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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: Tue, 24 Nov 2009 13:12:27 -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/Nov/24/t1259093992pz1toz22z0cak6o.htm/, Retrieved Tue, 24 Nov 2009 21:19:54 +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/Nov/24/t1259093992pz1toz22z0cak6o.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 «

153.3 154.5 155.2 156.9 157 157.4 157.2 157.5 158 158.5 159 159.3 160 160.8 161.9 162.5 162.7 162.8 162.9 163 164 164.7 164.8 164.9 165 165.8 166.1 167.2 167.7 168.3 168.6 168.9 169.1 169.5 169.6 169.7 169.8 170.4 170.9 171.9 171.9 172 172 172.4 173 173.7 173.8 173.8 173.9 174.6 175 175.9 176 175.1 175.6 175.9 176.7 176.1 176.1 176.2 176.3 177.8 178.5 179.4 179.5 179.6 179.7 179.7 179.8 179.9 180.2 180.4 180.4 181.3 181.9 182.5 182.7 183.1 183.6 183.7 183.8 183.9 184.1 184.4 184.5 185.9 186.6 187.6 187.8 187.9 188 188.3 188.4 188.5 188.5 188.6 188.6 189.4 190 191.9 192.5 193 193.5 193.9 194.2 194.9 194.9 194.9 194.9 195.5 196 196.2 196.2 196.2 196.2 197 197.7 198 198.2 198.5 198.6 199.5 200 201.3 202.2 202.9 203.5 203.5 204 204.1 204.3 204.5 204.8 205.1 205.7 206.5 206.9 207.1 207.8 208 208.5 208.6 209 209.1 209.7 209.8 209.9 210 210.8 211.4 211.7 212 212.2 2 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	0.984886	14.7404	0
2	0.970081	14.5188	0
3	0.955306	14.2977	0
4	0.941097	14.0851	0
5	0.926963	13.8735	0
6	0.91281	13.6617	0
7	0.898473	13.4471	0
8	0.884053	13.2313	0
9	0.869678	13.0161	0
10	0.85532	12.8013	0
11	0.841177	12.5896	0
12	0.826935	12.3764	0
13	0.812855	12.1657	0
14	0.799008	11.9585	0
15	0.785405	11.7549	0
16	0.771846	11.5519	0
17	0.758429	11.3511	0
18	0.745096	11.1516	0
19	0.732272	10.9596	0
20	0.719623	10.7703	0
21	0.70717	10.5839	0
22	0.694994	10.4017	0
23	0.682691	10.2176	0
24	0.670379	10.0333	0
25	0.657874	9.8462	0
26	0.645415	9.6597	0
27	0.63292	9.4727	0
28	0.620681	9.2895	0
29	0.60849	9.107	0
30	0.596318	8.9249	0
31	0.58411	8.7422	0
32	0.571897	8.5594	0
33	0.559601	8.3753	0
34	0.547357	8.1921	0
35	0.535024	8.0075	0
36	0.522666	7.8226	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.984886	14.7404	0
2	0.002685	0.0402	0.483991
3	-0.0064	-0.0958	0.461891
4	0.01132	0.1694	0.432811
5	-0.004443	-0.0665	0.473523
6	-0.007869	-0.1178	0.453174
7	-0.0132	-0.1976	0.421786
8	-0.010363	-0.1551	0.438444
9	-0.006193	-0.0927	0.463117
10	-0.007327	-0.1097	0.456388
11	-0.000704	-0.0105	0.495798
12	-0.010813	-0.1618	0.435793
13	-0.002341	-0.035	0.486043
14	0.000369	0.0055	0.497797
15	0.000545	0.0082	0.496747
16	-0.005857	-0.0877	0.465113
17	-0.002615	-0.0391	0.484407
18	-0.004418	-0.0661	0.473669
19	0.009466	0.1417	0.443734
20	-0.001191	-0.0178	0.492896
21	-0.000667	-0.01	0.496024
22	0.002608	0.039	0.484452
23	-0.010939	-0.1637	0.435047
24	-0.007437	-0.1113	0.455734
25	-0.013623	-0.2039	0.419313
26	-0.006408	-0.0959	0.46184
27	-0.008701	-0.1302	0.448252
28	0.000635	0.0095	0.496215
29	-0.005436	-0.0814	0.467613
30	-0.006854	-0.1026	0.459197
31	-0.00811	-0.1214	0.45175
32	-0.007328	-0.1097	0.45638
33	-0.010208	-0.1528	0.439352
34	-0.005986	-0.0896	0.464345
35	-0.010623	-0.159	0.436909
36	-0.008726	-0.1306	0.448105

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259093992pz1toz22z0cak6o/1zsac1259093545.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259093992pz1toz22z0cak6o/1zsac1259093545.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259093992pz1toz22z0cak6o/28k4q1259093545.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259093992pz1toz22z0cak6o/28k4q1259093545.ps (open in new window)

Parameters (Session):

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

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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