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*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: Mon, 13 Dec 2010 19:58:53 +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/13/t1292270301uhv6lghwp705wx4.htm/, Retrieved Mon, 13 Dec 2010 20:58:21 +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/13/t1292270301uhv6lghwp705wx4.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 «

76.14 75.93 74.49 74.73 75.56 84.19 79.30 74.70 77.09 74.88 77.56 74.08 68.38 71.63 64.65 69.13 58.10 50.28 46.95 41.76 43.91 41.53 54.04 72.69 99.29 114.57 132.55 131.52 122.77 109.05 101.84 93.75 90.82 89.43 91.27 82.15 76.91 70.13 73.67 68.19 65.10 65.10 60.60 57.58 53.40 61.00 58.13 57.95 61.97 71.81 72.51 68.29 68.61 68.00 60.93 59.71 62.36 56.47

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	0.943467	6.3989	0
2	0.820912	5.5677	1e-06
3	0.645749	4.3797	3.4e-05
4	0.451732	3.0638	0.001824
5	0.251353	1.7048	0.047493
6	0.063189	0.4286	0.335118
7	-0.10901	-0.7393	0.231727
8	-0.268423	-1.8205	0.037594
9	-0.41225	-2.796	0.003762
10	-0.527866	-3.5802	0.000412
11	-0.603666	-4.0943	8.5e-05
12	-0.636477	-4.3168	4.2e-05
13	-0.608917	-4.1299	7.6e-05
14	-0.536146	-3.6363	0.000348
15	-0.430771	-2.9216	0.002691
16	-0.321058	-2.1775	0.017304
17	-0.209198	-1.4188	0.081342
18	-0.107425	-0.7286	0.234972
19	-0.020473	-0.1389	0.445084
20	0.043967	0.2982	0.383448
21	0.09697	0.6577	0.25701
22	0.13096	0.8882	0.189523
23	0.151226	1.0257	0.155206
24	0.155129	1.0521	0.149116
25	0.152918	1.0371	0.152546
26	0.137827	0.9348	0.17739
27	0.115749	0.785	0.218225
28	0.091268	0.619	0.269483
29	0.066835	0.4533	0.326233
30	0.044141	0.2994	0.383
31	0.018561	0.1259	0.450184
32	0.00303	0.0206	0.491846
33	-0.009375	-0.0636	0.474788
34	-0.013858	-0.094	0.462762
35	-0.016622	-0.1127	0.455366
36	-0.014492	-0.0983	0.461065
37	-0.012608	-0.0855	0.466112
38	-0.0103	-0.0699	0.472305
39	-0.008241	-0.0559	0.477836
40	-0.00353	-0.0239	0.490501
41	-0.001312	-0.0089	0.49647
42	-0.001673	-0.0113	0.495498
43	-0.000481	-0.0033	0.498707
44	-0.000903	-0.0061	0.497569
45	9.3e-05	6e-04	0.499751
46	NA	NA	NA
47	NA	NA	NA
48	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.943467	6.3989	0
2	-0.630015	-4.273	4.8e-05
3	-0.336621	-2.2831	0.013547
4	0.092154	0.625	0.267523
5	-0.103298	-0.7006	0.243539
6	-0.051003	-0.3459	0.365491
7	-0.121837	-0.8263	0.206438
8	-0.279298	-1.8943	0.032242
9	-0.123277	-0.8361	0.203709
10	0.094404	0.6403	0.262583
11	0.067975	0.461	0.323475
12	-0.072162	-0.4894	0.313434
13	0.267446	1.8139	0.038109
14	-0.125495	-0.8511	0.199548
15	-0.175532	-1.1905	0.119975
16	-0.145215	-0.9849	0.164913
17	0.075956	0.5152	0.304455
18	-0.022119	-0.15	0.440703
19	-0.122916	-0.8337	0.204391
20	-0.227605	-1.5437	0.064758
21	0.034805	0.2361	0.407218
22	-0.063718	-0.4322	0.333823
23	0.097841	0.6636	0.255133
24	-0.012553	-0.0851	0.466259
25	0.131597	0.8925	0.188377
26	-0.170431	-1.1559	0.126841
27	-0.002936	-0.0199	0.4921
28	-0.075202	-0.51	0.306228
29	-0.032715	-0.2219	0.412693
30	0.014882	0.1009	0.460022
31	-0.143365	-0.9724	0.167981
32	-0.049747	-0.3374	0.368675
33	-0.035782	-0.2427	0.404663
34	0.00076	0.0052	0.497954
35	0.05133	0.3481	0.364662
36	-0.081318	-0.5515	0.291972
37	0.110125	0.7469	0.229462
38	-0.078339	-0.5313	0.298877
39	0.007563	0.0513	0.479657
40	-0.07404	-0.5022	0.308973
41	-0.033125	-0.2247	0.411618
42	-0.079184	-0.5371	0.296909
43	0.00132	0.009	0.496448
44	-0.077104	-0.5229	0.30176
45	0.057044	0.3869	0.350309
46	NA	NA	NA
47	NA	NA	NA
48	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/13/t1292270301uhv6lghwp705wx4/1m5fe1292270329.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/13/t1292270301uhv6lghwp705wx4/1m5fe1292270329.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/13/t1292270301uhv6lghwp705wx4/2m5fe1292270329.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/13/t1292270301uhv6lghwp705wx4/2m5fe1292270329.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 0 ; 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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