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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 05:38:30 -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/t1261917636y4tijlwhxqmqy1q.htm/, Retrieved Sun, 27 Dec 2009 13:40:38 +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/t1261917636y4tijlwhxqmqy1q.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 «

40,22 44,23 45,85 53,38 53,26 51,8 55,3 57,81 63,96 63,77 59,15 56,12 57,42 63,52 61,71 63,01 68,18 72,03 69,75 74,41 74,33 64,24 60,03 59,44 62,5 55,04 58,34 61,92 67,65 67,68 70,3 75,26 71,44 76,36 81,71 92,6 90,6 92,23 94,09 102,79 109,65 124,05 132,69 135,81 116,07 101,42 75,73 55,48 43,8 45,29 44,01 47,48 51,07 57,84 69,04 65,61 72,87 68,41 73,25 77,43

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	0.922225	7.1435	0
2	0.784363	6.0757	0
3	0.602247	4.665	9e-06
4	0.419489	3.2493	0.000949
5	0.243836	1.8887	0.031881
6	0.098273	0.7612	0.224754
7	-0.004382	-0.0339	0.486517
8	-0.077156	-0.5976	0.276163
9	-0.118165	-0.9153	0.181849
10	-0.135092	-1.0464	0.149783
11	-0.14179	-1.0983	0.138231
12	-0.152429	-1.1807	0.121188
13	-0.153485	-1.1889	0.119584
14	-0.14404	-1.1157	0.134493
15	-0.137985	-1.0688	0.144714
16	-0.136709	-1.0589	0.146934
17	-0.129279	-1.0014	0.16033
18	-0.109145	-0.8454	0.200613
19	-0.082041	-0.6355	0.263765
20	-0.045442	-0.352	0.363038
21	0.001277	0.0099	0.496071
22	0.033314	0.258	0.398627
23	0.053339	0.4132	0.340479
24	0.052686	0.4081	0.342324
25	0.042897	0.3323	0.370419
26	0.006262	0.0485	0.480737
27	-0.042524	-0.3294	0.371504
28	-0.09201	-0.7127	0.239395
29	-0.135214	-1.0474	0.149567
30	-0.168096	-1.3021	0.098935
31	-0.192924	-1.4944	0.070159
32	-0.198109	-1.5345	0.065076
33	-0.204882	-1.587	0.058884
34	-0.202348	-1.5674	0.061142
35	-0.19942	-1.5447	0.063839
36	-0.192297	-1.4895	0.070794
37	-0.193097	-1.4957	0.069984
38	-0.196284	-1.5204	0.06683
39	-0.195767	-1.5164	0.067334
40	-0.187354	-1.4512	0.075961
41	-0.169636	-1.314	0.096925
42	-0.13088	-1.0138	0.157377
43	-0.077199	-0.598	0.276052
44	-0.010176	-0.0788	0.468719
45	0.047089	0.3647	0.358291
46	0.094091	0.7288	0.234471
47	0.111707	0.8653	0.195167
48	0.109296	0.8466	0.200291
49	0.092135	0.7137	0.239097
50	0.076967	0.5962	0.276648
51	0.054892	0.4252	0.336108
52	0.032138	0.2489	0.402128
53	0.013011	0.1008	0.460029
54	-0.001743	-0.0135	0.494637
55	-0.001708	-0.0132	0.494743
56	-0.007945	-0.0615	0.475566
57	-0.007	-0.0542	0.478468
58	-0.009973	-0.0773	0.46934
59	-0.007808	-0.0605	0.475986
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.922225	7.1435	0
2	-0.44238	-3.4267	0.000554
3	-0.275596	-2.1348	0.018437
4	0.048672	0.377	0.353747
5	-0.070588	-0.5468	0.293281
6	0.031065	0.2406	0.405331
7	0.098764	0.765	0.223629
8	-0.10859	-0.8411	0.201807
9	0.008545	0.0662	0.473725
10	0.024321	0.1884	0.425604
11	-0.108842	-0.8431	0.201265
12	-0.09387	-0.7271	0.234993
13	0.121013	0.9374	0.176166
14	0.031822	0.2465	0.403071
15	-0.135205	-1.0473	0.149583
16	-0.024609	-0.1906	0.424733
17	0.072745	0.5635	0.287604
18	0.044907	0.3478	0.364586
19	0.012352	0.0957	0.462048
20	0.038157	0.2956	0.384292
21	0.034313	0.2658	0.395656
22	-0.153844	-1.1917	0.119041
23	0.022359	0.1732	0.431542
24	-0.059699	-0.4624	0.322724
25	-0.001199	-0.0093	0.496312
26	-0.090189	-0.6986	0.24375
27	-0.019685	-0.1525	0.439661
28	-0.010284	-0.0797	0.468386
29	-0.024021	-0.1861	0.426512
30	0.006472	0.0501	0.480093
31	-0.071296	-0.5523	0.291412
32	0.022159	0.1716	0.432147
33	-0.105928	-0.8205	0.207586
34	0.009845	0.0763	0.469734
35	-0.058225	-0.451	0.326804
36	-0.033027	-0.2558	0.39948
37	-0.042657	-0.3304	0.371118
38	-0.029646	-0.2296	0.409578
39	-0.035293	-0.2734	0.392749
40	0.035152	0.2723	0.393167
41	0.009464	0.0733	0.470902
42	0.086319	0.6686	0.25315
43	-0.011023	-0.0854	0.46612
44	0.046077	0.3569	0.361205
45	-0.113065	-0.8758	0.192316
46	-0.051199	-0.3966	0.346539
47	-0.072039	-0.558	0.289456
48	0.044826	0.3472	0.364821
49	0.050346	0.39	0.348965
50	0.060532	0.4689	0.320429
51	-0.101613	-0.7871	0.217164
52	-0.015641	-0.1212	0.451987
53	-0.02961	-0.2294	0.409687
54	0.000928	0.0072	0.497144
55	0.090774	0.7031	0.242347
56	-0.111175	-0.8612	0.196289
57	-0.017628	-0.1365	0.445922
58	0.019409	0.1503	0.440499
59	-0.000294	-0.0023	0.499094
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/27/t1261917636y4tijlwhxqmqy1q/1oz9i1261917508.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/27/t1261917636y4tijlwhxqmqy1q/1oz9i1261917508.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/27/t1261917636y4tijlwhxqmqy1q/2mqty1261917508.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/27/t1261917636y4tijlwhxqmqy1q/2mqty1261917508.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; 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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