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Paper

*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: Sun, 12 Dec 2010 14:26:53 +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/12/t1292164323xeurkypxozdnsi5.htm/, Retrieved Sun, 12 Dec 2010 15:32:05 +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/12/t1292164323xeurkypxozdnsi5.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 «

25.2609 16.8622 13.3181 12.5621 14.2754 12.2961 10.0871 13.5117 13.9921 13.6932 14.4211 15.3397 16.5182 15.2809 15.6204 15.5698 15.9458 16.4063 17.55 17.0353 16.0591 16.3643 14.6527 13.4664 13.3266 13.1823 12.113 13.354 13.4537 13.2715 13.1959 13.5542 12.124 10.967 10.9201 12.5971 14.3177 14.2471 16.0926 17.1334 16.5866 16.361 15.8494 15.5932 16.6387 16.8312 16.5044 16.5556 16.7469 15.9543 15.5888 14.3945 13.8889 12.9999 14.1022 19.6245 24.7658 25.9843 22.9635 19.6288 17.3363 13.311 14.6359 15.834 16.2415 15.9808 16.9726 16.8708 16.923 18.1138 16.7716 14.0299 13.822 14.2537 14.3985 15.2454 15.6683 16.1721 14.8679 14.1948 14.7056 15.3819 15.5001 14.7886 14.563 15.5528 15.9781 15.5139 15.3603 15.0512 14.7874 14.9624 13.9188 14.5146 13.7115 12.0738 12.5688 12.2547 11.8741 13.0261 13.8681 14.2137 14.4743 13.9764 13.1558 13.0991 13.7831 13.2546 13.3426 13.5011 12.8245 13.6596 13.8754 12.9011 11.871 12 etc...

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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.351142	6.0311	0
2	0.158895	2.7291	0.003366
3	0.014011	0.2406	0.405001
4	-0.101345	-1.7407	0.041394
5	-0.138862	-2.385	0.008854
6	-0.228436	-3.9235	5.4e-05
7	-0.116848	-2.0069	0.022835
8	-0.076127	-1.3075	0.096025
9	-0.056972	-0.9785	0.164308
10	0.072424	1.2439	0.107258
11	0.076207	1.3089	0.095794
12	0.005353	0.0919	0.463406
13	-0.108757	-1.868	0.03138
14	-0.083871	-1.4405	0.075389
15	-0.069778	-1.1985	0.115848
16	-0.157218	-2.7003	0.003664
17	-0.123882	-2.1278	0.017093
18	-0.063013	-1.0823	0.140004
19	-0.010163	-0.1746	0.430775
20	-0.007535	-0.1294	0.448557
21	0.046494	0.7986	0.212595
22	0.091562	1.5726	0.058437
23	0.104277	1.791	0.037158
24	0.019653	0.3375	0.367972
25	0.151231	2.5975	0.004931
26	0.061973	1.0644	0.144005
27	0.026822	0.4607	0.322684
28	0.011376	0.1954	0.422615
29	-0.030325	-0.5208	0.301431
30	0.006397	0.1099	0.456292
31	-0.075982	-1.305	0.096448
32	-0.070139	-1.2047	0.114646
33	-0.01644	-0.2824	0.38893
34	-0.012045	-0.2069	0.41812
35	0.0647	1.1113	0.133682
36	0.06689	1.1489	0.12577
37	0.061742	1.0604	0.144904
38	-0.015045	-0.2584	0.398135
39	-0.077787	-1.336	0.091283
40	-0.041745	-0.717	0.236972
41	-0.080243	-1.3782	0.084589
42	-0.063488	-1.0904	0.138205
43	-0.078095	-1.3413	0.090424
44	-0.024382	-0.4188	0.337841
45	0.030576	0.5252	0.299931
46	0.06528	1.1212	0.131554
47	0.107132	1.8401	0.033382
48	0.066892	1.1489	0.125763

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.351142	6.0311	0
2	0.0406	0.6973	0.243071
3	-0.06144	-1.0553	0.146083
4	-0.108109	-1.8568	0.032166
5	-0.074497	-1.2795	0.100859
6	-0.159839	-2.7453	0.003208
7	0.02437	0.4186	0.337918
8	-0.022529	-0.3869	0.349539
9	-0.047299	-0.8124	0.208613
10	0.084416	1.4499	0.074077
11	0.005057	0.0869	0.465419
12	-0.095451	-1.6394	0.051096
13	-0.138894	-2.3856	0.008842
14	-0.010888	-0.187	0.425893
15	-0.024009	-0.4124	0.340183
16	-0.125665	-2.1584	0.015853
17	-0.056279	-0.9666	0.167261
18	-0.025659	-0.4407	0.329872
19	-0.028992	-0.498	0.309444
20	-0.062227	-1.0688	0.14302
21	-0.001282	-0.022	0.491223
22	0.001298	0.0223	0.491112
23	0.045714	0.7852	0.216492
24	-0.067297	-1.1559	0.124337
25	0.14787	2.5398	0.005803
26	-0.044396	-0.7625	0.223179
27	0.012625	0.2168	0.414239
28	0.014124	0.2426	0.404246
29	-0.041032	-0.7047	0.240763
30	0.015348	0.2636	0.396134
31	-0.046813	-0.804	0.211011
32	-0.052426	-0.9004	0.18431
33	-0.00179	-0.0307	0.48775
34	0.019215	0.33	0.370805
35	0.05711	0.9809	0.163723
36	0.023332	0.4007	0.344453
37	0.001036	0.0178	0.492911
38	-0.031358	-0.5386	0.29529
39	-0.039663	-0.6812	0.248129
40	0.009711	0.1668	0.433823
41	-0.003534	-0.0607	0.475822
42	0.004145	0.0712	0.471648
43	-0.036577	-0.6282	0.265171
44	-0.014228	-0.2444	0.403558
45	0.009802	0.1684	0.433209
46	0.027122	0.4658	0.320839
47	0.03547	0.6092	0.271423
48	-0.027565	-0.4734	0.318122

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/12/t1292164323xeurkypxozdnsi5/1ap411292164010.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/12/t1292164323xeurkypxozdnsi5/1ap411292164010.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/12/t1292164323xeurkypxozdnsi5/2ap411292164010.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/12/t1292164323xeurkypxozdnsi5/2ap411292164010.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 48 ; par2 = 1 ; 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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