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*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 09:59:09 +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/t1292839293nyxrqgjiej5ktw2.htm/, Retrieved Mon, 20 Dec 2010 11:01:33 +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/t1292839293nyxrqgjiej5ktw2.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 «

2539.91 2502.66 2466.92 2513.17 2443.27 2293.41 2070.83 2029.60 2052.02 1864.44 1670.07 1810.99 1905.41 1862.83 2014.45 2197.82 2962.34 3047.03 3032.60 3504.37 3801.06 3857.62 3674.40 3720.98 3844.49 4116.68 4105.18 4435.23 4296.49 4202.52 4562.84 4621.40 4696.96 4591.27 4356.98 4502.64 4443.91 4290.89 4199.75 4138.52 3970.10 3862.27 3701.61 3570.12 3801.06 3895.51 3917.96 3813.06 3667.03

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

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.248728	1.7232	0.045641
2	0.032211	0.2232	0.412178
3	0.206544	1.431	0.079458
4	0.231478	1.6037	0.057667
5	0.268813	1.8624	0.034338
6	-0.061709	-0.4275	0.335451
7	-0.094881	-0.6574	0.257046
8	0.112376	0.7786	0.22003
9	-0.022596	-0.1566	0.438127
10	-0.222217	-1.5396	0.065117
11	0.064827	0.4491	0.327678
12	-0.096772	-0.6705	0.252891
13	-0.135107	-0.9361	0.176966
14	-0.001244	-0.0086	0.49658
15	-0.124025	-0.8593	0.197232
16	0.001628	0.0113	0.495524
17	-0.183908	-1.2741	0.104373
18	-0.243287	-1.6855	0.049187
19	0.025643	0.1777	0.42987
20	-0.109118	-0.756	0.226674
21	-0.217163	-1.5046	0.069496
22	-0.20117	-1.3937	0.084907
23	-0.170751	-1.183	0.121319
24	-0.084101	-0.5827	0.281423
25	-0.041057	-0.2845	0.388644
26	-0.121176	-0.8395	0.202666
27	-0.045234	-0.3134	0.37767
28	0.062519	0.4331	0.333426
29	0.015593	0.108	0.457211
30	0.056694	0.3928	0.348108
31	-0.011701	-0.0811	0.467862
32	0.006255	0.0433	0.482806
33	0.07373	0.5108	0.305911
34	0.031312	0.2169	0.414588
35	0.022487	0.1558	0.438424
36	0.038015	0.2634	0.396694
37	0.046314	0.3209	0.374849
38	0.036069	0.2499	0.401868
39	0.006707	0.0465	0.481564
40	-0.004146	-0.0287	0.488603
41	0.033461	0.2318	0.408829
42	0.03434	0.2379	0.40648
43	0.013422	0.093	0.46315
44	0.004734	0.0328	0.486986
45	0.002081	0.0144	0.494278
46	0.009752	0.0676	0.473205
47	0.005629	0.039	0.484526
48	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.248728	1.7232	0.045641
2	-0.031611	-0.219	0.413787
3	0.219955	1.5239	0.067049
4	0.14035	0.9724	0.167869
5	0.217074	1.5039	0.069575
6	-0.224971	-1.5586	0.062825
7	-0.096133	-0.666	0.25429
8	0.025948	0.1798	0.429043
9	-0.104513	-0.7241	0.236263
10	-0.209376	-1.4506	0.076698
11	0.291464	2.0193	0.024528
12	-0.207956	-1.4408	0.078072
13	-0.031012	-0.2149	0.415394
14	0.132807	0.9201	0.181057
15	-0.073291	-0.5078	0.306969
16	-0.091469	-0.6337	0.264638
17	-0.109743	-0.7603	0.22539
18	-0.109105	-0.7559	0.2267
19	-0.006123	-0.0424	0.483168
20	-0.093032	-0.6445	0.261145
21	0.014678	0.1017	0.459714
22	-0.208694	-1.4459	0.077355
23	-0.030812	-0.2135	0.415932
24	-0.028838	-0.1998	0.421243
25	0.040503	0.2806	0.390107
26	0.041973	0.2908	0.386229
27	-0.034255	-0.2373	0.406708
28	0.081495	0.5646	0.287483
29	0.033702	0.2335	0.408185
30	-0.141468	-0.9801	0.16597
31	-0.003198	-0.0222	0.491207
32	-0.078483	-0.5437	0.294566
33	-0.076817	-0.5322	0.29852
34	0.00514	0.0356	0.48587
35	0.009298	0.0644	0.474451
36	0.030786	0.2133	0.416001
37	0.013591	0.0942	0.462687
38	0.011523	0.0798	0.468351
39	-0.125965	-0.8727	0.193583
40	-0.101166	-0.7009	0.243374
41	0.004725	0.0327	0.487012
42	-0.060147	-0.4167	0.339375
43	0.005804	0.0402	0.484046
44	-0.038604	-0.2675	0.395131
45	-0.047323	-0.3279	0.37222
46	0.021051	0.1458	0.442327
47	-0.036072	-0.2499	0.401861
48	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292839293nyxrqgjiej5ktw2/1uu041292839146.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292839293nyxrqgjiej5ktw2/1uu041292839146.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292839293nyxrqgjiej5ktw2/2uu041292839146.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292839293nyxrqgjiej5ktw2/2uu041292839146.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; 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 (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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