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Paper-ACF2-Xt

*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: Wed, 16 Dec 2009 13:41:59 -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/16/t12609961931k208s8qb582qlc.htm/, Retrieved Wed, 16 Dec 2009 21:43:16 +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/16/t12609961931k208s8qb582qlc.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 «

98,8 100,5 110,4 96,4 101,9 106,2 81 94,7 101 109,4 102,3 90,7 96,2 96,1 106 103,1 102 104,7 86 92,1 106,9 112,6 101,7 92 97,4 97 105,4 102,7 98,1 104,5 87,4 89,9 109,8 111,7 98,6 96,9 95,1 97 112,7 102,9 97,4 111,4 87,4 96,8 114,1 110,3 103,9 101,6 94,6 95,9 104,7 102,8 98,1 113,9 80,9 95,7 113,2 105,9 108,8 102,3 99 100,7 115,5 100,7 109,9 114,6 85,4 100,5 114,8 116,5 112,9 102 106 105,3 118,8 106,1 109,3 117,2 92,5 104,2 112,5 122,4 113,3 100 110,7 112,8 109,8 117,3 109,1 115,9 96 99,8 116,8 115,7 99,4 94,3 91

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	0.067779	0.6249	0.266858
2	0.270187	2.491	0.007341
3	0.330274	3.045	0.001549
4	-0.059672	-0.5501	0.291831
5	0.189649	1.7485	0.041996
6	0.104661	0.9649	0.16866
7	-0.096391	-0.8887	0.18834
8	0.037217	0.3431	0.366178
9	-0.01795	-0.1655	0.434474
10	-0.036213	-0.3339	0.369653
11	-0.039796	-0.3669	0.357302
12	-0.049071	-0.4524	0.326061
13	-0.077849	-0.7177	0.237445
14	0.008221	0.0758	0.469882
15	-0.006461	-0.0596	0.47632
16	-0.110602	-1.0197	0.155381
17	0.028092	0.259	0.398132
18	-0.026244	-0.242	0.404697
19	-0.140439	-1.2948	0.099451
20	0.067355	0.621	0.268137
21	-0.012016	-0.1108	0.456027
22	-0.178771	-1.6482	0.051503
23	0.200073	1.8446	0.034291
24	-0.210995	-1.9453	0.027523
25	-0.07816	-0.7206	0.236567
26	0.093342	0.8606	0.195949
27	-0.186895	-1.7231	0.044255
28	-0.035394	-0.3263	0.372494
29	-0.039884	-0.3677	0.357002
30	-0.197527	-1.8211	0.036054
31	-0.03318	-0.3059	0.380212
32	-0.093388	-0.861	0.195832
33	-0.167224	-1.5417	0.063428
34	-0.113165	-1.0433	0.149877
35	-0.076606	-0.7063	0.240975
36	-0.07706	-0.7105	0.239684
37	0.073933	0.6816	0.248663
38	0.022441	0.2069	0.418295
39	0.015432	0.1423	0.4436
40	0.110587	1.0196	0.155416
41	0.084371	0.7779	0.219404
42	0.020569	0.1896	0.425024
43	0.060193	0.555	0.290191
44	0.127495	1.1754	0.121549
45	-0.059661	-0.55	0.291864
46	0.170585	1.5727	0.05975
47	-0.038583	-0.3557	0.361466
48	-0.130152	-1.1999	0.116749
49	0.0472	0.4352	0.332275
50	-0.153788	-1.4179	0.079944
51	-0.07514	-0.6928	0.245175
52	-0.019438	-0.1792	0.4291
53	-0.150147	-1.3843	0.084947
54	0.012746	0.1175	0.453364
55	-0.042333	-0.3903	0.348648
56	-0.1147	-1.0575	0.146645
57	0.02206	0.2034	0.419661
58	-0.032649	-0.301	0.382071
59	-0.047739	-0.4401	0.33048
60	0.058548	0.5398	0.295379

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.067779	0.6249	0.266858
2	0.266819	2.46	0.007961
3	0.323147	2.9793	0.001883
4	-0.165777	-1.5284	0.065065
5	0.024439	0.2253	0.411138
6	0.072719	0.6704	0.2522
7	-0.10858	-1.0011	0.15982
8	-0.10426	-0.9612	0.169581
9	0.026413	0.2435	0.404095
10	0.064255	0.5924	0.277576
11	-0.087965	-0.811	0.209815
12	-0.046012	-0.4242	0.336242
13	-0.012576	-0.1159	0.453986
14	0.074403	0.686	0.247302
15	0.018086	0.1667	0.433984
16	-0.126542	-1.1667	0.123305
17	0.026099	0.2406	0.405216
18	0.060051	0.5536	0.290638
19	-0.149164	-1.3752	0.086338
20	-0.000365	-0.0034	0.498663
21	0.146564	1.3513	0.0901
22	-0.162382	-1.4971	0.069037
23	0.109584	1.0103	0.157605
24	-0.147205	-1.3572	0.089161
25	-0.060514	-0.5579	0.289185
26	0.053088	0.4894	0.312892
27	-0.00766	-0.0706	0.471932
28	-0.116359	-1.0728	0.143203
29	-0.050451	-0.4651	0.321511
30	-0.033857	-0.3121	0.377847
31	-0.050569	-0.4662	0.321125
32	-0.043091	-0.3973	0.34608
33	-0.078979	-0.7282	0.234261
34	-0.083486	-0.7697	0.221805
35	0.010138	0.0935	0.462877
36	0.059281	0.5465	0.293062
37	0.118693	1.0943	0.138459
38	0.023674	0.2183	0.413872
39	0.043228	0.3985	0.345616
40	-0.014543	-0.1341	0.446827
41	0.023963	0.2209	0.41284
42	-0.027678	-0.2552	0.3996
43	-0.114354	-1.0543	0.147369
44	0.135883	1.2528	0.106861
45	0.004264	0.0393	0.484365
46	-0.037569	-0.3464	0.36496
47	-0.074218	-0.6843	0.247836
48	-0.110457	-1.0184	0.155697
49	-0.09316	-0.8589	0.196409
50	-0.040912	-0.3772	0.353487
51	-0.020054	-0.1849	0.426877
52	-0.053813	-0.4961	0.31054
53	0.005736	0.0529	0.478976
54	0.031567	0.291	0.385867
55	-0.023567	-0.2173	0.414258
56	-0.093441	-0.8615	0.195698
57	0.031921	0.2943	0.384625
58	-0.025027	-0.2307	0.409036
59	-0.05067	-0.4672	0.320791
60	0.000971	0.0089	0.49644

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609961931k208s8qb582qlc/11x7m1260996117.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609961931k208s8qb582qlc/11x7m1260996117.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609961931k208s8qb582qlc/2aaxa1260996117.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609961931k208s8qb582qlc/2aaxa1260996117.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = MA ; 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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