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Identifying Integration Processes 2

*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: Wed, 16 Dec 2009 13:29:09 -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/Dec/16/t1260995393pe1ro4ce7g834b5.htm/, Retrieved Wed, 16 Dec 2009 21:29:55 +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/Dec/16/t1260995393pe1ro4ce7g834b5.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 «

112 118 132 129 121 135 148 148 136 119 104 118 115 126 141 135 125 149 170 170 158 133 114 140 145 150 178 163 172 178 199 199 184 162 146 166 171 180 193 181 183 218 230 242 209 191 172 194 196 196 236 235 229 243 264 272 237 211 180 201 204 188 235 227 234 264 302 293 259 229 203 229 242 233 267 269 270 315 364 347 312 274 237 278 284 277 317 313 318 374 413 405 355 306 271 306 315 301 356 348 355 422 465 467 404 347 305 336 340 318 362 348 363 435 491 505 404 359 310 337 360 342 406 396 420 472 548 559 463 407 362 405 417 391 419 461 472 535 622 606 508 461 390 432

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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.199751	2.3887	0.009107
2	-0.120104	-1.4362	0.076559
3	-0.150772	-1.803	0.036749
4	-0.322074	-3.8514	8.8e-05
5	-0.083975	-1.0042	0.158492
6	0.025778	0.3083	0.379165
7	-0.110961	-1.3269	0.093329
8	-0.336721	-4.0266	4.6e-05
9	-0.115586	-1.3822	0.084531
10	-0.109267	-1.3066	0.096716
11	0.205852	2.4616	0.00751
12	0.84143	10.062	0
13	0.215087	2.5721	0.005565
14	-0.139554	-1.6688	0.04867
15	-0.115996	-1.3871	0.083784
16	-0.278943	-3.3357	0.000542
17	-0.051706	-0.6183	0.268674
18	0.012458	0.149	0.440891
19	-0.114358	-1.3675	0.086804
20	-0.337174	-4.032	4.5e-05
21	-0.107385	-1.2841	0.100585
22	-0.075211	-0.8994	0.184977
23	0.199475	2.3854	0.009186
24	0.736921	8.8123	0
25	0.197262	2.3589	0.009841
26	-0.123884	-1.4814	0.070345
27	-0.102699	-1.2281	0.110713
28	-0.210992	-2.5231	0.006363
29	-0.065357	-0.7816	0.217884
30	0.015728	0.1881	0.425538
31	-0.11537	-1.3796	0.084927
32	-0.289256	-3.459	0.000357
33	-0.126882	-1.5173	0.0657
34	-0.040707	-0.4868	0.313579
35	0.147411	1.7628	0.040037
36	0.657438	7.8618	0
37	0.192909	2.3069	0.01125
38	-0.134312	-1.6061	0.055224
39	-0.060237	-0.7203	0.236248
40	-0.162706	-1.9457	0.026828
41	-0.058027	-0.6939	0.244436
42	0.007366	0.0881	0.464964
43	-0.110954	-1.3268	0.093341
44	-0.285268	-3.4113	0.00042
45	-0.106176	-1.2697	0.103129
46	-0.033645	-0.4023	0.344018
47	0.124021	1.4831	0.070127
48	0.586899	7.0183	0
49	0.186538	2.2307	0.01363
50	-0.137754	-1.6473	0.050846
51	-0.049475	-0.5916	0.277514
52	-0.124159	-1.4847	0.069909
53	-0.028981	-0.3466	0.364714
54	0.004469	0.0534	0.478729
55	-0.094313	-1.1278	0.130643
56	-0.291733	-3.4886	0.000323
57	-0.095922	-1.1471	0.126636
58	-0.009558	-0.1143	0.45458
59	0.103458	1.2372	0.109025
60	0.521049	6.2308	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.199751	2.3887	0.009107
2	-0.166655	-1.9929	0.024088
3	-0.095875	-1.1465	0.126751
4	-0.310891	-3.7177	0.000144
5	0.007785	0.0931	0.46298
6	-0.07455	-0.8915	0.187084
7	-0.210284	-2.5146	0.006511
8	-0.494757	-5.9164	0
9	-0.192295	-2.2995	0.011462
10	-0.531875	-6.3603	0
11	-0.302293	-3.6149	0.000208
12	0.586041	7.008	0
13	0.025978	0.3107	0.378257
14	-0.181193	-2.1667	0.015955
15	0.120038	1.4355	0.076671
16	0.000408	0.0049	0.498059
17	0.02526	0.3021	0.381519
18	-0.124989	-1.4947	0.068604
19	0.087435	1.0456	0.148763
20	-0.054471	-0.6514	0.257923
21	-0.061824	-0.7393	0.230468
22	-0.025195	-0.3013	0.381815
23	0.033331	0.3986	0.345396
24	-0.009634	-0.1152	0.45422
25	-0.048057	-0.5747	0.283204
26	0.018487	0.2211	0.412677
27	0.027978	0.3346	0.369219
28	0.016309	0.195	0.422822
29	-0.093457	-1.1176	0.132808
30	0.008498	0.1016	0.459602
31	0.071461	0.8546	0.197114
32	0.109515	1.3096	0.096213
33	-0.093183	-1.1143	0.133508
34	0.063134	0.755	0.225752
35	-0.092056	-1.1008	0.136411
36	0.058404	0.6984	0.243029
37	-0.010291	-0.1231	0.451116
38	-0.076002	-0.9089	0.182478
39	0.087406	1.0452	0.148843
40	0.037026	0.4428	0.329303
41	-0.025502	-0.305	0.38042
42	0.047954	0.5734	0.283622
43	-0.004167	-0.0498	0.480164
44	-0.034889	-0.4172	0.338575
45	0.0232	0.2774	0.390923
46	0.016977	0.203	0.419706
47	0.016843	0.2014	0.42033
48	0.063478	0.7591	0.224524
49	-0.041633	-0.4979	0.309675
50	0.06009	0.7186	0.23679
51	-0.071228	-0.8518	0.197886
52	0.034095	0.4077	0.342044
53	0.088277	1.0556	0.146457
54	-0.012453	-0.1489	0.440913
55	0.06599	0.7891	0.215673
56	-0.008608	-0.1029	0.459079
57	0.042992	0.5141	0.303984
58	0.08413	1.006	0.158046
59	0.057857	0.6919	0.24507
60	0.015011	0.1795	0.428897

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260995393pe1ro4ce7g834b5/1hopp1260995346.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260995393pe1ro4ce7g834b5/1hopp1260995346.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260995393pe1ro4ce7g834b5/2zqnn1260995346.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260995393pe1ro4ce7g834b5/2zqnn1260995346.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 0.0 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 0.0 ; par3 = 1 ; 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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