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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: Mon, 20 Dec 2010 09:30:33 +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/20/t1292837290nvl106mox427ooa.htm/, Retrieved Mon, 20 Dec 2010 10:28:12 +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/20/t1292837290nvl106mox427ooa.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 «

112.3 117.3 111.1 102.2 104.3 122.9 107.6 121.3 131.5 89 104.4 128.9 135.9 133.3 121.3 120.5 120.4 137.9 126.1 133.2 151.1 105 119 140.4 156.6 137.1 122.7 125.8 139.3 134.9 149.2 132.3 149 117.2 119.6 152 149.4 127.3 114.1 102.1 107.7 104.4 102.1 96 109.3 90 83.9 112 114.3 103.6 91.7 80.8 87.2 109.2 102.7 95.1 117.5 85.1 92.1 113.5

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	3 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.225215	-1.7299	0.044437
2	-0.337446	-2.592	0.006005
3	0.036768	0.2824	0.389306
4	-0.051433	-0.3951	0.34711
5	0.065002	0.4993	0.309715
6	0.148083	1.1375	0.129974
7	0.030256	0.2324	0.408516
8	-0.004365	-0.0335	0.486684
9	-0.073752	-0.5665	0.286602
10	-0.215247	-1.6533	0.051787
11	-0.131026	-1.0064	0.15916
12	0.627285	4.8183	5e-06
13	-0.051204	-0.3933	0.347757
14	-0.362775	-2.7865	0.003577
15	0.013322	0.1023	0.459421
16	-0.002648	-0.0203	0.491919
17	0.048736	0.3743	0.354743
18	0.105679	0.8117	0.210104
19	-0.001798	-0.0138	0.494513
20	-0.012595	-0.0967	0.461627
21	-0.078925	-0.6062	0.273341
22	-0.148613	-1.1415	0.129133
23	-0.055316	-0.4249	0.336231
24	0.366176	2.8126	0.003331
25	0.02561	0.1967	0.422364
26	-0.288755	-2.218	0.01521
27	-0.010288	-0.079	0.46864
28	0.02285	0.1755	0.430637
29	0.013687	0.1051	0.458313
30	0.091993	0.7066	0.241296
31	0.006167	0.0474	0.48119
32	-0.057014	-0.4379	0.331518
33	-0.017732	-0.1362	0.446063
34	-0.043906	-0.3372	0.368563
35	-0.103312	-0.7936	0.215317
36	0.274589	2.1092	0.019592
37	0.020814	0.1599	0.436763
38	-0.22595	-1.7356	0.043931
39	0.066065	0.5075	0.306864
40	-0.012074	-0.0927	0.463211
41	-0.008504	-0.0653	0.474068
42	0.088103	0.6767	0.250609
43	0.024465	0.1879	0.425794
44	-0.089051	-0.684	0.248322
45	0.012904	0.0991	0.460692
46	-0.000155	-0.0012	0.499528
47	-0.081076	-0.6228	0.267922
48	0.166085	1.2757	0.103527
49	6.7e-05	5e-04	0.499795
50	-0.123981	-0.9523	0.172412
51	0.069667	0.5351	0.297288
52	-0.009123	-0.0701	0.472185
53	-0.026956	-0.2071	0.41834
54	0.031377	0.241	0.405191
55	0.01769	0.1359	0.446189
56	-0.023696	-0.182	0.428097
57	-0.005885	-0.0452	0.48205
58	0.006378	0.049	0.480548
59	NA	NA	NA
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.225215	-1.7299	0.044437
2	-0.408909	-3.1409	0.001316
3	-0.205425	-1.5779	0.059968
4	-0.320821	-2.4643	0.008331
5	-0.17817	-1.3686	0.088164
6	-0.020052	-0.154	0.439058
7	0.117618	0.9034	0.184983
8	0.251771	1.9339	0.028964
9	0.249118	1.9135	0.030269
10	-0.047267	-0.3631	0.358927
11	-0.46946	-3.606	0.00032
12	0.260512	2.001	0.024998
13	0.118152	0.9075	0.183906
14	-0.016265	-0.1249	0.450501
15	-0.089629	-0.6885	0.246934
16	-0.039738	-0.3052	0.380632
17	0.007979	0.0613	0.475668
18	-0.042966	-0.33	0.371273
19	-0.065605	-0.5039	0.308097
20	-0.100124	-0.7691	0.222461
21	-0.051253	-0.3937	0.347617
22	-0.037381	-0.2871	0.38751
23	-0.027231	-0.2092	0.417519
24	-0.110045	-0.8453	0.200687
25	-0.091621	-0.7038	0.242176
26	-0.037746	-0.2899	0.386441
27	0.022637	0.1739	0.431278
28	-0.008683	-0.0667	0.473526
29	-0.077453	-0.5949	0.277084
30	-0.047542	-0.3652	0.358144
31	-0.009777	-0.0751	0.470195
32	-0.095494	-0.7335	0.233078
33	-0.034771	-0.2671	0.39517
34	0.100104	0.7689	0.222506
35	-0.048474	-0.3723	0.355487
36	0.07425	0.5703	0.285312
37	-0.05855	-0.4497	0.327275
38	-0.069905	-0.537	0.29666
39	0.051077	0.3923	0.348115
40	-0.028517	-0.219	0.413686
41	-0.027449	-0.2108	0.416871
42	-0.073196	-0.5622	0.288045
43	0.046048	0.3537	0.362411
44	-0.046981	-0.3609	0.359742
45	-0.008823	-0.0678	0.4731
46	-0.095627	-0.7345	0.23277
47	-0.005377	-0.0413	0.483597
48	-0.004932	-0.0379	0.484956
49	-0.091632	-0.7038	0.242151
50	0.011208	0.0861	0.465842
51	-0.045664	-0.3508	0.363512
52	0.064937	0.4988	0.309891
53	0.03995	0.3069	0.380015
54	-0.048831	-0.3751	0.354474
55	-0.120001	-0.9217	0.180208
56	-0.008905	-0.0684	0.47285
57	-0.009194	-0.0706	0.471968
58	-0.048419	-0.3719	0.355645
59	NA	NA	NA
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292837290nvl106mox427ooa/13p8j1292837429.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292837290nvl106mox427ooa/13p8j1292837429.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292837290nvl106mox427ooa/23p8j1292837429.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292837290nvl106mox427ooa/23p8j1292837429.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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