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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: Fri, 11 Dec 2009 03:53:34 -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/11/t1260528915p6tkwclgjz71owv.htm/, Retrieved Fri, 11 Dec 2009 11:55:17 +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/11/t1260528915p6tkwclgjz71owv.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:

ACF1paper

Dataseries X:

» Textbox « » Textfile « » CSV «

627 696 825 677 656 785 412 352 839 729 696 641 695 638 762 635 721 854 418 367 824 687 601 676 740 691 683 594 729 731 386 331 707 715 657 653 642 643 718 654 632 731 392 344 792 852 649 629 685 617 715 715 629 916 531 357 917 828 708 858 775 785 1006 789 734 906 532 387 991 841

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	0.110985	0.9286	0.178152
2	-0.332742	-2.7839	0.00345
3	0.194973	1.6313	0.053663
4	0.036792	0.3078	0.379565
5	-0.056705	-0.4744	0.318335
6	0.181361	1.5174	0.066838
7	-0.025048	-0.2096	0.417306
8	0.040367	0.3377	0.368287
9	0.125619	1.051	0.148436
10	-0.30453	-2.5479	0.006518
11	0.047985	0.4015	0.344648
12	0.66731	5.5831	0
13	0.004351	0.0364	0.485534
14	-0.336869	-2.8184	0.003135
15	0.068384	0.5721	0.28453
16	-0.006799	-0.0569	0.4774
17	-0.079136	-0.6621	0.25504
18	0.034584	0.2894	0.386583
19	-0.085181	-0.7127	0.239208
20	-0.033451	-0.2799	0.390201
21	0.010609	0.0888	0.464763
22	-0.258273	-2.1609	0.017065
23	-0.004351	-0.0364	0.485531
24	0.471776	3.9472	9.3e-05
25	0.031631	0.2646	0.396029
26	-0.32572	-2.7252	0.004056
27	-0.034403	-0.2878	0.387162
28	-0.019777	-0.1655	0.434527
29	-0.101229	-0.8469	0.199958
30	0.006736	0.0564	0.47761
31	-0.072407	-0.6058	0.273304
32	-0.092534	-0.7742	0.220712
33	0.022567	0.1888	0.425394
34	-0.163469	-1.3677	0.087894
35	-0.049429	-0.4136	0.340232
36	0.366019	3.0623	0.001558

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.110985	0.9286	0.178152
2	-0.349363	-2.923	0.002333
3	0.327031	2.7361	0.003936
4	-0.236989	-1.9828	0.025658
5	0.250019	2.0918	0.020042
6	-0.013423	-0.1123	0.455451
7	-0.000437	-0.0037	0.498545
8	0.212795	1.7804	0.039677
9	-0.129036	-1.0796	0.142015
10	-0.224711	-1.8801	0.03213
11	0.309507	2.5895	0.005842
12	0.454927	3.8062	0.00015
13	-0.137448	-1.15	0.127035
14	-0.071968	-0.6021	0.274517
15	-0.23002	-1.9245	0.029179
16	0.061166	0.5118	0.305218
17	-0.075328	-0.6302	0.265294
18	-0.151219	-1.2652	0.104999
19	-0.053764	-0.4498	0.327115
20	-0.176666	-1.4781	0.071934
21	0.056614	0.4737	0.318605
22	-0.006933	-0.058	0.476954
23	-0.019431	-0.1626	0.435661
24	0.146323	1.2242	0.112486
25	0.054991	0.4601	0.323441
26	-0.00896	-0.075	0.470228
27	-0.057468	-0.4808	0.316075
28	-0.11385	-0.9525	0.17205
29	-0.017277	-0.1445	0.442742
30	0.0356	0.2978	0.383351
31	-0.104271	-0.8724	0.192988
32	-0.082818	-0.6929	0.24533
33	0.068546	0.5735	0.284073
34	-0.015913	-0.1331	0.447234
35	0.057537	0.4814	0.315872
36	-0.060851	-0.5091	0.306137

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260528915p6tkwclgjz71owv/16qnl1260528813.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260528915p6tkwclgjz71owv/16qnl1260528813.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260528915p6tkwclgjz71owv/2emsh1260528813.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260528915p6tkwclgjz71owv/2emsh1260528813.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 36 ; 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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