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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, 04 Dec 2009 08:39:29 -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/04/t1259941209u2y2ciq2wxu272b.htm/, Retrieved Fri, 04 Dec 2009 16:40:11 +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/04/t1259941209u2y2ciq2wxu272b.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 «

1258 1199 1158 1427 934 709 1186 986 1033 1257 1105 1179 1092 1092 1087 2028 2039 2010 754 760 715 855 971 815 915 843 761 1858 2968 4061 3661 3269 2857 2568 2274 1987 683 381 71 1772 3485 5181 4479 3782 3067 2489 1903 1330 736 483 242 1334 2423 3523 2986 2462 1908 1575 1237 904

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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.474751	3.6466	0.000282
2	0.126631	0.9727	0.167344
3	-0.343845	-2.6411	0.00528
4	-0.31412	-2.4128	0.009478
5	-0.300024	-2.3045	0.012365
6	-0.167872	-1.2895	0.101137
7	-0.238525	-1.8321	0.035989
8	-0.218314	-1.6769	0.049426
9	-0.250857	-1.9269	0.029408
10	0.042441	0.326	0.372791
11	0.284619	2.1862	0.01639
12	0.626038	4.8087	5e-06
13	0.402704	3.0932	0.001512
14	0.147776	1.1351	0.130465
15	-0.23345	-1.7932	0.039036
16	-0.200949	-1.5435	0.064026
17	-0.199719	-1.5341	0.065179
18	-0.046789	-0.3594	0.360291
19	-0.077077	-0.592	0.278044
20	-0.063025	-0.4841	0.315052
21	-0.172023	-1.3213	0.095746
22	-0.057666	-0.4429	0.329714
23	0.005407	0.0415	0.483506
24	0.246403	1.8927	0.031656
25	0.176245	1.3538	0.090487
26	0.127331	0.9781	0.166021
27	-0.07125	-0.5473	0.293124
28	-0.054036	-0.4151	0.339802
29	-0.043671	-0.3354	0.369239
30	-0.032239	-0.2476	0.40264
31	-0.004258	-0.0327	0.48701
32	0.01056	0.0811	0.467814
33	-0.062251	-0.4782	0.317152
34	-0.059509	-0.4571	0.324641
35	-0.079946	-0.6141	0.270762
36	0.025874	0.1987	0.421575

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.474751	3.6466	0.000282
2	-0.127493	-0.9793	0.165717
3	-0.460749	-3.5391	0.000395
4	0.088945	0.6832	0.248578
5	-0.132081	-1.0145	0.157235
6	-0.207045	-1.5903	0.058551
7	-0.283866	-2.1804	0.016614
8	-0.236934	-1.8199	0.036922
9	-0.350231	-2.6902	0.004637
10	-0.040805	-0.3134	0.377531
11	0.012469	0.0958	0.462013
12	0.279921	2.1501	0.017828
13	-0.15567	-1.1957	0.118294
14	-0.109721	-0.8428	0.201376
15	-0.028652	-0.2201	0.413283
16	0.120924	0.9288	0.178379
17	-0.019076	-0.1465	0.442002
18	0.059571	0.4576	0.324471
19	0.180213	1.3842	0.085749
20	0.130543	1.0027	0.160046
21	0.013863	0.1065	0.45778
22	0.049696	0.3817	0.352018
23	-0.090874	-0.698	0.243953
24	-0.045229	-0.3474	0.36476
25	-0.072828	-0.5594	0.289002
26	0.004038	0.031	0.48768
27	0.047055	0.3614	0.359533
28	-0.072517	-0.557	0.289813
29	0.00641	0.0492	0.480448
30	-0.282204	-2.1676	0.017116
31	0.005929	0.0455	0.481914
32	-0.029335	-0.2253	0.411252
33	-0.107495	-0.8257	0.206155
34	-0.010839	-0.0833	0.466964
35	0.026236	0.2015	0.420493
36	-0.071621	-0.5501	0.292152

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259941209u2y2ciq2wxu272b/14d911259941167.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259941209u2y2ciq2wxu272b/14d911259941167.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259941209u2y2ciq2wxu272b/2470r1259941167.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259941209u2y2ciq2wxu272b/2470r1259941167.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 1 ; 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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