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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: Thu, 03 Dec 2009 12:45:01 -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/03/t1259869608b0rzg5t3le8grr9.htm/, Retrieved Thu, 03 Dec 2009 20:46:51 +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/03/t1259869608b0rzg5t3le8grr9.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 «

1915 1843 1761 2858 3968 5061 4661 4269 3857 3568 3274 2987 1683 1381 1071 2772 4485 6181 5479 4782 4067 3489 2903 2330 1736 1483 1242 2334 3423 4523 3986 3462 2908 2575 2237 1904 1610 1251 941 2450 3946 5409 4741 4069 3539 3189 2960 2704 1697 1598 1456 2316 3083 4158 3469 2892 2578 2233 1947 2049

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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.378944	2.5979	0.006243
2	-0.016728	-0.1147	0.454594
3	-0.217138	-1.4886	0.071633
4	-0.1574	-1.0791	0.14303
5	-0.075375	-0.5167	0.30388
6	-0.024205	-0.1659	0.434458
7	-0.007608	-0.0522	0.479313
8	0.061019	0.4183	0.338807
9	0.229631	1.5743	0.061066
10	0.037821	0.2593	0.398271
11	-0.294611	-2.0198	0.024565
12	-0.481752	-3.3027	0.000918
13	-0.305566	-2.0949	0.0208
14	-0.053357	-0.3658	0.358078
15	0.133905	0.918	0.181651
16	0.0508	0.3483	0.364597
17	-0.048909	-0.3353	0.369443
18	-0.09741	-0.6678	0.25376
19	0.025798	0.1769	0.430187
20	0.017885	0.1226	0.451468
21	-0.063574	-0.4358	0.332474
22	-0.022996	-0.1577	0.437704
23	0.199322	1.3665	0.089144
24	0.244415	1.6756	0.050226
25	0.239198	1.6399	0.053856
26	0.044989	0.3084	0.37956
27	-0.156906	-1.0757	0.143777
28	-0.10063	-0.6899	0.246829
29	0.042907	0.2942	0.384967
30	0.08579	0.5881	0.279625
31	-0.00819	-0.0562	0.47773
32	0.021346	0.1463	0.44214
33	0.041714	0.286	0.388077
34	0.038035	0.2608	0.39771
35	-0.054233	-0.3718	0.355856
36	-0.219679	-1.506	0.069374

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.378944	2.5979	0.006243
2	-0.187209	-1.2834	0.102814
3	-0.167803	-1.1504	0.127899
4	-0.005994	-0.0411	0.483697
5	-0.043037	-0.295	0.384629
6	-0.039921	-0.2737	0.392764
7	-0.02264	-0.1552	0.438658
8	0.062773	0.4304	0.334454
9	0.209493	1.4362	0.078783
10	-0.17527	-1.2016	0.117772
11	-0.299335	-2.0521	0.022875
12	-0.261467	-1.7925	0.039743
13	-0.075549	-0.5179	0.303466
14	-0.057968	-0.3974	0.346432
15	-0.007792	-0.0534	0.478811
16	-0.157394	-1.079	0.143039
17	-0.141022	-0.9668	0.169296
18	-0.208923	-1.4323	0.079337
19	0.036059	0.2472	0.402911
20	0.023268	0.1595	0.436972
21	-0.047201	-0.3236	0.37384
22	-0.073276	-0.5024	0.308882
23	0.056273	0.3858	0.350698
24	-0.133353	-0.9142	0.182634
25	0.101764	0.6977	0.244414
26	-0.01792	-0.1229	0.451372
27	-0.130599	-0.8953	0.187584
28	-0.109553	-0.7511	0.228181
29	-0.068605	-0.4703	0.320146
30	-0.055151	-0.3781	0.35353
31	-0.067478	-0.4626	0.32289
32	-0.038549	-0.2643	0.396361
33	0.004832	0.0331	0.486857
34	-0.079242	-0.5433	0.29476
35	-0.028806	-0.1975	0.42215
36	-0.103813	-0.7117	0.240082

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259869608b0rzg5t3le8grr9/130z71259869498.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259869608b0rzg5t3le8grr9/130z71259869498.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259869608b0rzg5t3le8grr9/2c5fu1259869498.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259869608b0rzg5t3le8grr9/2c5fu1259869498.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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