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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: Fri, 24 Dec 2010 11:38:30 +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/24/t1293190614k1bj0hik4t9nm7z.htm/, Retrieved Fri, 24 Dec 2010 12:36:54 +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/24/t1293190614k1bj0hik4t9nm7z.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 «

12008 9169 8788 8417 8247 8197 8236 8253 7733 8366 8626 8863 10102 8463 9114 8563 8872 8301 8301 8278 7736 7973 8268 9476 11100 8962 9173 8738 8459 8078 8411 8291 7810 8616 8312 9692 9911 8915 9452 9112 8472 8230 8384 8625 8221 8649 8625 10443 10357 8586 8892 8329 8101 7922 8120 7838 7735 8406 8209 9451 10041 9411 10405 8467 8464 8102 7627 7513 7510 8291 8064 9383

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.420701	3.5698	0.00032
2	0.227057	1.9266	0.028986
3	-0.026365	-0.2237	0.411806
4	-0.269141	-2.2837	0.01267
5	-0.337099	-2.8604	0.002767
6	-0.429438	-3.6439	0.000252
7	-0.348298	-2.9554	0.002109
8	-0.326429	-2.7698	0.003565
9	-0.05789	-0.4912	0.312384
10	0.081015	0.6874	0.247007
11	0.282198	2.3945	0.009623
12	0.591205	5.0165	2e-06
13	0.248793	2.1111	0.019119
14	0.237259	2.0132	0.023916
15	0.031822	0.27	0.393959
16	-0.16458	-1.3965	0.083426
17	-0.226267	-1.9199	0.029414
18	-0.312358	-2.6504	0.004939
19	-0.264632	-2.2455	0.013904
20	-0.27992	-2.3752	0.010102
21	-0.077005	-0.6534	0.257786
22	0.04203	0.3566	0.361204
23	0.322896	2.7399	0.003872
24	0.528329	4.483	1.4e-05
25	0.161095	1.3669	0.087949
26	0.126988	1.0775	0.14242
27	-0.051806	-0.4396	0.330776
28	-0.198388	-1.6834	0.048317
29	-0.22807	-1.9352	0.028444
30	-0.262828	-2.2302	0.014427
31	-0.211671	-1.7961	0.038338
32	-0.196476	-1.6672	0.049914
33	-0.019074	-0.1618	0.435939
34	0.037347	0.3169	0.376119
35	0.259394	2.201	0.01547
36	0.358348	3.0407	0.001645
37	0.154232	1.3087	0.097399
38	0.18595	1.5778	0.059493
39	-0.029028	-0.2463	0.403072
40	-0.151809	-1.2881	0.100911
41	-0.179486	-1.523	0.066071
42	-0.21038	-1.7851	0.039226
43	-0.15427	-1.309	0.097344
44	-0.144046	-1.2223	0.112796
45	0.006292	0.0534	0.478783
46	0.067969	0.5767	0.282958
47	0.269358	2.2856	0.012613
48	0.276031	2.3422	0.01097
49	0.085844	0.7284	0.234362
50	0.111724	0.948	0.173148
51	-0.029201	-0.2478	0.402505
52	-0.078175	-0.6633	0.254617
53	-0.109459	-0.9288	0.17805
54	-0.141573	-1.2013	0.116789
55	-0.128774	-1.0927	0.139088
56	-0.136331	-1.1568	0.125587
57	-0.035608	-0.3021	0.381707
58	-0.02447	-0.2076	0.41805
59	0.121501	1.031	0.153003
60	0.156494	1.3279	0.094204

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.420701	3.5698	0.00032
2	0.060835	0.5162	0.303648
3	-0.172776	-1.4661	0.073493
4	-0.270365	-2.2941	0.012351
5	-0.146616	-1.2441	0.108753
6	-0.235724	-2.0002	0.024626
7	-0.137322	-1.1652	0.123889
8	-0.258259	-2.1914	0.01583
9	0.016646	0.1412	0.444034
10	-0.067662	-0.5741	0.283836
11	0.076724	0.651	0.258552
12	0.393171	3.3362	0.000673
13	-0.295759	-2.5096	0.007168
14	0.049811	0.4227	0.3369
15	0.004813	0.0408	0.483767
16	-0.096384	-0.8178	0.208072
17	0.03371	0.286	0.387836
18	-0.024883	-0.2111	0.416686
19	-0.009628	-0.0817	0.467558
20	-0.050477	-0.4283	0.334853
21	-0.065582	-0.5565	0.289803
22	0.082337	0.6987	0.24351
23	0.201178	1.7071	0.046061
24	0.155191	1.3168	0.096035
25	-0.263494	-2.2358	0.014232
26	-0.156145	-1.3249	0.094691
27	0.035647	0.3025	0.38158
28	-0.068624	-0.5823	0.281094
29	-0.013122	-0.1113	0.455828
30	0.02072	0.1758	0.430467
31	-0.017313	-0.1469	0.441809
32	-0.008375	-0.0711	0.471772
33	-0.065019	-0.5517	0.291429
34	-0.079665	-0.676	0.250611
35	-0.053647	-0.4552	0.325165
36	-0.04897	-0.4155	0.339496
37	0.062265	0.5283	0.299446
38	0.020233	0.1717	0.432084
39	-0.094186	-0.7992	0.213404
40	-0.027745	-0.2354	0.407275
41	-0.007533	-0.0639	0.474607
42	-0.007874	-0.0668	0.473458
43	0.083903	0.7119	0.239401
44	0.032479	0.2756	0.391825
45	0.040706	0.3454	0.365399
46	-0.014117	-0.1198	0.452493
47	-0.062002	-0.5261	0.300217
48	0.00439	0.0373	0.485194
49	0.013544	0.1149	0.454414
50	0.041537	0.3525	0.362764
51	0.129104	1.0955	0.138478
52	0.090288	0.7661	0.223055
53	0.013983	0.1186	0.452943
54	-0.039636	-0.3363	0.368802
55	-0.052269	-0.4435	0.329361
56	-0.032764	-0.278	0.390899
57	-0.018305	-0.1553	0.438502
58	-0.041181	-0.3494	0.363891
59	-0.084264	-0.715	0.23846
60	0.010979	0.0932	0.463019

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293190614k1bj0hik4t9nm7z/137m61293190707.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293190614k1bj0hik4t9nm7z/137m61293190707.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293190614k1bj0hik4t9nm7z/237m61293190707.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293190614k1bj0hik4t9nm7z/237m61293190707.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; 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 (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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