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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: Sun, 20 Dec 2009 12:04:50 -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/Dec/20/t1261335953p0j069fvu79famk.htm/, Retrieved Sun, 20 Dec 2009 20:05:55 +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/Dec/20/t1261335953p0j069fvu79famk.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 «

100.00 97.57 93.71 92.70 89.66 89.05 98.99 105.68 101.62 98.38 94.12 93.31 94.73 93.31 90.87 89.86 88.44 87.42 98.17 103.45 104.06 102.03 95.54 95.54 96.55 96.35 95.33 93.51 92.29 92.49 104.87 106.49 106.09 105.27 103.25 103.85 105.27 104.87 103.45 103.25 101.62 102.84 115.42 117.65 117.24 114.60 110.95 112.58 114.00 113.79 112.58 110.34 108.92 110.14 120.49 123.94 124.34 123.94 120.49 120.69 119.88 119.47 118.46 116.23 115.01 115.42 125.96 127.59 127.38 124.14 120.69 121.10 120.28 119.68 117.65 116.43 116.23 116.23 125.76 126.98 125.76 119.27 114.81 112.98 113.79 111.36 107.91 106.69 103.65 101.22 112.58 114.60 109.94 106.90 103.45 104.26 104.87 103.04 100.00 99.39 95.13 96.96 107.10 108.32 105.07 102.64 101.83 104.67

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	0.012661	0.1234	0.451024
2	-0.009578	-0.0934	0.462909
3	0.014659	0.1429	0.443346
4	0.07168	0.6986	0.243239
5	0.106414	1.0372	0.151138
6	0.100635	0.9809	0.164575
7	0.018844	0.1837	0.427332
8	0.103143	1.0053	0.15865
9	0.131903	1.2856	0.100848
10	-0.034226	-0.3336	0.36971
11	0.017075	0.1664	0.434087
12	-0.189372	-1.8458	0.03402
13	0.049778	0.4852	0.314333
14	0.244202	2.3802	0.009651
15	-0.022111	-0.2155	0.414914
16	-0.011484	-0.1119	0.455556
17	-0.071581	-0.6977	0.24354
18	0.004587	0.0447	0.482219
19	0.040726	0.3969	0.346147
20	0.000238	0.0023	0.499075
21	0.022252	0.2169	0.41438
22	0.06121	0.5966	0.276095
23	0.147264	1.4354	0.077235
24	-0.116901	-1.1394	0.128699
25	-0.159599	-1.5556	0.061567
26	-0.204778	-1.9959	0.024402
27	0.05887	0.5738	0.283732
28	-0.022356	-0.2179	0.413988
29	0.101273	0.9871	0.163053
30	-0.08319	-0.8108	0.209742
31	-0.073435	-0.7158	0.237949
32	0.013198	0.1286	0.448956
33	-0.090719	-0.8842	0.189406
34	-0.075463	-0.7355	0.231918
35	-0.04509	-0.4395	0.330655
36	0.023173	0.2259	0.410896
37	0.064064	0.6244	0.266925
38	0.054141	0.5277	0.299469
39	-0.146394	-1.4269	0.078447
40	-0.085257	-0.831	0.204033
41	0.000999	0.0097	0.496124
42	-0.026195	-0.2553	0.399516
43	0.055648	0.5424	0.294411
44	-0.080007	-0.7798	0.218721
45	-0.082628	-0.8054	0.211312
46	-0.025736	-0.2508	0.401239
47	-0.15546	-1.5152	0.066516
48	-0.073819	-0.7195	0.236799
49	-0.074831	-0.7294	0.233788
50	0.046838	0.4565	0.324529
51	-0.016448	-0.1603	0.436487
52	-0.013546	-0.132	0.447619
53	-0.172508	-1.6814	0.047985
54	0.002886	0.0281	0.488807
55	-0.089166	-0.8691	0.193495
56	-0.021356	-0.2082	0.417778
57	0.046157	0.4499	0.326908
58	-0.047188	-0.4599	0.323307
59	0.009505	0.0926	0.463193
60	-0.009093	-0.0886	0.464783

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.012661	0.1234	0.451024
2	-0.00974	-0.0949	0.462284
3	0.014908	0.1453	0.442388
4	0.07124	0.6944	0.244574
5	0.105516	1.0284	0.153175
6	0.101745	0.9917	0.161934
7	0.019622	0.1913	0.424369
8	0.100867	0.9831	0.16402
9	0.121037	1.1797	0.120529
10	-0.054195	-0.5282	0.299285
11	-0.003002	-0.0293	0.488358
12	-0.231728	-2.2586	0.013098
13	0.002512	0.0245	0.490258
14	0.21191	2.0654	0.020802
15	-0.038584	-0.3761	0.353851
16	0.018342	0.1788	0.429246
17	-0.07485	-0.7295	0.233732
18	0.003105	0.0303	0.487962
19	0.026412	0.2574	0.398702
20	-0.006906	-0.0673	0.473239
21	0.083734	0.8161	0.20823
22	2.3e-05	2e-04	0.499911
23	0.138675	1.3516	0.08985
24	-0.155124	-1.512	0.066932
25	-0.193336	-1.8844	0.031283
26	-0.149801	-1.4601	0.073784
27	-0.027401	-0.2671	0.394995
28	-0.082532	-0.8044	0.21158
29	0.134731	1.3132	0.09614
30	-0.017098	-0.1666	0.434001
31	0.020328	0.1981	0.421681
32	0.059291	0.5779	0.282352
33	-0.026915	-0.2623	0.396817
34	-0.026337	-0.2567	0.398981
35	-0.00144	-0.014	0.494415
36	-0.038262	-0.3729	0.355016
37	-0.03598	-0.3507	0.363299
38	0.074598	0.7271	0.234479
39	-0.024203	-0.2359	0.407007
40	-0.053553	-0.522	0.301452
41	0.00467	0.0455	0.481896
42	-0.063653	-0.6204	0.268237
43	-0.022425	-0.2186	0.413726
44	-0.017422	-0.1698	0.432762
45	-0.075627	-0.7371	0.231433
46	-0.028689	-0.2796	0.390185
47	-0.068509	-0.6677	0.252957
48	0.0087	0.0848	0.4663
49	-0.050313	-0.4904	0.312493
50	0.03861	0.3763	0.353758
51	-0.06147	-0.5991	0.275253
52	-0.103301	-1.0069	0.158282
53	-0.050228	-0.4896	0.312787
54	0.059367	0.5786	0.282102
55	-0.035011	-0.3412	0.366835
56	0.018326	0.1786	0.429309
57	0.057356	0.559	0.288725
58	-0.050491	-0.4921	0.311883
59	-0.025792	-0.2514	0.401028
60	-0.010714	-0.1044	0.458527

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/20/t1261335953p0j069fvu79famk/1gl7h1261335888.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/20/t1261335953p0j069fvu79famk/1gl7h1261335888.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/20/t1261335953p0j069fvu79famk/2bq871261335888.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/20/t1261335953p0j069fvu79famk/2bq871261335888.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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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