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WS 8: ACF (Lambda 0.1 + D 1 + d 2)

*Unverified author*

R Software Module: /rwasp_autocorrelation.wasp (opens new window with default values)

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Thu, 26 Nov 2009 08:36:56 -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/26/t12592498989yad82yh26mg1gw.htm/, Retrieved Thu, 26 Nov 2009 16:38:20 +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/26/t12592498989yad82yh26mg1gw.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 «

79.8 83.4 113.6 112.9 104 109.9 99 106.3 128.9 111.1 102.9 130 87 87.5 117.6 103.4 110.8 112.6 102.5 112.4 135.6 105.1 127.7 137 91 90.5 122.4 123.3 124.3 120 118.1 119 142.7 123.6 129.6 151.6 110.4 99.2 130.5 136.2 129.7 128 121.6 135.8 143.8 147.5 136.2 156.6 123.3 104.5 139.8 136.5 112.1 118.5 94.4 102.3 111.4 99.2 87.8 115.8

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	-0.673528	-4.5681	1.8e-05
2	0.122165	0.8286	0.205814
3	0.217108	1.4725	0.073848
4	-0.250242	-1.6972	0.048206
5	0.057323	0.3888	0.349616
6	0.218274	1.4804	0.072791
7	-0.361027	-2.4486	0.009106
8	0.304592	2.0658	0.022251
9	-0.180698	-1.2256	0.113302
10	0.040439	0.2743	0.392551
11	0.079309	0.5379	0.29662
12	-0.115072	-0.7805	0.21956
13	0.033313	0.2259	0.411126
14	0.055712	0.3779	0.353637
15	-0.039627	-0.2688	0.394657
16	-0.058403	-0.3961	0.346928
17	0.106357	0.7214	0.237172
18	-0.036127	-0.245	0.403764
19	-0.057526	-0.3902	0.34911
20	0.04609	0.3126	0.378
21	0.114092	0.7738	0.221501
22	-0.319363	-2.166	0.017764
23	0.369209	2.5041	0.007943
24	-0.205593	-1.3944	0.084947
25	-0.030845	-0.2092	0.417607
26	0.137304	0.9312	0.178295
27	-0.068916	-0.4674	0.321207
28	-0.074323	-0.5041	0.308304
29	0.20744	1.4069	0.083085
30	-0.256121	-1.7371	0.044531
31	0.187298	1.2703	0.10518
32	-0.081763	-0.5545	0.290947
33	-0.031538	-0.2139	0.415786
34	0.119048	0.8074	0.21179
35	-0.079925	-0.5421	0.29519
36	-0.062092	-0.4211	0.337811

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.673528	-4.5681	1.8e-05
2	-0.606696	-4.1148	7.9e-05
3	-0.171804	-1.1652	0.124966
4	-0.034477	-0.2338	0.408075
5	-0.180069	-1.2213	0.114099
6	0.184064	1.2484	0.109104
7	0.016482	0.1118	0.45574
8	0.095766	0.6495	0.259618
9	-0.152149	-1.0319	0.153752
10	-0.119647	-0.8115	0.210633
11	-0.004574	-0.031	0.487693
12	-0.040249	-0.273	0.393044
13	-0.060396	-0.4096	0.341991
14	-0.10928	-0.7412	0.231177
15	0.17322	1.1748	0.123053
16	-0.08361	-0.5671	0.286713
17	-0.104143	-0.7063	0.241771
18	0.076744	0.5205	0.302604
19	0.072047	0.4886	0.313707
20	-0.136371	-0.9249	0.179919
21	0.16443	1.1152	0.135275
22	-0.122565	-0.8313	0.205056
23	-0.057577	-0.3905	0.348982
24	-0.005736	-0.0389	0.484568
25	-0.040215	-0.2727	0.393133
26	-0.09288	-0.6299	0.265925
27	0.021362	0.1449	0.442719
28	0.060869	0.4128	0.340824
29	0.040171	0.2725	0.393246
30	0.05174	0.3509	0.363625
31	-0.025733	-0.1745	0.431107
32	-0.150469	-1.0205	0.156407
33	-0.15491	-1.0507	0.149453
34	-0.007878	-0.0534	0.47881
35	0.075061	0.5091	0.306562
36	0.050563	0.3429	0.366605

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/26/t12592498989yad82yh26mg1gw/1jfv51259249815.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t12592498989yad82yh26mg1gw/1jfv51259249815.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t12592498989yad82yh26mg1gw/2jlvf1259249815.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t12592498989yad82yh26mg1gw/2jlvf1259249815.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = -2.0 ; par3 = 2 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 36 ; par2 = 0.1 ; par3 = 2 ; 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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