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Olie-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: Mon, 20 Dec 2010 12:23:54 +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/t1292847719ywf9lt7h78kdrcy.htm/, Retrieved Mon, 20 Dec 2010 13:22:02 +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/t1292847719ywf9lt7h78kdrcy.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 «

25.64 27.97 27.62 23.31 29.07 29.58 28.63 29.92 32.68 31.54 32.43 26.54 25.85 27.60 25.71 25.38 28.57 27.64 25.36 25.90 26.29 21.74 19.20 19.32 19.82 20.36 24.31 25.97 25.61 24.67 25.59 26.09 28.37 27.34 24.46 27.46 30.23 32.33 29.87 24.87 25.48 27.28 28.24 29.58 26.95 29.08 28.76 29.59 30.70 30.52 32.67 33.19 37.13 35.54 37.75 41.84 42.94 49.14 44.61 40.22 44.23 45.85 53.38 53.26 51.80 55.30 57.81 63.96 63.77 59.15 56.12 57.42 63.52 61.71 63.01 68.18 72.03 69.75 74.41 74.33 64.24 60.03 59.44 62.50 55.04 58.34 61.92 67.65 67.68 70.30 75.26 71.44 76.36 81.71 92.60 90.60 92.23 94.09 102.79 109.65 124.05 132.69 135.81 116.07 101.42 75.73 55.48 43.80 45.29 44.01 47.48 51.07 57.84 69.04 65.61 72.87 68.41 73.25 77.43 75.28 77.33 74.31 79.70 85.47 77.98 75.69 75.20 77.21 77.85 83.53 85.99

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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.452021	5.1538	0
2	0.294697	3.3601	0.000512
3	0.046212	0.5269	0.299582
4	-0.068723	-0.7836	0.217362
5	-0.195225	-2.2259	0.013871
6	-0.274239	-3.1268	0.00109
7	-0.188552	-2.1498	0.01671
8	-0.177957	-2.029	0.022249
9	-0.174862	-1.9937	0.024137
10	-0.049684	-0.5665	0.286019
11	0.013362	0.1523	0.439574
12	-0.063479	-0.7238	0.235251
13	-0.108593	-1.2381	0.108947
14	-0.042323	-0.4826	0.315111
15	0.034016	0.3878	0.349383
16	-0.063215	-0.7208	0.236176
17	-0.089825	-1.0242	0.153831
18	-0.05278	-0.6018	0.274185
19	0.02775	0.3164	0.376105
20	-0.0248	-0.2828	0.388903
21	0.098995	1.1287	0.130549
22	0.082325	0.9387	0.174825
23	0.07392	0.8428	0.200439
24	0.00094	0.0107	0.495732
25	0.106972	1.2197	0.1124
26	0.071822	0.8189	0.207173
27	-0.004516	-0.0515	0.479505
28	-0.012255	-0.1397	0.444546
29	-0.040695	-0.464	0.321716
30	-0.004205	-0.0479	0.480916
31	-0.09068	-1.0339	0.151548
32	-0.038203	-0.4356	0.331931
33	-0.013083	-0.1492	0.440828
34	-0.005788	-0.066	0.47374
35	0.067067	0.7647	0.222924
36	0.068433	0.7803	0.218329
37	0.06516	0.7429	0.229431
38	-0.037666	-0.4295	0.334151
39	-0.033422	-0.3811	0.351889
40	0.003572	0.0407	0.483788
41	-0.026505	-0.3022	0.381491
42	-0.036394	-0.415	0.339428
43	-0.074419	-0.8485	0.198857
44	-0.003771	-0.043	0.482883
45	0.013559	0.1546	0.438688
46	0.035167	0.401	0.344553
47	0.048794	0.5563	0.28947
48	-0.001291	-0.0147	0.494141
49	-0.087774	-1.0008	0.159398
50	-0.020675	-0.2357	0.407007
51	-0.001856	-0.0212	0.491575
52	-0.02079	-0.237	0.4065
53	-0.023057	-0.2629	0.396527
54	-0.10185	-1.1613	0.123829
55	-0.002497	-0.0285	0.488665
56	0.018762	0.2139	0.415473
57	-0.000905	-0.0103	0.495891
58	0.035206	0.4014	0.344388
59	-0.012307	-0.1403	0.444313
60	-0.00222	-0.0253	0.489923

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.452021	5.1538	0
2	0.113582	1.295	0.098803
3	-0.156871	-1.7886	0.038004
4	-0.090262	-1.0291	0.15266
5	-0.132171	-1.507	0.06712
6	-0.148103	-1.6886	0.046843
7	0.039689	0.4525	0.325823
8	-0.063581	-0.7249	0.234898
9	-0.134029	-1.5282	0.064451
10	0.066757	0.7611	0.223973
11	0.008228	0.0938	0.4627
12	-0.203201	-2.3168	0.011038
13	-0.117965	-1.345	0.090482
14	0.043765	0.499	0.309312
15	0.045595	0.5199	0.302023
16	-0.165827	-1.8907	0.030444
17	-0.134748	-1.5364	0.06344
18	-0.030856	-0.3518	0.362772
19	0.072001	0.8209	0.206591
20	-0.104441	-1.1908	0.11795
21	0.049557	0.565	0.286511
22	-0.060718	-0.6923	0.244994
23	-0.028133	-0.3208	0.374452
24	-0.05058	-0.5767	0.282569
25	0.088548	1.0096	0.157279
26	-0.062745	-0.7154	0.237822
27	-0.042848	-0.4885	0.312993
28	0.049019	0.5589	0.288594
29	-0.101277	-1.1547	0.125159
30	-0.005505	-0.0628	0.475024
31	-0.042765	-0.4876	0.313329
32	0.006479	0.0739	0.470612
33	-3.3e-05	-4e-04	0.499848
34	0.006671	0.0761	0.469742
35	0.090136	1.0277	0.152998
36	-0.054939	-0.6264	0.266074
37	-0.018609	-0.2122	0.41615
38	-0.055516	-0.633	0.26393
39	0.053836	0.6138	0.270201
40	0.000909	0.0104	0.495872
41	-0.007527	-0.0858	0.465868
42	-0.011001	-0.1254	0.45019
43	-0.074415	-0.8485	0.198869
44	0.039186	0.4468	0.327887
45	0.071216	0.812	0.20914
46	-0.019591	-0.2234	0.4118
47	-0.032238	-0.3676	0.356894
48	-0.018852	-0.215	0.415071
49	-0.128751	-1.468	0.072262
50	0.083671	0.954	0.170927
51	0.018053	0.2058	0.41862
52	-0.047042	-0.5364	0.296313
53	0.013233	0.1509	0.440151
54	-0.171595	-1.9565	0.026276
55	0.03168	0.3612	0.359266
56	0.065197	0.7434	0.229302
57	-0.084698	-0.9657	0.167992
58	-0.024088	-0.2746	0.392011
59	0.000793	0.009	0.496398
60	-0.10598	-1.2084	0.114553

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292847719ywf9lt7h78kdrcy/1yqd01292847831.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292847719ywf9lt7h78kdrcy/1yqd01292847831.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292847719ywf9lt7h78kdrcy/28zc31292847831.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292847719ywf9lt7h78kdrcy/28zc31292847831.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292847719ywf9lt7h78kdrcy/38zc31292847831.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292847719ywf9lt7h78kdrcy/38zc31292847831.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 2 ; 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 (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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