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WS08 - PACF d = 0/ D=1 / lambda = 1

*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, 25 Nov 2009 13:36:50 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/25/t1259181482c2badiip6ydor5o.htm/, Retrieved Wed, 25 Nov 2009 21:38:04 +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/2009/Nov/25/t1259181482c2badiip6ydor5o.htm/},
    year = {2009},
}
@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 = {2009},
    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 «

423.4 404.1 500 472.6 496.1 562 434.8 538.2 577.6 518.1 625.2 561.2 523.3 536.1 607.3 637.3 606.9 652.9 617.2 670.4 729.9 677.2 710 844.3 748.2 653.9 742.6 854.2 808.4 1819 1936.5 1966.1 2083.1 1620.1 1527.6 1795 1685.1 1851.8 2164.4 1981.8 1726.5 2144.6 1758.2 1672.9 1837.3 1596.1 1446 1898.4 1964.1 1755.9 2255.3 1881.2 2117.9 1656.5 1544.1 2098.9 2133.3 1963.5 1801.2 2365.4 1936.5 1667.6 1983.5 2058.6 2448.3 1858.1 1625.4 2130.6 2515.7 2230.2 2086.9 2235 2100.2 2288.6 2490 2573.7 2543.8 2004.7 2390 2338.4 2724.5 2292.5 2386 2477.9 2337 2605.1 2560.8 2839.3 2407.2 2085.2 2735.6 2798.7 3053.2 2405 2471.9 2727.3 2790.7 2385.4 3206.6 2705.6 3518.4 1954.9 2584.3 2535.8 2685.9 2866 2236.6 2934.9 2668.6 2371.2 3165.9 2887.2 3112.2 2671.2 2432.6 2812.3 3095.7 2862.9 2607.3 2862.5

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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.890213	9.7518	0
2	0.864792	9.4733	0
3	0.832978	9.1248	0
4	0.814408	8.9214	0
5	0.801514	8.7802	0
6	0.765301	8.3834	0
7	0.753893	8.2585	0
8	0.729424	7.9904	0
9	0.691557	7.5756	0
10	0.650358	7.1243	0
11	0.632532	6.929	0
12	0.642942	7.0431	0
13	0.578099	6.3328	0
14	0.541422	5.931	0
15	0.52515	5.7527	0
16	0.506481	5.5482	0
17	0.488236	5.3484	0
18	0.465872	5.1034	1e-06
19	0.440708	4.8277	2e-06
20	0.418317	4.5824	6e-06
21	0.375185	4.1099	3.6e-05
22	0.331157	3.6276	0.000211
23	0.31645	3.4665	0.000366
24	0.30168	3.3047	0.000627
25	0.265626	2.9098	0.002156
26	0.231692	2.5381	0.006214
27	0.213207	2.3356	0.010587
28	0.181153	1.9844	0.024745
29	0.146301	1.6026	0.055821
30	0.137696	1.5084	0.067042
31	0.134101	1.469	0.072224
32	0.136921	1.4999	0.068134
33	0.117455	1.2867	0.100346
34	0.099508	1.0901	0.138937
35	0.097054	1.0632	0.144918
36	0.098771	1.082	0.140715
37	0.073368	0.8037	0.211578
38	0.056742	0.6216	0.267699
39	0.060222	0.6597	0.255356
40	0.053461	0.5856	0.279608
41	0.041267	0.4521	0.326021
42	0.029448	0.3226	0.373786
43	0.032191	0.3526	0.362489
44	0.01068	0.117	0.45353
45	-0.00965	-0.1057	0.457994
46	-0.034457	-0.3775	0.353248
47	-0.052297	-0.5729	0.283897
48	-0.039934	-0.4375	0.331282
49	-0.067559	-0.7401	0.23035
50	-0.083087	-0.9102	0.182279
51	-0.087669	-0.9604	0.169402
52	-0.097879	-1.0722	0.14289
53	-0.104995	-1.1502	0.126181
54	-0.121984	-1.3363	0.091996
55	-0.127993	-1.4021	0.081735
56	-0.144051	-1.578	0.058599
57	-0.148543	-1.6272	0.053158
58	-0.166683	-1.8259	0.035174
59	-0.174498	-1.9115	0.029161
60	-0.164164	-1.7983	0.037319

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.890213	9.7518	0
2	0.34846	3.8172	0.000107
3	0.116203	1.2729	0.10275
4	0.10284	1.1266	0.131089
5	0.099799	1.0932	0.138238
6	-0.065899	-0.7219	0.235884
7	0.055666	0.6098	0.271575
8	-0.003095	-0.0339	0.486507
9	-0.11304	-1.2383	0.109013
10	-0.118012	-1.2928	0.09929
11	0.051793	0.5674	0.285764
12	0.200408	2.1954	0.015031
13	-0.264886	-2.9017	0.002209
14	-0.115812	-1.2687	0.103509
15	0.136457	1.4948	0.068794
16	0.037715	0.4131	0.340118
17	-0.029318	-0.3212	0.374324
18	0.07679	0.8412	0.200957
19	-0.063607	-0.6968	0.243645
20	-0.087698	-0.9607	0.169321
21	-0.064479	-0.7063	0.240676
22	-0.055987	-0.6133	0.270418
23	-0.007582	-0.0831	0.466975
24	-0.036645	-0.4014	0.344409
25	0.010792	0.1182	0.453043
26	-0.008375	-0.0917	0.463528
27	-0.007651	-0.0838	0.466671
28	-0.059527	-0.6521	0.257797
29	-0.057674	-0.6318	0.264366
30	0.121851	1.3348	0.092232
31	0.15487	1.6965	0.046191
32	0.074966	0.8212	0.206578
33	0.001871	0.0205	0.49184
34	0.017779	0.1948	0.422956
35	-0.035072	-0.3842	0.350759
36	0.021828	0.2391	0.405714
37	-0.085943	-0.9415	0.174181
38	-0.089774	-0.9834	0.163689
39	0.030475	0.3338	0.369542
40	0.06838	0.7491	0.22764
41	0.017666	0.1935	0.423439
42	-0.07961	-0.8721	0.192451
43	-0.007239	-0.0793	0.468463
44	-0.139051	-1.5232	0.065166
45	-0.023647	-0.259	0.398026
46	0.029229	0.3202	0.374692
47	-0.079605	-0.872	0.192468
48	0.061159	0.67	0.252084
49	-0.0014	-0.0153	0.493893
50	-0.087556	-0.9591	0.169711
51	-0.058452	-0.6403	0.261595
52	0.011861	0.1299	0.448418
53	0.035331	0.387	0.349711
54	-0.017572	-0.1925	0.423841
55	-0.017309	-0.1896	0.424967
56	1.4e-05	2e-04	0.49994
57	0.01902	0.2084	0.417654
58	-0.055113	-0.6037	0.27358
59	0.003708	0.0406	0.483835
60	0.051753	0.5669	0.285911

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/25/t1259181482c2badiip6ydor5o/1cifr1259181408.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/25/t1259181482c2badiip6ydor5o/1cifr1259181408.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/25/t1259181482c2badiip6ydor5o/2a7811259181408.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/25/t1259181482c2badiip6ydor5o/2a7811259181408.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = MA ; 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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