32	-0.049788	-0.5174	0.302962
33	0.016966	0.1763	0.430187
34	-0.013247	-0.1377	0.445382
35	-0.00241	-0.025	0.490034
36	-0.012296	-0.1278	0.44928
37	0.022324	0.232	0.408488
38	0.013074	0.1359	0.446088
39	-0.039457	-0.41	0.341293
40	-0.029876	-0.3105	0.378399
41	-0.003417	-0.0355	0.485869
42	0.028478	0.296	0.383917
43	-0.020677	-0.2149	0.415133
44	0.003335	0.0347	0.486207
45	-0.033805	-0.3513	0.36302
46	-0.036777	-0.3822	0.351534
47	-0.056949	-0.5918	0.277599
48	-0.013187	-0.137	0.445626
49	-0.013945	-0.1449	0.442521
50	-0.030816	-0.3202	0.3747
51	0.01762	0.1831	0.427526
52	-0.028753	-0.2988	0.38283
53	-0.013761	-0.143	0.443274
54	-0.035975	-0.3739	0.354618
55	-0.04505	-0.4682	0.3203
56	-0.00225	-0.0234	0.490696
57	0.021436	0.2228	0.41207
58	0.021703	0.2255	0.41099
59	0.033704	0.3503	0.363411
60	-0.036328	-0.3775	0.35326

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259058067wwy8oczc30xpc5v/1m6qc1259057683.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259058067wwy8oczc30xpc5v/1m6qc1259057683.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259058067wwy8oczc30xpc5v/22tlp1259057683.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259058067wwy8oczc30xpc5v/22tlp1259057683.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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