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ws 9: acf

*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: Tue, 07 Dec 2010 09:25:48 +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/07/t1291713862s629hwu0csvkn8n.htm/, Retrieved Tue, 07 Dec 2010 10:24:22 +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/07/t1291713862s629hwu0csvkn8n.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 «

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 93.2 103.1 94.1 91.8 102.7 82.6 89.1 104.5 105.1 95.1 88.7 86.3 91.8 111.5 99.7 97.5 111.7 86.2 95.4

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	0.26661	2.1985	0.015659
2	0.033653	0.2775	0.391116
3	0.197655	1.6299	0.053873
4	0.121119	0.9988	0.160723
5	0.359711	2.9663	0.002078
6	0.419511	3.4594	0.00047
7	0.270282	2.2288	0.014568
8	0.082996	0.6844	0.248024
9	0.046117	0.3803	0.352459
10	-0.131488	-1.0843	0.141035
11	0.10252	0.8454	0.200426
12	0.530372	4.3736	2.1e-05
13	0.024833	0.2048	0.419179
14	-0.202743	-1.6719	0.049574
15	-0.143557	-1.1838	0.120306
16	-0.099368	-0.8194	0.207708
17	0.082206	0.6779	0.250071
18	0.060175	0.4962	0.31067
19	-0.016043	-0.1323	0.447572
20	-0.175017	-1.4432	0.076773
21	-0.206658	-1.7041	0.04646
22	-0.276339	-2.2788	0.012914
23	-0.100819	-0.8314	0.204337
24	0.181283	1.4949	0.069784
25	-0.128167	-1.0569	0.14715
26	-0.312456	-2.5766	0.006077
27	-0.283703	-2.3395	0.011128
28	-0.138009	-1.1381	0.129546
29	-0.036233	-0.2988	0.383008
30	-0.070689	-0.5829	0.280938
31	-0.057706	-0.4759	0.317852
32	-0.224853	-1.8542	0.034025
33	-0.219597	-1.8108	0.037291
34	-0.176644	-1.4566	0.074908
35	-0.149115	-1.2296	0.111536
36	0.154217	1.2717	0.103904
37	-0.095226	-0.7853	0.217517
38	-0.273837	-2.2581	0.013576
39	-0.133966	-1.1047	0.136588
40	-0.088201	-0.7273	0.234763
41	-0.01611	-0.1328	0.447353
42	0.067253	0.5546	0.2905
43	-0.009913	-0.0817	0.467544
44	-0.146199	-1.2056	0.116077
45	-0.018915	-0.156	0.438257
46	-0.047383	-0.3907	0.34861
47	-0.034024	-0.2806	0.389946
48	0.206994	1.7069	0.0462
49	0.013801	0.1138	0.454863
50	-0.085483	-0.7049	0.241637
51	0.019763	0.163	0.435514
52	0.005825	0.048	0.480914
53	0.04344	0.3582	0.360645
54	0.113209	0.9335	0.176921
55	0.036958	0.3048	0.380739
56	-0.052884	-0.4361	0.332074
57	0.043482	0.3586	0.360518
58	-0.008371	-0.069	0.472584
59	0.006309	0.052	0.47933
60	0.120236	0.9915	0.16248

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.26661	2.1985	0.015659
2	-0.040292	-0.3323	0.370359
3	0.214645	1.77	0.040604
4	0.01212	0.0999	0.460341
5	0.378202	3.1187	0.001332
6	0.256046	2.1114	0.019208
7	0.223292	1.8413	0.034969
8	-0.075838	-0.6254	0.26691
9	-0.056518	-0.4661	0.321332
10	-0.495224	-4.0837	6e-05
11	-0.133528	-1.1011	0.137368
12	0.35031	2.8887	0.002592
13	-0.141596	-1.1676	0.123518
14	-0.198656	-1.6382	0.053004
15	-0.184667	-1.5228	0.066222
16	0.134988	1.1131	0.134784
17	0.022364	0.1844	0.427118
18	-0.086967	-0.7171	0.23787
19	0.016816	0.1387	0.445063
20	-0.030566	-0.2521	0.400881
21	0.025753	0.2124	0.416228
22	0.002617	0.0216	0.491422
23	-0.058297	-0.4807	0.316127
24	-0.110851	-0.9141	0.181948
25	-0.052287	-0.4312	0.333855
26	0.025158	0.2075	0.418135
27	-0.008512	-0.0702	0.472122
28	0.04199	0.3463	0.365108
29	-0.056525	-0.4661	0.32131
30	-0.014046	-0.1158	0.454065
31	0.070894	0.5846	0.280374
32	-0.043242	-0.3566	0.361253
33	-0.070218	-0.579	0.282239
34	0.011598	0.0956	0.462043
35	-0.181805	-1.4992	0.069225
36	0.115142	0.9495	0.172869
37	-0.144424	-1.1909	0.118907
38	0.007697	0.0635	0.474789
39	0.073552	0.6065	0.273093
40	-0.051741	-0.4267	0.335485
41	-0.013747	-0.1134	0.45504
42	0.189845	1.5655	0.061054
43	-0.026228	-0.2163	0.414709
44	-0.045246	-0.3731	0.355116
45	0.063141	0.5207	0.302143
46	0.024371	0.201	0.420661
47	-0.071105	-0.5863	0.279793
48	-0.18	-1.4843	0.071173
49	0.037207	0.3068	0.379962
50	0.041926	0.3457	0.365307
51	-0.059112	-0.4874	0.313755
52	-0.018868	-0.1556	0.438408
53	-0.068393	-0.564	0.287311
54	-0.07875	-0.6494	0.259136
55	-0.001522	-0.0126	0.495011
56	0.084784	0.6991	0.243422
57	-0.074192	-0.6118	0.271355
58	-0.059413	-0.4899	0.31288
59	0.040422	0.3333	0.369955
60	0.000213	0.0018	0.499301

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291713862s629hwu0csvkn8n/1dfrk1291713944.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291713862s629hwu0csvkn8n/1dfrk1291713944.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291713862s629hwu0csvkn8n/2dfrk1291713944.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291713862s629hwu0csvkn8n/2dfrk1291713944.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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