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*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: Sun, 21 Dec 2008 06:20:21 -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/21/t1229865771as9q6jhxr1migdn.htm/, Retrieved Sun, 21 Dec 2008 14:22:51 +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/21/t1229865771as9q6jhxr1migdn.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 «

13139,7 14532,2 15167 16071,1 14827,5 15082 14772,7 16083 14272,5 15223,3 14897,3 13062,6 12603,8 13629,8 14421,1 13978,3 12927,9 13429,9 13470,1 14785,8 14292 14308,8 14013 13240,9 12153,4 14289,7 15669,2 14169,5 14569,8 14469,1 14264,9 15320,9 14433,5 13691,5 14194,1 13519,2 11857,9 14616 15643,4 14077,2 14887,5 14159,9 14643 17192,5 15386,1 14287,1 17526,6 14497 14398,3 16629,6 16670,7 16614,8 16869,2 15663,9 16359,9 18447,7 16889 16505 18320,9 15052,1 15699,8 18135,3 16768,7 18883 19021 18101,9 17776,1 21489,9 17065,3 18690 18953,1 16398,9 16895,7 18553 19270 19422,1 17579,4 18637,3 18076,7 20438,6 18075,2 19563 19899,2 19227,5 17789,6 19220,8 21968,9 21131,5 19484,6 22404,1 21099 22486,5 23707,5 21897,5 23326,4 23765,4 20444

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	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.821474	8.0906	0
2	0.751391	7.4003	0
3	0.774276	7.6257	0
4	0.713741	7.0295	0
5	0.688725	6.7832	0
6	0.709381	6.9866	0
7	0.614826	6.0553	0
8	0.607877	5.9869	0
9	0.60692	5.9775	0
10	0.524114	5.1619	1e-06
11	0.563499	5.5498	0
12	0.632917	6.2335	0
13	0.500573	4.9301	2e-06
14	0.453687	4.4683	1.1e-05
15	0.453133	4.4628	1.1e-05
16	0.413232	4.0699	4.8e-05
17	0.414232	4.0797	4.6e-05
18	0.406051	3.9991	6.2e-05
19	0.337114	3.3202	0.000634
20	0.338614	3.335	0.000605
21	0.32623	3.213	0.000892
22	0.261949	2.5799	0.005691
23	0.303596	2.9901	0.001767
24	0.316717	3.1193	0.001194
25	0.230086	2.2661	0.012834
26	0.186518	1.837	0.034636
27	0.166707	1.6419	0.051927
28	0.135893	1.3384	0.091949
29	0.128165	1.2623	0.104937
30	0.086024	0.8472	0.199474
31	0.045355	0.4467	0.328047
32	0.033249	0.3275	0.37201
33	-0.006359	-0.0626	0.475097
34	-0.050068	-0.4931	0.311524
35	-0.021336	-0.2101	0.417001
36	-0.011855	-0.1168	0.453646
37	-0.072532	-0.7144	0.23836
38	-0.118941	-1.1714	0.122148
39	-0.126467	-1.2456	0.107964
40	-0.147197	-1.4497	0.075181
41	-0.160954	-1.5852	0.058087
42	-0.194806	-1.9186	0.028987
43	-0.215802	-2.1254	0.018047
44	-0.217686	-2.144	0.017268
45	-0.247284	-2.4355	0.008349
46	-0.276573	-2.7239	0.003826
47	-0.270861	-2.6677	0.004476
48	-0.254451	-2.506	0.006937
49	-0.291018	-2.8662	0.002547
50	-0.33441	-3.2936	0.000691
51	-0.339269	-3.3414	0.000592
52	-0.335093	-3.3003	0.000676
53	-0.348869	-3.436	0.000435
54	-0.358488	-3.5307	0.000318
55	-0.372572	-3.6694	0.000199
56	-0.36648	-3.6094	0.000244
57	-0.36507	-3.5955	0.000256
58	-0.370494	-3.6489	0.000213
59	-0.364685	-3.5917	0.000259
60	-0.327018	-3.2208	0.00087

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.821474	8.0906	0
2	0.235473	2.3191	0.011243
3	0.354673	3.4931	0.00036
4	-0.032722	-0.3223	0.37397
5	0.106671	1.0506	0.148029
6	0.140086	1.3797	0.085428
7	-0.222414	-2.1905	0.015441
8	0.129973	1.2801	0.101784
9	-0.047827	-0.471	0.319333
10	-0.112538	-1.1084	0.135221
11	0.258782	2.5487	0.00619
12	0.235161	2.3161	0.01133
13	-0.347281	-3.4203	0.000458
14	-0.144555	-1.4237	0.07887
15	-0.068421	-0.6739	0.250999
16	0.112226	1.1053	0.135882
17	0.008512	0.0838	0.466682
18	-0.037111	-0.3655	0.357766
19	0.055124	0.5429	0.294218
20	-0.047816	-0.4709	0.319373
21	0.010275	0.1012	0.459802
22	-0.016988	-0.1673	0.433735
23	0.049476	0.4873	0.313578
24	-0.088107	-0.8678	0.193835
25	-0.035077	-0.3455	0.365247
26	-0.094852	-0.9342	0.176265
27	-0.031859	-0.3138	0.377182
28	-0.028151	-0.2773	0.391088
29	-0.077648	-0.7647	0.22314
30	-0.055211	-0.5438	0.293927
31	0.06689	0.6588	0.255797
32	-0.053054	-0.5225	0.301248
33	-0.069333	-0.6829	0.248163
34	-0.014617	-0.144	0.442917
35	0.028031	0.2761	0.391538
36	0.117924	1.1614	0.124161
37	-0.118824	-1.1703	0.122378
38	-0.056472	-0.5562	0.289682
39	0.033107	0.3261	0.372538
40	-0.103538	-1.0197	0.155196
41	-0.014741	-0.1452	0.442433
42	-0.032064	-0.3158	0.376419
43	0.0202	0.1989	0.42136
44	0.040653	0.4004	0.344875
45	-0.041368	-0.4074	0.342294
46	0.019682	0.1938	0.423353
47	-0.129733	-1.2777	0.102198
48	0.00022	0.0022	0.499139
49	0.037355	0.3679	0.356873
50	-0.051129	-0.5036	0.307854
51	-0.008041	-0.0792	0.468522
52	0.023634	0.2328	0.408216
53	-4.1e-05	-4e-04	0.499839
54	0.046455	0.4575	0.324158
55	-0.075925	-0.7478	0.228202
56	0.04647	0.4577	0.324103
57	0.02236	0.2202	0.413079
58	0.04921	0.4847	0.314505
59	-0.004501	-0.0443	0.482368
60	-0.01661	-0.1636	0.435197

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/21/t1229865771as9q6jhxr1migdn/11do21229865616.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/21/t1229865771as9q6jhxr1migdn/11do21229865616.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/21/t1229865771as9q6jhxr1migdn/20s331229865616.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/21/t1229865771as9q6jhxr1migdn/20s331229865616.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = -0.6 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = 60 ; par2 = -0.6 ; 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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