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workshop 9 link 2

*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: Wed, 15 Dec 2010 15:36:18 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/15/t1292427328n2oj91zgoqa3w4r.htm/, Retrieved Wed, 15 Dec 2010 16:35:30 +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/2010/Dec/15/t1292427328n2oj91zgoqa3w4r.htm/},
    year = {2010},
}
@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 = {2010},
    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 «

33 24 24 31 25 28 24 25 16 17 11 12 39 19 14 15 7 12 12 14 9 8 4 7 3 5 0 -2 6 11 9 17 21 21 41 57 65 68 73 71 71 70 69 65 57 57 57 55 65 65 64 60 43 47 40 31 27 24 23 17

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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.00446	0.0343	0.486392
2	0.091565	0.7033	0.242309
3	0.251607	1.9326	0.029043
4	-0.08877	-0.6819	0.249
5	0.130837	1.005	0.159505
6	0.056548	0.4343	0.332809
7	0.097504	0.7489	0.228433
8	-0.07994	-0.614	0.270777
9	0.009765	0.075	0.470232
10	-0.087986	-0.6758	0.250894
11	-0.049134	-0.3774	0.353615
12	0.044574	0.3424	0.36664
13	0.04089	0.3141	0.377285
14	-0.000112	-9e-04	0.499658
15	-0.119828	-0.9204	0.180552
16	-0.019919	-0.153	0.439459
17	-0.015763	-0.1211	0.45202
18	-0.200445	-1.5396	0.064496
19	-0.014591	-0.1121	0.455573
20	-0.088158	-0.6772	0.250477
21	-0.297936	-2.2885	0.012854
22	-0.007384	-0.0567	0.47748
23	-0.007902	-0.0607	0.475904
24	-0.109299	-0.8395	0.202276
25	-0.031676	-0.2433	0.404306
26	-0.01711	-0.1314	0.447944
27	-0.136882	-1.0514	0.148678
28	-0.035937	-0.276	0.391743
29	0.010447	0.0802	0.468157
30	-0.016028	-0.1231	0.451217
31	0.047399	0.3641	0.35855
32	-0.046746	-0.3591	0.360416
33	-0.021646	-0.1663	0.434258
34	-0.027472	-0.211	0.416801
35	-0.076459	-0.5873	0.279624
36	0.12954	0.995	0.161897
37	-0.013415	-0.103	0.459139
38	0.034264	0.2632	0.396663
39	0.086837	0.667	0.253683
40	-0.178777	-1.3732	0.087442
41	0.081036	0.6224	0.268023
42	0.020834	0.16	0.436702
43	-0.00575	-0.0442	0.482462
44	0.01594	0.1224	0.451484
45	0.008227	0.0632	0.474915
46	0.072531	0.5571	0.289776
47	-0.067808	-0.5208	0.302212
48	0.036552	0.2808	0.389938

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.00446	0.0343	0.486392
2	0.091547	0.7032	0.242352
3	0.252952	1.943	0.028398
4	-0.100608	-0.7728	0.221367
5	0.091206	0.7006	0.243164
6	0.010221	0.0785	0.468845
7	0.137249	1.0542	0.148038
8	-0.169642	-1.303	0.098811
9	0.006673	0.0513	0.479648
10	-0.15476	-1.1887	0.119653
11	0.048002	0.3687	0.356832
12	-0.008947	-0.0687	0.47272
13	0.153402	1.1783	0.121704
14	-0.058151	-0.4467	0.328376
15	-0.088412	-0.6791	0.249864
16	-0.079347	-0.6095	0.272275
17	0.077461	0.595	0.277062
18	-0.243184	-1.8679	0.03337
19	-0.003121	-0.024	0.490477
20	-0.129448	-0.9943	0.162066
21	-0.15559	-1.1951	0.118413
22	-0.023043	-0.177	0.430058
23	0.175104	1.345	0.091886
24	-0.032695	-0.2511	0.40129
25	-0.050346	-0.3867	0.35018
26	-0.056868	-0.4368	0.33192
27	-0.047402	-0.3641	0.358541
28	-0.055138	-0.4235	0.336726
29	-0.033329	-0.256	0.399419
30	0.01436	0.1103	0.456271
31	0.039832	0.306	0.380359
32	-0.045268	-0.3477	0.364646
33	0.009095	0.0699	0.472272
34	0.020242	0.1555	0.438485
35	-0.139773	-1.0736	0.143682
36	0.044997	0.3456	0.365424
37	-0.047139	-0.3621	0.359294
38	0.079321	0.6093	0.272341
39	-0.095306	-0.7321	0.233515
40	-0.14872	-1.1423	0.128963
41	0.026295	0.202	0.420315
42	-0.029655	-0.2278	0.410302
43	-0.011819	-0.0908	0.463985
44	-0.024442	-0.1877	0.425863
45	-0.027682	-0.2126	0.416174
46	0.055262	0.4245	0.336382
47	-0.050234	-0.3859	0.350497
48	-0.059255	-0.4551	0.325336

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292427328n2oj91zgoqa3w4r/1wu6v1292427376.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292427328n2oj91zgoqa3w4r/1wu6v1292427376.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292427328n2oj91zgoqa3w4r/2wu6v1292427376.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292427328n2oj91zgoqa3w4r/2wu6v1292427376.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; 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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