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Statistiek Paper 7

*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, 22 Dec 2010 14:16:49 +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/22/t1293027485k84pi113kafprd8.htm/, Retrieved Wed, 22 Dec 2010 15:18:09 +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/22/t1293027485k84pi113kafprd8.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 «

5732 6938 6660 6695 6484 7716 5927 4768 7081 6947 7723 7319 6285 6655 7331 6468 7653 7330 5907 5257 7029 8885 9477 6822 8595 8738 11380 9831 10560 10336 8872 7598 9713 10858 10430 7516 8344 8623 9238 10350 9415 9550 8301 6405 10251 10082 8683 7829 6712 7354 8402 8211 8377 9133 8301 5932 9080 9459 9647 8646 7503 10000 10441 6435 8102 9983 8662 6575 9088 9336 9089

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	5 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.635528	4.8816	4e-06
2	0.58058	4.4595	1.9e-05
3	0.563136	4.3255	3e-05
4	0.426003	3.2722	0.000893
5	0.418638	3.2156	0.001057
6	0.297743	2.287	0.0129
7	0.194625	1.4949	0.07013
8	0.122073	0.9377	0.176122
9	-0.059965	-0.4606	0.323389
10	-0.059824	-0.4595	0.323775
11	-0.098194	-0.7542	0.226853
12	-0.13963	-1.0725	0.143927
13	-0.143886	-1.1052	0.136777
14	-0.167303	-1.2851	0.101894
15	-0.153248	-1.1771	0.121938
16	-0.284913	-2.1885	0.016304
17	-0.209041	-1.6057	0.056842
18	-0.188568	-1.4484	0.076397
19	-0.294686	-2.2635	0.013648
20	-0.255829	-1.9651	0.027061
21	-0.273994	-2.1046	0.019798
22	-0.287363	-2.2073	0.015598
23	-0.213082	-1.6367	0.053507
24	-0.32032	-2.4604	0.008412
25	-0.176896	-1.3588	0.089696
26	-0.145883	-1.1205	0.133511
27	-0.136448	-1.0481	0.149438
28	-0.024943	-0.1916	0.42436
29	-0.037616	-0.2889	0.386821
30	-0.035664	-0.2739	0.392543
31	0.008616	0.0662	0.473728
32	0.059927	0.4603	0.323492
33	0.076712	0.5892	0.278975
34	0.058852	0.4521	0.326445
35	0.039513	0.3035	0.381285
36	0.022726	0.1746	0.43101
37	-0.020005	-0.1537	0.439201
38	-0.030965	-0.2378	0.406413
39	-0.030211	-0.2321	0.40865
40	0.022376	0.1719	0.432062
41	-0.037123	-0.2851	0.388264
42	-0.076653	-0.5888	0.279127
43	-0.038823	-0.2982	0.383296
44	-0.051249	-0.3936	0.34763
45	-0.012714	-0.0977	0.461269
46	0.002219	0.017	0.493229
47	-0.020131	-0.1546	0.43882
48	-0.019397	-0.149	0.441036
49	-0.015461	-0.1188	0.452934
50	0.012934	0.0993	0.460599
51	0.007407	0.0569	0.477411
52	-0.000373	-0.0029	0.498863
53	0.006126	0.0471	0.481315
54	-0.005415	-0.0416	0.483482
55	0.006187	0.0475	0.481128
56	0.000378	0.0029	0.498845
57	0.004656	0.0358	0.485796
58	-0.00114	-0.0088	0.496522
59	NA	NA	NA
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.635528	4.8816	4e-06
2	0.296399	2.2767	0.013224
3	0.211784	1.6267	0.05456
4	-0.081168	-0.6235	0.267692
5	0.068374	0.5252	0.30071
6	-0.131137	-1.0073	0.158956
7	-0.116107	-0.8918	0.188053
8	-0.113631	-0.8728	0.19315
9	-0.25502	-1.9588	0.027431
10	0.021974	0.1688	0.43327
11	0.039338	0.3022	0.381795
12	0.085281	0.6551	0.257488
13	0.029891	0.2296	0.4096
14	0.060666	0.466	0.321472
15	0.032299	0.2481	0.402462
16	-0.320736	-2.4636	0.008345
17	0.033983	0.261	0.397489
18	-0.06736	-0.5174	0.303405
19	-0.198762	-1.5267	0.066087
20	-0.063137	-0.485	0.314748
21	0.03243	0.2491	0.402074
22	0.032902	0.2527	0.40068
23	0.143354	1.1011	0.137658
24	-0.115036	-0.8836	0.190247
25	0.141033	1.0833	0.141543
26	0.054811	0.421	0.337637
27	0.057008	0.4379	0.331534
28	-0.039038	-0.2999	0.382671
29	-0.09643	-0.7407	0.230908
30	-0.172858	-1.3278	0.094687
31	-0.1079	-0.8288	0.20528
32	0.037879	0.291	0.386053
33	-0.027389	-0.2104	0.417048
34	0.089109	0.6845	0.248182
35	-0.04019	-0.3087	0.379318
36	0.026687	0.205	0.419144
37	-0.019587	-0.1504	0.440462
38	-0.086991	-0.6682	0.25331
39	0.01818	0.1396	0.44471
40	-0.035145	-0.27	0.394069
41	-0.034229	-0.2629	0.396765
42	-0.092794	-0.7128	0.2394
43	-0.029652	-0.2278	0.410309
44	0.027307	0.2097	0.417294
45	0.08513	0.6539	0.257859
46	-0.044582	-0.3424	0.366619
47	0.038868	0.2985	0.383167
48	-0.04046	-0.3108	0.378533
49	0.062425	0.4795	0.31668
50	0.039117	0.3005	0.382439
51	-0.082677	-0.6351	0.263924
52	-0.009525	-0.0732	0.470961
53	-0.050635	-0.3889	0.349361
54	-0.092651	-0.7117	0.239738
55	-0.037124	-0.2852	0.388261
56	0.07053	0.5418	0.295015
57	-0.067213	-0.5163	0.303798
58	-0.029693	-0.2281	0.410188
59	NA	NA	NA
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293027485k84pi113kafprd8/1yvmz1293027403.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293027485k84pi113kafprd8/1yvmz1293027403.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293027485k84pi113kafprd8/2rmmk1293027403.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293027485k84pi113kafprd8/2rmmk1293027403.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293027485k84pi113kafprd8/3rmmk1293027403.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293027485k84pi113kafprd8/3rmmk1293027403.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; 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 (par8 != '') par8 <- as.numeric(par8)

ox <- x

if (par8 == '') {

if (par2 == 0) {

x <- log(x)

} else {

x <- (x ^ par2 - 1) / par2

}

} else {

x <- log(x,base=par8)

}

if (par3 > 0) x <- diff(x,lag=1,difference=par3)

if (par4 > 0) x <- diff(x,lag=par5,difference=par4)

bitmap(file='picts.png')

op <- par(mfrow=c(2,1))

plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')

if (par8=='') {

mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')

mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')

} else {

mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')

mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')

}

plot(x,type='l', main=mytitle,xlab='time',ylab='value')

par(op)

dev.off()

bitmap(file='pic1.png')

racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)

dev.off()

bitmap(file='pic2.png')

rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)

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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