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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, 18 Dec 2009 07:21:47 -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/18/t1261146161iua8qvkfkrtg1ul.htm/, Retrieved Fri, 18 Dec 2009 15:22:43 +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/2009/Dec/18/t1261146161iua8qvkfkrtg1ul.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 «

97.4 97 105.4 102.7 98.1 104.5 87.4 89.9 109.8 111.7 98.6 96.9 95.1 97 112.7 102.9 97.4 111.4 87.4 96.8 114.1 110.3 103.9 101.6 94.6 95.9 104.7 102.8 98.1 113.9 80.9 95.7 113.2 105.9 108.8 102.3 99 100.7 115.5 100.7 109.9 114.6 85.4 100.5 114.8 116.5 112.9 102 106 105.3 118.8 106.1 109.3 117.2 92.5 104.2 112.5 122.4 113.3 100 110.7 112.8 109.8 117.3 109.1 115.9 96 99.8 116.8 115.7 99.4 94.3 91 93.2 103.1 94.1 91.8 102.7 82.6 89.1 104.5

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	-0.604055	-4.9812	2e-06
2	0.017621	0.1453	0.442451
3	0.341349	2.8148	0.003189
4	-0.34228	-2.8225	0.003122
5	0.133257	1.0989	0.137851
6	0.139725	1.1522	0.126636
7	-0.265562	-2.1899	0.015984
8	0.169908	1.4011	0.082866
9	-0.041029	-0.3383	0.368076
10	-0.094623	-0.7803	0.218967
11	0.197665	1.63	0.053864
12	-0.222061	-1.8312	0.035729
13	0.087346	0.7203	0.236912
14	0.009825	0.081	0.467832
15	0.037388	0.3083	0.379393
16	-0.117806	-0.9715	0.167383
17	0.119245	0.9833	0.164469
18	0.001122	0.0093	0.496323
19	-0.124287	-1.0249	0.154522
20	0.112924	0.9312	0.177524
21	0.071693	0.5912	0.278174
22	-0.296804	-2.4475	0.008486
23	0.400397	3.3018	0.000767
24	-0.264292	-2.1794	0.016384
25	-0.028403	-0.2342	0.40776
26	0.260377	2.1471	0.017676
27	-0.249444	-2.057	0.021764
28	0.062524	0.5156	0.303907
29	0.111074	0.9159	0.181468
30	-0.181723	-1.4985	0.069312
31	0.116841	0.9635	0.169356
32	0.040561	0.3345	0.369527
33	-0.171584	-1.4149	0.080828
34	0.190529	1.5711	0.060396
35	-0.159977	-1.3192	0.095762
36	0.064552	0.5323	0.298124

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.604055	-4.9812	2e-06
2	-0.546767	-4.5088	1.3e-05
3	0.061844	0.51	0.305859
4	0.024991	0.2061	0.418671
5	0.001921	0.0158	0.493703
6	0.154039	1.2702	0.104165
7	0.013135	0.1083	0.457032
8	-0.054326	-0.448	0.327796
9	-0.153997	-1.2699	0.104226
10	-0.153264	-1.2638	0.1053
11	0.087753	0.7236	0.235889
12	-0.056174	-0.4632	0.322343
13	-0.065117	-0.537	0.296522
14	-0.171043	-1.4105	0.081481
15	0.186749	1.54	0.064104
16	-0.023196	-0.1913	0.424437
17	-0.023107	-0.1905	0.424725
18	0.126509	1.0432	0.150271
19	0.008451	0.0697	0.472324
20	-0.131884	-1.0875	0.140318
21	0.084608	0.6977	0.243873
22	-0.197526	-1.6288	0.053985
23	0.219909	1.8134	0.037091
24	-0.016602	-0.1369	0.445757
25	-0.028627	-0.2361	0.407047
26	-0.023749	-0.1958	0.422661
27	0.170986	1.41	0.081551
28	-0.039049	-0.322	0.374216
29	-0.083692	-0.6901	0.246227
30	-0.00975	-0.0804	0.468077
31	0.033533	0.2765	0.391493
32	-0.028937	-0.2386	0.406059
33	0.028871	0.2381	0.406269
34	-0.037933	-0.3128	0.377693
35	-0.01475	-0.1216	0.451774
36	-0.093236	-0.7688	0.222323

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/18/t1261146161iua8qvkfkrtg1ul/10ut91261146104.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/18/t1261146161iua8qvkfkrtg1ul/10ut91261146104.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/18/t1261146161iua8qvkfkrtg1ul/25vze1261146104.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/18/t1261146161iua8qvkfkrtg1ul/25vze1261146104.ps (open in new window)

Parameters (Session):

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

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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