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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: Fri, 24 Dec 2010 15:46:54 +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/24/t12932054761wbzf6z65hxi7xu.htm/, Retrieved Fri, 24 Dec 2010 16:44:36 +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/24/t12932054761wbzf6z65hxi7xu.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 «

19685.6 19601.7 16006.9 17681.2 19790.4 17014.2 17424.5 18908.9 15692.1 15160 15794.3 16032.1 16065 16236.8 12521 14762.1 15446.9 13635 14212.6 15021.7 14134.3 13721.4 14384.5 15638.6 19711.6 20359.8 16141.4 20056.9 20605.5 19325.8 20547.7 19211.2 19009.5 18746.8 16471.5 18957.2 20515.2 18374.4 16192.9 18147.5 19301.4 18344.7 17183.6 19630 17167.2 17428.5 16016.5 18466.5 18406.6 18174.1 14851.9 16260.7 18329.6 18003.8 15903.8 19554.2 16554.2 16198.9 16571.8 17535.2 16198.1

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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.348734	-2.4161	0.009771
2	0.027364	0.1896	0.425219
3	0.452524	3.1352	0.001465
4	-0.2659	-1.8422	0.035813
5	0.153418	1.0629	0.146571
6	0.159728	1.1066	0.136985
7	-0.304405	-2.109	0.020095
8	0.137149	0.9502	0.173386
9	-0.057704	-0.3998	0.345543
10	-0.162067	-1.1228	0.133547
11	0.072117	0.4996	0.309805
12	-0.118598	-0.8217	0.207663
13	-0.138477	-0.9594	0.171084
14	0.009886	0.0685	0.472839
15	0.016274	0.1128	0.455349
16	-0.122175	-0.8465	0.20075
17	-0.002165	-0.015	0.494048
18	0.002789	0.0193	0.492332
19	-0.061047	-0.4229	0.337112
20	0.133242	0.9231	0.180279
21	-0.086788	-0.6013	0.275241
22	-0.056932	-0.3944	0.347504
23	0.235038	1.6284	0.054994
24	-0.211874	-1.4679	0.074326
25	0.114021	0.79	0.216717
26	0.105251	0.7292	0.234712
27	-0.179953	-1.2468	0.109269
28	0.103545	0.7174	0.238307
29	0.064084	0.444	0.329524
30	-0.083503	-0.5785	0.282807
31	0.040273	0.279	0.390713
32	0.016056	0.1112	0.455945
33	-0.067115	-0.465	0.322021
34	0.056341	0.3903	0.349004
35	-0.00999	-0.0692	0.472553
36	-0.083524	-0.5787	0.282758
37	-0.031125	-0.2156	0.415092
38	0.060225	0.4173	0.339177
39	-0.066674	-0.4619	0.323108
40	-0.004945	-0.0343	0.486406
41	0.022804	0.158	0.437564
42	-0.036476	-0.2527	0.400786
43	0.016671	0.1155	0.454265
44	0.005936	0.0411	0.483683
45	-0.000676	-0.0047	0.49814
46	-0.001289	-0.0089	0.496456
47	-0.002601	-0.018	0.492848
48	NA	NA	NA
49	NA	NA	NA
50	NA	NA	NA
51	NA	NA	NA
52	NA	NA	NA
53	NA	NA	NA
54	NA	NA	NA
55	NA	NA	NA
56	NA	NA	NA
57	NA	NA	NA
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.348734	-2.4161	0.009771
2	-0.107302	-0.7434	0.230429
3	0.490251	3.3966	0.00069
4	0.08151	0.5647	0.287448
5	0.052321	0.3625	0.359288
6	0.020856	0.1445	0.442858
7	-0.240268	-1.6646	0.051251
8	-0.199155	-1.3798	0.087023
9	-0.169899	-1.1771	0.12248
10	-0.018754	-0.1299	0.448581
11	0.02603	0.1803	0.428823
12	0.045827	0.3175	0.37612
13	-0.086876	-0.6019	0.275039
14	-0.170672	-1.1824	0.121426
15	0.079863	0.5533	0.291311
16	0.03104	0.215	0.41532
17	-0.032701	-0.2266	0.410865
18	-0.072127	-0.4997	0.309781
19	-0.046032	-0.3189	0.375585
20	0.118456	0.8207	0.207941
21	-0.046789	-0.3242	0.373612
22	-0.135415	-0.9382	0.176423
23	0.106822	0.7401	0.231427
24	-0.076759	-0.5318	0.298659
25	0.000905	0.0063	0.497512
26	-0.032178	-0.2229	0.412265
27	0.025029	0.1734	0.43153
28	-0.074575	-0.5167	0.30388
29	0.010861	0.0753	0.470164
30	0.0963	0.6672	0.253925
31	-0.083179	-0.5763	0.28356
32	0.027162	0.1882	0.425763
33	-0.03597	-0.2492	0.402132
34	-0.04113	-0.285	0.388451
35	-0.050812	-0.352	0.363175
36	-0.033543	-0.2324	0.40861
37	-0.115741	-0.8019	0.213287
38	-0.02666	-0.1847	0.42712
39	0.123055	0.8525	0.199072
40	0.055324	0.3833	0.351597
41	-0.022084	-0.153	0.439518
42	0.036813	0.255	0.399887
43	-0.04965	-0.344	0.36618
44	-0.108453	-0.7514	0.228045
45	-0.056357	-0.3905	0.348964
46	-0.020151	-0.1396	0.444776
47	0.075342	0.522	0.30204
48	NA	NA	NA
49	NA	NA	NA
50	NA	NA	NA
51	NA	NA	NA
52	NA	NA	NA
53	NA	NA	NA
54	NA	NA	NA
55	NA	NA	NA
56	NA	NA	NA
57	NA	NA	NA
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/24/t12932054761wbzf6z65hxi7xu/1wf461293205611.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t12932054761wbzf6z65hxi7xu/1wf461293205611.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t12932054761wbzf6z65hxi7xu/2wf461293205611.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t12932054761wbzf6z65hxi7xu/2wf461293205611.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ;

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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