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ACF 3

*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: Thu, 26 Nov 2009 15:47:12 -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/Nov/26/t1259275695200hb16yoqjgtls.htm/, Retrieved Thu, 26 Nov 2009 23:48:17 +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/Nov/26/t1259275695200hb16yoqjgtls.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 «

96.2 96.8 109.9 88 91.1 106.4 68.6 100.1 108 106 108.6 91.5 99.2 98 96.6 102.8 96.9 110 70.5 101.9 109.6 107.8 113 93.8 108 102.8 116.3 89.2 106.7 112.1 74.2 108.8 111.5 118.8 118.9 97.6 116.4 107.9 121.2 97.9 113.4 117.6 79.6 115.9 115.7 129.1 123.3 96.7 121.2 118.2 102.1 125.4 116.7 121.3 85.3 114.2 124.4 131 118.3 99.6

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	-0.696595	-4.7756	9e-06
2	0.207994	1.4259	0.080248
3	0.049584	0.3399	0.367713
4	-0.129831	-0.8901	0.188979
5	0.110874	0.7601	0.225491
6	-0.042897	-0.2941	0.384993
7	-0.047601	-0.3263	0.372809
8	0.079921	0.5479	0.293173
9	-0.020553	-0.1409	0.444275
10	-0.035021	-0.2401	0.405651
11	0.09737	0.6675	0.253848
12	-0.161893	-1.1099	0.136348
13	0.151365	1.0377	0.152359
14	-0.104907	-0.7192	0.237788
15	0.071181	0.488	0.313911
16	-0.022803	-0.1563	0.438221
17	-0.047804	-0.3277	0.372286
18	0.100112	0.6863	0.247938
19	-0.103431	-0.7091	0.240886
20	0.058054	0.398	0.346218
21	0.050149	0.3438	0.366262
22	-0.209157	-1.4339	0.07911
23	0.342026	2.3448	0.011656
24	-0.340388	-2.3336	0.011973
25	0.197975	1.3572	0.090592
26	-0.07452	-0.5109	0.305911
27	0.012272	0.0841	0.466653
28	0.044139	0.3026	0.381765
29	-0.071387	-0.4894	0.313416
30	0.056334	0.3862	0.350543
31	-0.001883	-0.0129	0.494877
32	-0.045532	-0.3122	0.378154
33	0.033201	0.2276	0.410466
34	0.033366	0.2287	0.410031
35	-0.165938	-1.1376	0.130524
36	0.256314	1.7572	0.042698
37	-0.172312	-1.1813	0.121711
38	0.035378	0.2425	0.404709
39	0.019983	0.137	0.44581
40	-0.041148	-0.2821	0.389555
41	0.061835	0.4239	0.33678
42	-0.038248	-0.2622	0.397151
43	-0.024941	-0.171	0.432483
44	0.045046	0.3088	0.379412
45	-0.013766	-0.0944	0.462605
46	-0.001914	-0.0131	0.494792
47	NA	NA	NA
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	-0.696595	-4.7756	9e-06
2	-0.538606	-3.6925	0.000289
3	-0.280991	-1.9264	0.030058
4	-0.268156	-1.8384	0.036165
5	-0.208201	-1.4274	0.080044
6	-0.131522	-0.9017	0.185916
7	-0.223773	-1.5341	0.065854
8	-0.259092	-1.7762	0.041083
9	-0.166016	-1.1381	0.130414
10	-0.145281	-0.996	0.162175
11	0.078042	0.535	0.297576
12	0.000859	0.0059	0.497664
13	0.027338	0.1874	0.426068
14	-0.063411	-0.4347	0.332875
15	0.011302	0.0775	0.469283
16	0.092286	0.6327	0.265004
17	0.012325	0.0845	0.466512
18	0.058194	0.399	0.345865
19	-0.028229	-0.1935	0.423691
20	-0.088411	-0.6061	0.273677
21	0.143177	0.9816	0.165668
22	-0.150511	-1.0319	0.153711
23	0.186812	1.2807	0.103289
24	0.053047	0.3637	0.358868
25	0.061832	0.4239	0.336787
26	-0.141655	-0.9711	0.168226
27	-0.143496	-0.9838	0.165136
28	-0.061554	-0.422	0.337478
29	-0.143693	-0.9851	0.164807
30	-0.086751	-0.5947	0.277437
31	-0.050106	-0.3435	0.366374
32	-0.09824	-0.6735	0.251965
33	-0.04052	-0.2778	0.391197
34	0.051489	0.353	0.362836
35	-0.107073	-0.7341	0.233281
36	-0.126279	-0.8657	0.195519
37	0.077003	0.5279	0.300024
38	0.059096	0.4051	0.343606
39	-0.013333	-0.0914	0.46378
40	-0.03072	-0.2106	0.417053
41	-0.063386	-0.4346	0.332937
42	0.060067	0.4118	0.341179
43	0.048374	0.3316	0.370819
44	-0.024002	-0.1645	0.435003
45	0.047497	0.3256	0.373076
46	-0.073221	-0.502	0.309013
47	NA	NA	NA
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/2009/Nov/26/t1259275695200hb16yoqjgtls/1p4qe1259275630.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259275695200hb16yoqjgtls/1p4qe1259275630.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259275695200hb16yoqjgtls/2krrn1259275630.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259275695200hb16yoqjgtls/2krrn1259275630.ps (open in new window)

Parameters (Session):

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

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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