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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, 27 Dec 2009 03:35:52 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/27/t1261910190s633r8xs8xvkkxv.htm/, Retrieved Sun, 27 Dec 2009 11:36:32 +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/2009/Dec/27/t1261910190s633r8xs8xvkkxv.htm/},
    year = {2009},
}
@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 = {2009},
    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 «

28029 29383 36438 32034 22679 24319 18004 17537 20366 22782 19169 13807 29743 25591 29096 26482 22405 27044 17970 18730 19684 19785 18479 10698 31956 29506 34506 27165 26736 23691 18157 17328 18205 20995 17382 9367 31124 26551 30651 25859 25100 25778 20418 18688 20424 24776 19814 12738 31566 30111 30019 31934 25826 26835 20205 17789 20520 22518 15572 11509 25447 24090 27786 26195 20516 22759 19028 16971 20036 22485

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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.403478	-3.0462	0.001753
2	0.187412	1.4149	0.081264
3	-0.164473	-1.2417	0.109708
4	-0.077962	-0.5886	0.279227
5	-0.073668	-0.5562	0.290131
6	0.104931	0.7922	0.21576
7	-0.106263	-0.8023	0.212865
8	0.21437	1.6185	0.055543
9	-0.010178	-0.0768	0.46951
10	-0.062872	-0.4747	0.318418
11	0.015745	0.1189	0.452899
12	-0.197093	-1.488	0.071129
13	-0.046191	-0.3487	0.364287
14	-0.013313	-0.1005	0.460146
15	0.062682	0.4732	0.318926
16	0.019388	0.1464	0.44207
17	0.080373	0.6068	0.273196
18	-0.046486	-0.351	0.363457
19	-0.003264	-0.0246	0.490212
20	-0.09231	-0.6969	0.244342
21	0.165391	1.2487	0.108444
22	-0.254294	-1.9199	0.029942
23	0.276167	2.085	0.020779
24	-0.139607	-1.054	0.148163
25	0.154498	1.1664	0.124148
26	-0.006414	-0.0484	0.480772
27	0.022909	0.173	0.431648
28	-0.127048	-0.9592	0.170757
29	0.133661	1.0091	0.158592
30	-0.124276	-0.9383	0.176035
31	0.034379	0.2596	0.39807
32	-0.000909	-0.0069	0.497274
33	-0.09591	-0.7241	0.235981
34	0.127289	0.961	0.170303
35	-0.028234	-0.2132	0.415981
36	-0.048296	-0.3646	0.358369
37	0.00198	0.015	0.494061
38	-0.059414	-0.4486	0.327723
39	-0.007108	-0.0537	0.478695
40	0.080313	0.6063	0.273345
41	-0.055561	-0.4195	0.338222
42	0.043857	0.3311	0.370887
43	0.019601	0.148	0.44144
44	-0.02047	-0.1545	0.438863
45	0.014284	0.1078	0.45725
46	0.008436	0.0637	0.47472
47	0.032167	0.2429	0.404495
48	-0.047618	-0.3595	0.360271
49	0.01269	0.0958	0.462005
50	0.07314	0.5522	0.291486
51	0.000457	0.0035	0.498628
52	-0.026634	-0.2011	0.420674
53	-0.028786	-0.2173	0.414363
54	-0.005152	-0.0389	0.484554
55	-0.007488	-0.0565	0.477556
56	-0.005349	-0.0404	0.483963
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	-0.403478	-3.0462	0.001753
2	0.029404	0.222	0.412554
3	-0.094701	-0.715	0.238771
4	-0.215547	-1.6273	0.05459
5	-0.203201	-1.5341	0.065265
6	0.01626	0.1228	0.451365
7	-0.107778	-0.8137	0.2096
8	0.08375	0.6323	0.26486
9	0.140855	1.0634	0.146035
10	-0.055248	-0.4171	0.339081
11	-0.015073	-0.1138	0.454899
12	-0.167816	-1.267	0.105157
13	-0.215072	-1.6238	0.054973
14	-0.193497	-1.4609	0.074771
15	-0.077903	-0.5882	0.279376
16	-0.118981	-0.8983	0.186405
17	-0.100976	-0.7624	0.224497
18	-0.048208	-0.364	0.358617
19	-0.068464	-0.5169	0.303617
20	-0.115307	-0.8705	0.193827
21	0.198478	1.4985	0.069764
22	-0.181314	-1.3689	0.088202
23	0.007684	0.058	0.476969
24	-0.05078	-0.3834	0.351432
25	-0.040949	-0.3092	0.379164
26	0.00033	0.0025	0.49901
27	0.032734	0.2471	0.402844
28	-0.070871	-0.5351	0.297343
29	0.01396	0.1054	0.458216
30	0.07363	0.5559	0.290229
31	-0.073159	-0.5523	0.291438
32	-0.091237	-0.6888	0.246864
33	-0.100623	-0.7597	0.225285
34	-0.042529	-0.3211	0.374661
35	-0.004225	-0.0319	0.487332
36	-0.06504	-0.491	0.312642
37	-0.066023	-0.4985	0.310037
38	-0.096473	-0.7284	0.23469
39	0.000503	0.0038	0.498493
40	0.037987	0.2868	0.387654
41	-0.027493	-0.2076	0.418152
42	-0.065703	-0.496	0.310885
43	0.023136	0.1747	0.430979
44	-0.121486	-0.9172	0.181452
45	-0.019797	-0.1495	0.440858
46	-0.067069	-0.5064	0.307279
47	0.072546	0.5477	0.293016
48	-0.090821	-0.6857	0.247847
49	-0.0745	-0.5625	0.288002
50	0.021121	0.1595	0.436936
51	0.073733	0.5567	0.289964
52	-0.042997	-0.3246	0.373329
53	-0.049026	-0.3701	0.356327
54	0.022329	0.1686	0.433363
55	-0.094767	-0.7155	0.238619
56	-0.028763	-0.2172	0.41443
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/2009/Dec/27/t1261910190s633r8xs8xvkkxv/1d7cq1261910149.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/27/t1261910190s633r8xs8xvkkxv/1d7cq1261910149.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/27/t1261910190s633r8xs8xvkkxv/28rmb1261910149.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/27/t1261910190s633r8xs8xvkkxv/28rmb1261910149.ps (open in new window)

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; 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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