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workshop 9

*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 14:08:26 -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/t1259874604evctyw1fpart4tf.htm/, Retrieved Thu, 03 Dec 2009 22:10:06 +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/t1259874604evctyw1fpart4tf.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 «

283.042 276.687 277.915 277.128 277.103 275.037 270.150 267.140 264.993 287.259 291.186 292.300 288.186 281.477 282.656 280.190 280.408 276.836 275.216 274.352 271.311 289.802 290.726 292.300 278.506 269.826 265.861 269.034 264.176 255.198 253.353 246.057 235.372 258.556 260.993 254.663 250.643 243.422 247.105 248.541 245.039 237.080 237.085 225.554 226.839 247.934 248.333 246.969 245.098 246.263 255.765 264.319 268.347 273.046 273.963 267.430 271.993 292.710 295.881 293.299

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	0.880317	6.8189	0
2	0.739708	5.7298	0
3	0.632905	4.9025	4e-06
4	0.581352	4.5031	1.6e-05
5	0.560501	4.3416	2.8e-05
6	0.507633	3.9321	0.00011
7	0.415039	3.2149	0.001051
8	0.307304	2.3804	0.010244
9	0.241496	1.8706	0.033139
10	0.201046	1.5573	0.06233
11	0.210726	1.6323	0.053929
12	0.196259	1.5202	0.066855
13	0.060597	0.4694	0.32025
14	-0.066969	-0.5187	0.302924
15	-0.161447	-1.2506	0.107974
16	-0.192354	-1.49	0.070736
17	-0.190626	-1.4766	0.072509
18	-0.216021	-1.6733	0.049739
19	-0.265469	-2.0563	0.022055
20	-0.332843	-2.5782	0.006202
21	-0.357947	-2.7726	0.003698
22	-0.356843	-2.7641	0.003785
23	-0.315414	-2.4432	0.008759
24	-0.30261	-2.344	0.011204
25	-0.364663	-2.8247	0.003208
26	-0.413815	-3.2054	0.001081
27	-0.424644	-3.2893	0.000842
28	-0.383556	-2.971	0.002132
29	-0.334496	-2.591	0.005999
30	-0.298198	-2.3098	0.012177
31	-0.28065	-2.1739	0.016834
32	-0.275432	-2.1335	0.018492
33	-0.231801	-1.7955	0.038804
34	-0.178464	-1.3824	0.08599
35	-0.117538	-0.9104	0.183116
36	-0.080531	-0.6238	0.267565

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.880317	6.8189	0
2	-0.156634	-1.2133	0.114889
3	0.080257	0.6217	0.268258
4	0.158769	1.2298	0.111782
5	0.082273	0.6373	0.263181
6	-0.135662	-1.0508	0.148775
7	-0.129815	-1.0055	0.159338
8	-0.089229	-0.6912	0.246063
9	0.077585	0.601	0.275063
10	-0.042903	-0.3323	0.370402
11	0.190233	1.4735	0.072916
12	-0.086686	-0.6715	0.252249
13	-0.503969	-3.9037	0.000121
14	0.078924	0.6113	0.271641
15	-0.031709	-0.2456	0.403407
16	-0.013527	-0.1048	0.45845
17	0.046112	0.3572	0.361104
18	-0.042318	-0.3278	0.372104
19	0.053416	0.4138	0.340262
20	-0.157758	-1.222	0.113246
21	0.039117	0.303	0.38147
22	0.023844	0.1847	0.427044
23	-0.085442	-0.6618	0.255306
24	-0.005491	-0.0425	0.483109
25	-0.092093	-0.7133	0.239199
26	0.007983	0.0618	0.47545
27	0.071056	0.5504	0.292045
28	-0.087627	-0.6788	0.249952
29	-0.004573	-0.0354	0.485931
30	0.069424	0.5378	0.296367
31	0.010168	0.0788	0.468742
32	0.00635	0.0492	0.480468
33	0.046069	0.3568	0.361228
34	-0.013623	-0.1055	0.458157
35	-0.130146	-1.0081	0.158725
36	0.046274	0.3584	0.360637

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259874604evctyw1fpart4tf/1otrt1259874504.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259874604evctyw1fpart4tf/1otrt1259874504.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259874604evctyw1fpart4tf/2s5oh1259874504.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259874604evctyw1fpart4tf/2s5oh1259874504.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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