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Paper 11

*Unverified author*

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

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Wed, 24 Dec 2008 05:01:22 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/24/t1230120109y8k5mhn6js1ghmh.htm/, Retrieved Wed, 24 Dec 2008 13:01:51 +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/2008/Dec/24/t1230120109y8k5mhn6js1ghmh.htm/},
    year = {2008},
}
@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 = {2008},
    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 «

65.1 72.5 70.6 81.9 72 70.9 71.1 65.1 78.1 92 77.8 63.3 56.2 79.2 69 66.1 77.5 69.3 70.2 70.2 78.2 85.4 82.4 61.2 52.2 85.3 79.9 72.2 85.7 75.5 69.2 77.6 85.3 77 89.9 60 54.3 84 69.9 75.1 81.7 69.9 68.3 77.3 77.4 85.3 91 60.6 57.6 93.8 78.7 80.3 89.8 77.5 71.7 83.2 86.2 100.7 100.8 57.1

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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.123103	0.9536	0.172068
2	-0.266149	-2.0616	0.021794
3	0.007033	0.0545	0.478367
4	-0.103237	-0.7997	0.213529
5	0.111683	0.8651	0.195216
6	0.343233	2.6587	0.005021
7	0.047128	0.365	0.358179
8	-0.086585	-0.6707	0.252498
9	-0.045274	-0.3507	0.363524
10	-0.337002	-2.6104	0.005702
11	0.106358	0.8238	0.206645
12	0.600528	4.6517	9e-06
13	4.7e-05	4e-04	0.499856
14	-0.240038	-1.8593	0.033943
15	-0.091066	-0.7054	0.241647
16	-0.147919	-1.1458	0.128218
17	0.064757	0.5016	0.308891
18	0.214232	1.6594	0.051124
19	-0.009338	-0.0723	0.471289
20	-0.093045	-0.7207	0.23694
21	-0.067732	-0.5246	0.300881
22	-0.276241	-2.1398	0.018226
23	0.15049	1.1657	0.124177
24	0.420428	3.2566	0.000928
25	0.007115	0.0551	0.478117
26	-0.108602	-0.8412	0.20178
27	-0.120455	-0.933	0.177268
28	-0.064778	-0.5018	0.308833
29	0.069202	0.536	0.296958
30	0.110984	0.8597	0.196694
31	0.014263	0.1105	0.456198
32	-0.055084	-0.4267	0.335569
33	-0.119372	-0.9246	0.179427
34	-0.213833	-1.6563	0.051437
35	0.064885	0.5026	0.308543
36	0.238198	1.8451	0.034982
37	0.010834	0.0839	0.4667
38	-0.153831	-1.1916	0.119062
39	-0.137326	-1.0637	0.145858
40	-0.035309	-0.2735	0.392704
41	-0.006475	-0.0502	0.480082
42	0.011702	0.0906	0.464039
43	-0.028251	-0.2188	0.413763
44	-0.06269	-0.4856	0.314512
45	-0.124874	-0.9673	0.168647
46	-0.106265	-0.8231	0.206848
47	0.05519	0.4275	0.335273
48	0.106659	0.8262	0.205987
49	0.025172	0.195	0.423034
50	-0.095239	-0.7377	0.23178
51	-0.088402	-0.6848	0.248067
52	-0.022531	-0.1745	0.431022
53	-0.014347	-0.1111	0.455941
54	0.017384	0.1347	0.446668
55	-0.001099	-0.0085	0.496618
56	-0.060588	-0.4693	0.320274
57	-0.035057	-0.2716	0.393449
58	-0.029529	-0.2287	0.409929
59	0.026956	0.2088	0.417657
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.123103	0.9536	0.172068
2	-0.285632	-2.2125	0.015375
3	0.093221	0.7221	0.236524
4	-0.218551	-1.6929	0.047832
5	0.231806	1.7956	0.0388
6	0.213831	1.6563	0.051439
7	0.070164	0.5435	0.294404
8	0.036295	0.2811	0.389784
9	-0.027492	-0.213	0.416044
10	-0.379567	-2.9401	0.002327
11	0.212662	1.6473	0.052365
12	0.387613	3.0024	0.00195
13	-0.07342	-0.5687	0.285839
14	-0.094935	-0.7354	0.232491
15	-0.079962	-0.6194	0.269005
16	-0.015623	-0.121	0.452041
17	-0.078559	-0.6085	0.27257
18	-0.078142	-0.6053	0.273635
19	0.015681	0.1215	0.451864
20	-0.066583	-0.5158	0.303962
21	0.088708	0.6871	0.247324
22	-0.006513	-0.0504	0.479966
23	0.147441	1.1421	0.12898
24	-0.002607	-0.0202	0.491977
25	0.095828	0.7423	0.230407
26	0.056568	0.4382	0.331417
27	-0.079792	-0.6181	0.269437
28	0.085512	0.6624	0.255134
29	-0.128473	-0.9952	0.16183
30	-0.087358	-0.6767	0.250608
31	0.006083	0.0471	0.481287
32	-0.054136	-0.4193	0.338235
33	-0.013914	-0.1078	0.457267
34	-0.05546	-0.4296	0.334515
35	-0.09181	-0.7112	0.239872
36	0.020422	0.1582	0.437419
37	-0.038002	-0.2944	0.384749
38	-0.067728	-0.5246	0.30089
39	0.030189	0.2338	0.407952
40	-0.001449	-0.0112	0.495541
41	-0.013069	-0.1012	0.459852
42	-0.063281	-0.4902	0.312899
43	-0.066534	-0.5154	0.304095
44	-0.012559	-0.0973	0.461413
45	-0.050681	-0.3926	0.348012
46	0.109407	0.8475	0.200053
47	-0.021615	-0.1674	0.433796
48	-0.057705	-0.447	0.32825
49	-0.036783	-0.2849	0.388342
50	0.066212	0.5129	0.304961
51	-0.045076	-0.3492	0.364095
52	-0.137356	-1.064	0.145805
53	0.010999	0.0852	0.466195
54	-0.007529	-0.0583	0.476843
55	-0.007121	-0.0552	0.478097
56	-0.019151	-0.1483	0.441284
57	0.107335	0.8314	0.204518
58	-0.010326	-0.08	0.468257
59	0.009792	0.0758	0.469897
60	NA	NA	NA

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/24/t1230120109y8k5mhn6js1ghmh/169ki1230120081.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/24/t1230120109y8k5mhn6js1ghmh/169ki1230120081.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/24/t1230120109y8k5mhn6js1ghmh/2yh1b1230120081.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/24/t1230120109y8k5mhn6js1ghmh/2yh1b1230120081.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1.0 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = 60 ; par2 = 1.0 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

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 (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='lags',ylab='ACF')

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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