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paper - ACF link 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: Sun, 13 Dec 2009 05:15:54 -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/13/t12607066727443py20xtludgw.htm/, Retrieved Sun, 13 Dec 2009 13:17:54 +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/13/t12607066727443py20xtludgw.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 «

1213,8 1245,6 1306,3 1255,8 1257,6 1287,8 1300,4 1320,9 1370,8 1327,3 1320 1345,3 1346,7 1395,4 1462 1491,6 1461,8 1477,9 1490,3 1521,1 1561,9 1552,6 1523,6 1548,3 1552,4 1587 1621,3 1648,7 1641,8 1650,6 1688,6 1670,7 1682,2 1678,9 1650,6 1662,4 1664,5 1683,2 1736,2 1747,6 1749 1759,7 1793,6 1817,4 1858,4 1839,9 1809,1 1877,7 1880,3 1930,9 2039,3 1992,7 1987,8 1984,4 2016,5 2016,7 2064,1 2031,5 2000,3 2057,8 2041,2 2093,2 2158,3 2128,8 2131,9 2170,3 2190,8 2217,7 2254,4 2223,3 2210,5 2250,8 2249,1 2288,6 2329,2 2313,8 2309,8 2345,9 2361,3 2372 2410,4 2398,5 2362,3 2419,1 2421,6 2465 2480,5 2506,1 2506,6 2525,8 2550 2578,3 2807,8 2815,3 2767,7 2815,4 2838,8 2864 2948,6 2922,8 2917,2 2936,8 2993,4 3007,8 3046,3 3011,5 2958,6 3019,8 2998,5 3040,4 3166 3110 3099,2 3150,3 3163,6 3182,6 3244,4 3223,2 3143,6 3217 3182,3 3217,2 3262,5 3227,9 3171,6 3219 3195,4 3221,6 3262,1 3179,5 3133,6 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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.976907	11.7635	0
2	0.955009	11.4998	0
3	0.93532	11.2627	0
4	0.913864	11.0044	0
5	0.89253	10.7475	0
6	0.872822	10.5102	0
7	0.851637	10.2551	0
8	0.831433	10.0118	0
9	0.812907	9.7887	0
10	0.792711	9.5455	0
11	0.773895	9.3189	0
12	0.756269	9.1067	0
13	0.736808	8.8723	0
14	0.718513	8.652	0
15	0.703319	8.4691	0
16	0.68681	8.2703	0
17	0.668775	8.0531	0
18	0.651366	7.8435	0
19	0.632817	7.6201	0
20	0.614054	7.3942	0
21	0.597301	7.1925	0
22	0.578448	6.9654	0
23	0.558534	6.7256	0
24	0.539546	6.497	0
25	0.519473	6.2553	0
26	0.498939	6.008	0
27	0.480607	5.7873	0
28	0.460451	5.5446	0
29	0.439961	5.2978	0
30	0.420352	5.0617	1e-06
31	0.400166	4.8186	2e-06
32	0.379616	4.5712	5e-06
33	0.360658	4.3429	1.3e-05
34	0.340609	4.1015	3.4e-05
35	0.31916	3.8432	9.1e-05
36	0.299977	3.6122	0.000209

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.976907	11.7635	0
2	0.014477	0.1743	0.430928
3	0.037874	0.4561	0.324511
4	-0.046471	-0.5596	0.288312
5	-0.008098	-0.0975	0.461225
6	0.02107	0.2537	0.400038
7	-0.039735	-0.4785	0.316515
8	0.011654	0.1403	0.444295
9	0.02173	0.2617	0.396978
10	-0.041103	-0.4949	0.310693
11	0.020303	0.2445	0.4036
12	0.009643	0.1161	0.453862
13	-0.042193	-0.5081	0.306087
14	0.014081	0.1696	0.432797
15	0.050603	0.6093	0.271625
16	-0.025762	-0.3102	0.378419
17	-0.041071	-0.4946	0.310828
18	-0.008729	-0.1051	0.458214
19	-0.029503	-0.3553	0.361455
20	-0.013591	-0.1637	0.435115
21	0.024166	0.291	0.385734
22	-0.047779	-0.5753	0.282976
23	-0.031561	-0.38	0.352234
24	-0.006858	-0.0826	0.467147
25	-0.029092	-0.3503	0.363304
26	-0.01817	-0.2188	0.413558
27	0.020534	0.2473	0.402528
28	-0.044178	-0.532	0.297779
29	-0.012153	-0.1463	0.441927
30	-0.01266	-0.1524	0.439524
31	-0.02271	-0.2735	0.392441
32	-0.017484	-0.2105	0.416773
33	0.006247	0.0752	0.470069
34	-0.029574	-0.3561	0.361133
35	-0.037682	-0.4537	0.325344
36	0.01583	0.1906	0.424544

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/13/t12607066727443py20xtludgw/1swo01260706553.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/13/t12607066727443py20xtludgw/1swo01260706553.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/13/t12607066727443py20xtludgw/202kv1260706553.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/13/t12607066727443py20xtludgw/202kv1260706553.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

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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