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R Software Module: /rwasp_autocorrelation.wasp (opens new window with default values)

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Thu, 19 Aug 2010 08:44:46 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Aug/19/t1282207530u0yh21403y9syb6.htm/, Retrieved Thu, 19 Aug 2010 10:45:32 +0200

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/Aug/19/t1282207530u0yh21403y9syb6.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:

DeGroodtOlivierStap21V

Dataseries X:

» Textbox « » Textfile « » CSV «

356 355 354 352 372 371 356 346 347 347 348 350 353 351 348 351 370 370 351 335 330 328 332 334 343 334 336 343 365 364 351 326 320 312 315 316 319 311 315 322 336 339 317 295 291 283 285 289 296 283 285 289 306 306 283 258 255 248 244 249 258 252 246 249 267 284 261 235 229 218 218 229 237 231 229 233 245 256 224 194 192 178 170 187 192 182 178 186 204 224 194 173 178 168 152 163 172 170 156 155 178 194 164 135 139 135 109 121 131 135 119 121 151 169 135 105 112 105 82 81

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	5 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.870557	8.5297	0
2	0.732917	7.1811	0
3	0.562664	5.513	0
4	0.407995	3.9975	6.3e-05
5	0.219637	2.152	0.016953
6	0.013626	0.1335	0.447037
7	-0.168941	-1.6553	0.050567
8	-0.313798	-3.0746	0.001373
9	-0.419432	-4.1096	4.2e-05
10	-0.553577	-5.4239	0
11	-0.620885	-6.0834	0
12	-0.667783	-6.5429	0
13	-0.562451	-5.5109	0
14	-0.466772	-4.5734	7e-06
15	-0.33319	-3.2646	0.00076
16	-0.182381	-1.787	0.03855
17	-0.022642	-0.2218	0.412453
18	0.110306	1.0808	0.141254
19	0.196031	1.9207	0.028868
20	0.271713	2.6622	0.004551
21	0.330668	3.2399	0.000822
22	0.395838	3.8784	9.6e-05
23	0.373119	3.6558	0.000209
24	0.355393	3.4821	0.000375
25	0.296017	2.9004	0.00231
26	0.261158	2.5588	0.006033
27	0.172526	1.6904	0.047098
28	0.056077	0.5494	0.29199
29	-0.057607	-0.5644	0.286888
30	-0.132181	-1.2951	0.099195
31	-0.171347	-1.6788	0.048217
32	-0.212642	-2.0835	0.019933
33	-0.231167	-2.265	0.012882
34	-0.238566	-2.3375	0.010746
35	-0.181071	-1.7741	0.039607
36	-0.147561	-1.4458	0.075746
37	-0.100769	-0.9873	0.162981
38	-0.088179	-0.864	0.194879
39	-0.035597	-0.3488	0.364009
40	0.024282	0.2379	0.406228
41	0.080802	0.7917	0.215245
42	0.132502	1.2983	0.098656
43	0.157795	1.5461	0.062689
44	0.169504	1.6608	0.050009
45	0.143822	1.4092	0.081009
46	0.105638	1.035	0.151626
47	0.037932	0.3717	0.355484
48	-0.000938	-0.0092	0.496342
49	-0.061566	-0.6032	0.273893
50	-0.095413	-0.9349	0.176104
51	-0.136929	-1.3416	0.091442
52	-0.160671	-1.5743	0.05936
53	-0.169918	-1.6649	0.049601
54	-0.194	-1.9008	0.030164
55	-0.194795	-1.9086	0.029651
56	-0.173398	-1.6989	0.046284
57	-0.121952	-1.1949	0.117539
58	-0.07481	-0.733	0.232677
59	-0.005297	-0.0519	0.47936
60	0.031966	0.3132	0.377404

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.870557	8.5297	0
2	-0.103056	-1.0097	0.157579
3	-0.214643	-2.1031	0.019038
4	-0.037393	-0.3664	0.357447
5	-0.244738	-2.3979	0.009211
6	-0.253614	-2.4849	0.007345
7	-0.068118	-0.6674	0.253053
8	-0.042232	-0.4138	0.339978
9	-0.042163	-0.4131	0.340222
10	-0.332122	-3.2541	0.000786
11	0.024799	0.243	0.404272
12	-0.139994	-1.3717	0.086683
13	0.442316	4.3338	1.8e-05
14	-0.092938	-0.9106	0.182393
15	0.102254	1.0019	0.15946
16	0.104055	1.0195	0.155259
17	-0.09414	-0.9224	0.179321
18	-0.188715	-1.849	0.033766
19	-0.090458	-0.8863	0.188835
20	0.019384	0.1899	0.424887
21	0.092684	0.9081	0.183047
22	-0.081511	-0.7986	0.213236
23	-0.106273	-1.0413	0.150186
24	0.047312	0.4636	0.322006
25	0.203333	1.9923	0.024592
26	0.104632	1.0252	0.153927
27	-0.055248	-0.5413	0.294771
28	-0.019789	-0.1939	0.423333
29	-0.121527	-1.1907	0.118349
30	-0.062195	-0.6094	0.271854
31	-0.017801	-0.1744	0.430953
32	0.096143	0.942	0.174276
33	0.061695	0.6045	0.273473
34	0.018009	0.1765	0.430154
35	-0.010421	-0.1021	0.459444
36	0.05008	0.4907	0.312385
37	0.073171	0.7169	0.237579
38	-0.126937	-1.2437	0.108316
39	-0.017634	-0.1728	0.431595
40	0.013436	0.1316	0.447771
41	-0.002276	-0.0223	0.491128
42	0.074864	0.7335	0.232515
43	-0.079505	-0.779	0.218952
44	-0.048536	-0.4755	0.317738
45	0.013374	0.131	0.448008
46	-0.091658	-0.8981	0.1857
47	-0.00139	-0.0136	0.49458
48	-0.011755	-0.1152	0.454272
49	-0.022802	-0.2234	0.411844
50	-0.063591	-0.6231	0.26736
51	-0.043147	-0.4228	0.336709
52	0.000316	0.0031	0.498769
53	0.063504	0.6222	0.267638
54	-0.001236	-0.0121	0.495182
55	0.052288	0.5123	0.304803
56	0.029188	0.286	0.387753
57	-0.073531	-0.7205	0.236498
58	-0.162004	-1.5873	0.057866
59	0.040592	0.3977	0.34586
60	-0.039421	-0.3863	0.350083

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282207530u0yh21403y9syb6/1zyst1282207480.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282207530u0yh21403y9syb6/1zyst1282207480.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282207530u0yh21403y9syb6/2zyst1282207480.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282207530u0yh21403y9syb6/2zyst1282207480.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 2 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 2 ; 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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