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Paper: AutoCorrelation Function d=D=1

*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: Mon, 14 Dec 2009 02:34:01 -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/14/t126078329167v1osy177h7szp.htm/, Retrieved Mon, 14 Dec 2009 10:34:53 +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/14/t126078329167v1osy177h7szp.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 «

423 427 441 449 452 462 455 461 461 463 462 456 455 456 472 472 471 465 459 465 468 467 463 460 462 461 476 476 471 453 443 442 444 438 427 424 416 406 431 434 418 412 404 409 412 406 398 397 385 390 413 413 401 397 397 409 419 424 428 430

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	0.202072	1.3853	0.086245
2	0.22005	1.5086	0.069049
3	0.320627	2.1981	0.016451
4	0.182965	1.2543	0.10796
5	0.116995	0.8021	0.213273
6	0.128482	0.8808	0.191447
7	-0.019097	-0.1309	0.448198
8	0.210796	1.4451	0.077526
9	-0.04831	-0.3312	0.370985
10	-0.071642	-0.4911	0.312803
11	0.22028	1.5102	0.068848
12	0.005309	0.0364	0.485561
13	-0.032334	-0.2217	0.412764
14	0.170759	1.1707	0.123817
15	0.08111	0.5561	0.290403
16	0.065228	0.4472	0.328398
17	0.046344	0.3177	0.376054
18	-0.055214	-0.3785	0.353371
19	0.085008	0.5828	0.281411
20	-0.052812	-0.3621	0.359465
21	-0.170219	-1.167	0.124556
22	-0.137498	-0.9426	0.175343
23	-0.058345	-0.4	0.345486
24	-0.21309	-1.4609	0.075352
25	-0.127993	-0.8775	0.192345
26	-0.209191	-1.4341	0.079076
27	-0.145814	-0.9996	0.1613
28	-0.183583	-1.2586	0.107198
29	-0.095863	-0.6572	0.257128
30	-0.073596	-0.5045	0.308117
31	0.012028	0.0825	0.467316
32	-0.12223	-0.838	0.203145
33	-0.008312	-0.057	0.477401
34	-0.01473	-0.101	0.459997
35	0.00954	0.0654	0.474066
36	-0.051888	-0.3557	0.361818

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.202072	1.3853	0.086245
2	0.186846	1.281	0.103247
3	0.266521	1.8272	0.037014
4	0.070835	0.4856	0.314747
5	-0.01671	-0.1146	0.454641
6	-0.004773	-0.0327	0.487016
7	-0.133782	-0.9172	0.18187
8	0.200243	1.3728	0.088166
9	-0.133664	-0.9164	0.18208
10	-0.087284	-0.5984	0.276227
11	0.22746	1.5594	0.062807
12	-0.030816	-0.2113	0.416798
13	-0.028138	-0.1929	0.423933
14	0.104686	0.7177	0.23825
15	0.069995	0.4799	0.316775
16	-0.034411	-0.2359	0.407263
17	-0.047139	-0.3232	0.374
18	-0.080535	-0.5521	0.29174
19	-0.028977	-0.1987	0.421694
20	-0.038907	-0.2667	0.39542
21	-0.093714	-0.6425	0.261845
22	-0.230187	-1.5781	0.060627
23	0.081036	0.5556	0.290575
24	-0.039898	-0.2735	0.392823
25	-0.059901	-0.4107	0.341595
26	-0.112615	-0.772	0.221976
27	-0.042197	-0.2893	0.386817
28	-0.07435	-0.5097	0.306316
29	0.094809	0.65	0.259435
30	0.050947	0.3493	0.364221
31	0.02833	0.1942	0.423421
32	-0.0255	-0.1748	0.430988
33	0.07243	0.4966	0.310909
34	-0.047552	-0.326	0.372937
35	0.084838	0.5816	0.281801
36	0.038408	0.2633	0.39673

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/14/t126078329167v1osy177h7szp/1aulc1260783239.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/14/t126078329167v1osy177h7szp/1aulc1260783239.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/14/t126078329167v1osy177h7szp/2kz4r1260783239.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/14/t126078329167v1osy177h7szp/2kz4r1260783239.ps (open in new window)

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 1 ; 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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