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workshop 9 - tutorial 7

*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, 03 Dec 2010 10:18:34 +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/03/t1291371406735324hftueingr.htm/, Retrieved Fri, 03 Dec 2010 11:16:48 +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/03/t1291371406735324hftueingr.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 «

1579 2146 2462 3695 4831 5134 6250 5760 6249 2917 1741 2359 1511 2059 2635 2867 4403 5720 4502 5749 5627 2846 1762 2429 1169 2154 2249 2687 4359 5382 4459 6398 4596 3024 1887 2070 1351 2218 2461 3028 4784 4975 4607 6249 4809 3157 1910 2228 1594 2467 2222 3607 4685 4962 5770 5480 5000 3228 1993 2288 1580 2111 2192 3601 4665 4876 5813 5589 5331 3075 2002 2306 1507 1992 2487 3490 4647 5594 5611 5788 6204 3013 1931 2549 1504 2090 2702 2939 4500 6208 6415 5657 5964 3163 1997 2422

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	-0.227011	-2.0806	0.020259
2	0.041993	0.3849	0.350651
3	0.29318	2.687	0.004344
4	-0.068264	-0.6256	0.266621
5	0.075001	0.6874	0.246864
6	0.195769	1.7943	0.038185
7	-0.126132	-1.156	0.125475
8	0.046289	0.4242	0.336236
9	0.206586	1.8934	0.030874
10	-0.036415	-0.3338	0.3697
11	0.051705	0.4739	0.318405
12	0.075029	0.6877	0.246783
13	-0.122177	-1.1198	0.133001
14	0.266087	2.4387	0.008423
15	-0.092346	-0.8464	0.199876
16	-0.070394	-0.6452	0.260286
17	0.13605	1.2469	0.107946
18	-0.060963	-0.5587	0.288916
19	-0.153578	-1.4076	0.081475
20	0.07607	0.6972	0.243802
21	-0.052513	-0.4813	0.315782
22	-0.206344	-1.8912	0.031024
23	0.270032	2.4749	0.007669
24	-0.182614	-1.6737	0.048956
25	-0.09401	-0.8616	0.195677
26	0.156022	1.43	0.078218
27	-0.095755	-0.8776	0.191328
28	-0.03422	-0.3136	0.377288
29	0.050968	0.4671	0.320809
30	-0.083726	-0.7674	0.222509
31	-0.018826	-0.1725	0.431714
32	0.121268	1.1114	0.134775
33	-0.152255	-1.3954	0.083281
34	-0.040735	-0.3733	0.354917
35	0.079737	0.7308	0.233466
36	-0.183671	-1.6834	0.048008
37	0.226019	2.0715	0.02069
38	-0.102973	-0.9438	0.173999
39	-0.06143	-0.563	0.287461
40	0.09184	0.8417	0.201165
41	0.028538	0.2616	0.397151
42	-0.03025	-0.2772	0.391137
43	0.089522	0.8205	0.207131
44	-0.005246	-0.0481	0.480884
45	-0.049634	-0.4549	0.325176
46	0.120011	1.0999	0.137255
47	-0.024965	-0.2288	0.409786
48	-0.136841	-1.2542	0.10663

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.227011	-2.0806	0.020259
2	-0.010059	-0.0922	0.463383
3	0.316886	2.9043	0.002351
4	0.078925	0.7234	0.235735
5	0.052858	0.4844	0.314664
6	0.152024	1.3933	0.083599
7	-0.062858	-0.5761	0.283043
8	-0.065221	-0.5978	0.275804
9	0.139023	1.2742	0.10306
10	0.10656	0.9766	0.165775
11	0.031049	0.2846	0.388339
12	-0.022682	-0.2079	0.417913
13	-0.136545	-1.2515	0.10712
14	0.193392	1.7725	0.039972
15	-0.051689	-0.4737	0.318457
16	-0.081172	-0.744	0.22949
17	0.003903	0.0358	0.485776
18	-0.011192	-0.1026	0.459271
19	-0.213566	-1.9574	0.026813
20	-0.132855	-1.2176	0.113386
21	0.061461	0.5633	0.287365
22	-0.12963	-1.1881	0.119075
23	0.155096	1.4215	0.07944
24	-0.030713	-0.2815	0.389513
25	-0.025267	-0.2316	0.408717
26	0.003627	0.0332	0.48678
27	0.068493	0.6277	0.265936
28	0.013086	0.1199	0.452411
29	0.021767	0.1995	0.421179
30	0.038211	0.3502	0.363528
31	-0.026373	-0.2417	0.404797
32	0.088988	0.8156	0.208522
33	-0.038057	-0.3488	0.364056
34	-0.081478	-0.7468	0.228648
35	-0.021852	-0.2003	0.420874
36	-0.044285	-0.4059	0.342931
37	0.120802	1.1072	0.135691
38	-0.032346	-0.2965	0.383808
39	0.012622	0.1157	0.454092
40	-0.097113	-0.8901	0.187989
41	0.035607	0.3263	0.37249
42	0.085741	0.7858	0.21709
43	0.071026	0.651	0.258424
44	0.023809	0.2182	0.413896
45	0.025718	0.2357	0.407117
46	-0.069645	-0.6383	0.262504
47	-0.00335	-0.0307	0.487791
48	-0.103505	-0.9486	0.172764

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/03/t1291371406735324hftueingr/11twq1291371511.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/03/t1291371406735324hftueingr/11twq1291371511.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/03/t1291371406735324hftueingr/21twq1291371511.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/03/t1291371406735324hftueingr/21twq1291371511.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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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