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paper - time-series (3)

*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: Fri, 10 Dec 2010 15:30:46 +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/10/t129199494681m8gewcxkw5g7e.htm/, Retrieved Fri, 10 Dec 2010 16:29:06 +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/10/t129199494681m8gewcxkw5g7e.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 «

296.95 296.84 287.54 287.81 283.99 275.79 269.52 278.35 283.43 289.46 282.30 293.55 304.78 300.99 315.29 316.21 331.79 329.38 317.27 317.98 340.28 339.21 336.71 340.11 347.72 328.68 303.05 299.83 320.04 317.94 303.31 308.85 319.19 314.52 312.39 315.77 320.23 309.45 296.54 297.28 301.39 306.68 305.91 314.76 323.34 341.58 330.12 318.16 317.84 325.39 327.56 329.77 333.29 346.10 358.00 344.82 313.30 301.26 306.38 319.31

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	0.217021	1.667	0.05041
2	-0.368968	-2.8341	0.003141
3	-0.212738	-1.6341	0.053785
4	0.21804	1.6748	0.049634
5	-0.007399	-0.0568	0.477434
6	-0.309693	-2.3788	0.010312
7	-0.108469	-0.8332	0.204055
8	0.325162	2.4976	0.007656
9	0.162825	1.2507	0.107994
10	-0.191136	-1.4681	0.073689
11	-0.121961	-0.9368	0.176339
12	0.065917	0.5063	0.30726
13	0.01863	0.1431	0.44335
14	-0.17827	-1.3693	0.088045
15	-0.151515	-1.1638	0.124593
16	0.043349	0.333	0.37017
17	0.054386	0.4177	0.338825
18	-0.160074	-1.2296	0.111872
19	-0.068362	-0.5251	0.300741
20	0.131874	1.0129	0.157612
21	0.143562	1.1027	0.137314
22	-0.029695	-0.2281	0.410182
23	-0.053784	-0.4131	0.340507
24	-0.016273	-0.125	0.450476
25	0.0919	0.7059	0.241516
26	-0.054341	-0.4174	0.338951
27	-0.107779	-0.8279	0.205541
28	-0.093972	-0.7218	0.23663
29	0.091355	0.7017	0.242809
30	0.153139	1.1763	0.122103
31	0.160293	1.2312	0.111561
32	-0.007225	-0.0555	0.477966
33	0.007051	0.0542	0.478495
34	0.033867	0.2601	0.397832
35	-0.062783	-0.4822	0.315707
36	-0.083111	-0.6384	0.262846
37	0.030798	0.2366	0.406908
38	0.105777	0.8125	0.209889
39	0.004532	0.0348	0.486173
40	-0.079812	-0.613	0.2711
41	-0.059035	-0.4535	0.325943
42	0.005012	0.0385	0.48471
43	-0.012925	-0.0993	0.460626
44	-0.047821	-0.3673	0.357348
45	-0.000994	-0.0076	0.496967
46	0.023277	0.1788	0.429356
47	-0.007779	-0.0598	0.476278
48	-0.067762	-0.5205	0.302336
49	-0.07138	-0.5483	0.292783
50	0.035366	0.2717	0.393418
51	0.0584	0.4486	0.327689
52	0.029854	0.2293	0.40971
53	0.00857	0.0658	0.473869
54	0.028388	0.2181	0.414071
55	0.012394	0.0952	0.462239
56	-0.006181	-0.0475	0.481147
57	-0.01858	-0.1427	0.443501
58	-0.000921	-0.0071	0.497189
59	NA	NA	NA
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.217021	1.667	0.05041
2	-0.436631	-3.3538	0.000699
3	-0.003816	-0.0293	0.488359
4	0.161013	1.2368	0.110537
5	-0.276406	-2.1231	0.018975
6	-0.152775	-1.1735	0.122658
7	0.023886	0.1835	0.427528
8	0.150333	1.1547	0.126428
9	-0.064082	-0.4922	0.312195
10	-0.029175	-0.2241	0.411727
11	0.048091	0.3694	0.356578
12	-0.151977	-1.1674	0.123881
13	-0.026531	-0.2038	0.419611
14	-0.06443	-0.4949	0.311256
15	-0.135155	-1.0381	0.151719
16	-0.088297	-0.6782	0.250142
17	-0.10939	-0.8402	0.202083
18	-0.228204	-1.7529	0.04241
19	-0.022548	-0.1732	0.431546
20	-0.029697	-0.2281	0.410177
21	-0.039354	-0.3023	0.381748
22	-0.000911	-0.007	0.497221
23	0.010985	0.0844	0.46652
24	-0.148519	-1.1408	0.129282
25	0.090366	0.6941	0.245167
26	-0.088554	-0.6802	0.24952
27	-0.122584	-0.9416	0.175123
28	-0.220999	-1.6975	0.047433
29	-0.030347	-0.2331	0.408244
30	-0.050747	-0.3898	0.349046
31	0.090948	0.6986	0.243779
32	-0.0392	-0.3011	0.382197
33	0.0103	0.0791	0.468604
34	0.007787	0.0598	0.476254
35	-0.080841	-0.621	0.268511
36	0.078315	0.6016	0.274889
37	0.10963	0.8421	0.201571
38	0.011604	0.0891	0.464639
39	-0.06607	-0.5075	0.30685
40	-0.031511	-0.242	0.404795
41	-0.096819	-0.7437	0.23001
42	-0.147553	-1.1334	0.130821
43	0.07222	0.5547	0.290587
44	-0.070754	-0.5435	0.294426
45	-0.039285	-0.3018	0.381951
46	-0.027397	-0.2104	0.417025
47	0.03809	0.2926	0.385437
48	-0.02617	-0.201	0.420689
49	0.060548	0.4651	0.321792
50	0.03709	0.2849	0.388362
51	-0.038821	-0.2982	0.383303
52	0.038966	0.2993	0.382879
53	0.022613	0.1737	0.431351
54	-0.076189	-0.5852	0.280317
55	0.047755	0.3668	0.357535
56	-0.060122	-0.4618	0.322961
57	-0.015373	-0.1181	0.453202
58	0.001219	0.0094	0.49628
59	NA	NA	NA
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/10/t129199494681m8gewcxkw5g7e/1w6hi1291995042.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t129199494681m8gewcxkw5g7e/1w6hi1291995042.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t129199494681m8gewcxkw5g7e/2w6hi1291995042.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t129199494681m8gewcxkw5g7e/2w6hi1291995042.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 4 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 4 ; 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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