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*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, 21 Dec 2010 20:22:04 +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/Dec/21/t1292962782idi24zmiwsnivkv.htm/, Retrieved Tue, 21 Dec 2010 21:19:43 +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/2010/Dec/21/t1292962782idi24zmiwsnivkv.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

320 324 343 295 301 367 196 182 342 361 333 330 345 323 365 323 316 358 235 169 430 409 407 341 326 374 364 349 300 385 304 196 443 414 325 388 356 386 444 387 327 448 225 182 460 411 342 361 377 331 428 340 352 461 221 198 422 329 320 375 364 351 380 319 322 386 221 187 343 342 365 313 356 337 389 326 343 357 220 218 391 425 332 298 360 336 325 393 301 426 265 210 429 440 357 431 442 422 544 420 396 482 261 211 448 468 464 425

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.220102	2.1566	0.016769
2	0.298088	2.9206	0.002177
3	0.30258	2.9647	0.001911
4	0.009203	0.0902	0.464168
5	0.186853	1.8308	0.035118
6	0.246959	2.4197	0.008708
7	0.04478	0.4388	0.330912
8	0.323203	3.1667	0.001033
9	0.183102	1.794	0.037979
10	0.02241	0.2196	0.413335
11	0.219176	2.1475	0.017137
12	-0.150688	-1.4764	0.07155
13	-0.039245	-0.3845	0.350723
14	0.094035	0.9214	0.179588
15	0.143218	1.4032	0.081885
16	0.013828	0.1355	0.446256
17	0.174726	1.712	0.045066
18	0.028221	0.2765	0.391376
19	0.018012	0.1765	0.430146
20	0.054335	0.5324	0.29785
21	-0.013283	-0.1301	0.448361
22	-0.056077	-0.5494	0.291989
23	0.035178	0.3447	0.365545
24	-0.137102	-1.3433	0.091168
25	-0.037979	-0.3721	0.355315
26	0.032662	0.32	0.374822
27	-0.267305	-2.619	0.005124
28	-0.027206	-0.2666	0.395188
29	-0.087305	-0.8554	0.197228
30	-0.20639	-2.0222	0.022969
31	-0.070815	-0.6938	0.244728
32	-0.151813	-1.4875	0.070086
33	-0.245923	-2.4095	0.008939
34	-0.071327	-0.6989	0.243165
35	-0.153525	-1.5042	0.067902
36	-0.169496	-1.6607	0.050017
37	-0.049335	-0.4834	0.314963
38	-0.225043	-2.205	0.014922
39	-0.087937	-0.8616	0.195526
40	-0.090597	-0.8877	0.188469
41	-0.161647	-1.5838	0.058262
42	-0.156021	-1.5287	0.064815
43	-0.066339	-0.65	0.258627
44	-0.115351	-1.1302	0.130603
45	-0.098853	-0.9686	0.1676
46	-0.097618	-0.9565	0.170621
47	-0.212346	-2.0806	0.020069
48	-0.123454	-1.2096	0.114703

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.220102	2.1566	0.016769
2	0.262352	2.5705	0.005846
3	0.221698	2.1722	0.016152
4	-0.164502	-1.6118	0.055146
5	0.086388	0.8464	0.199711
6	0.226219	2.2165	0.01451
7	-0.049305	-0.4831	0.315065
8	0.182797	1.791	0.038219
9	0.064461	0.6316	0.264579
10	-0.125236	-1.2271	0.1114
11	0.048724	0.4774	0.317081
12	-0.246457	-2.4148	0.008819
13	-0.049205	-0.4821	0.315414
14	0.064614	0.6331	0.264092
15	0.326282	3.1969	0.000941
16	-0.218009	-2.136	0.01761
17	0.005574	0.0546	0.478281
18	0.127038	1.2447	0.108134
19	-0.062105	-0.6085	0.272145
20	-0.000357	-0.0035	0.498608
21	0.065176	0.6386	0.262303
22	-0.144918	-1.4199	0.079437
23	-0.076694	-0.7514	0.227111
24	-0.180026	-1.7639	0.040466
25	-0.020962	-0.2054	0.418853
26	0.018366	0.1799	0.428786
27	-0.056312	-0.5517	0.291202
28	-0.026971	-0.2643	0.396074
29	-0.020724	-0.2031	0.419762
30	-0.026708	-0.2617	0.397064
31	-0.042058	-0.4121	0.340599
32	-0.049784	-0.4878	0.313407
33	-0.024366	-0.2387	0.405908
34	-0.07839	-0.7681	0.222168
35	0.109157	1.0695	0.143759
36	-0.192058	-1.8818	0.031448
37	-0.004416	-0.0433	0.482788
38	0.004338	0.0425	0.483092
39	0.082743	0.8107	0.209769
40	-0.088826	-0.8703	0.193149
41	0.04926	0.4826	0.315224
42	-0.030007	-0.294	0.384695
43	-0.033134	-0.3246	0.373079
44	0.103623	1.0153	0.15626
45	-0.061468	-0.6023	0.274209
46	-0.162404	-1.5912	0.057423
47	-0.033691	-0.3301	0.37102
48	0.007202	0.0706	0.471947

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292962782idi24zmiwsnivkv/1mzmg1292962920.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292962782idi24zmiwsnivkv/1mzmg1292962920.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292962782idi24zmiwsnivkv/2mzmg1292962920.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292962782idi24zmiwsnivkv/2mzmg1292962920.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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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