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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 09:44:34 +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/t1292838645wkqmqeu4p3ztxly.htm/, Retrieved Mon, 20 Dec 2010 10:50:47 +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/t1292838645wkqmqeu4p3ztxly.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	2 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.970056	6.7904	0
2	0.927409	6.4919	0
3	0.881258	6.1688	0
4	0.826788	5.7875	0
5	0.761236	5.3286	1e-06
6	0.682464	4.7772	8e-06
7	0.600218	4.2015	5.6e-05
8	0.519003	3.633	0.000335
9	0.431717	3.022	0.001993
10	0.339374	2.3756	0.010738
11	0.250686	1.7548	0.042772
12	0.159923	1.1195	0.1342
13	0.072456	0.5072	0.307148
14	-0.01217	-0.0852	0.46623
15	-0.094329	-0.6603	0.256077
16	-0.170869	-1.1961	0.11871
17	-0.234788	-1.6435	0.053339
18	-0.290021	-2.0301	0.023894
19	-0.336087	-2.3526	0.011351
20	-0.372497	-2.6075	0.006027
21	-0.399882	-2.7992	0.003654
22	-0.418667	-2.9307	0.002563
23	-0.43091	-3.0164	0.002024
24	-0.435758	-3.0503	0.001842
25	-0.433278	-3.0329	0.001933
26	-0.423215	-2.9625	0.002349
27	-0.408131	-2.8569	0.00313
28	-0.386143	-2.703	0.004709
29	-0.369097	-2.5837	0.006404
30	-0.352515	-2.4676	0.008571
31	-0.327896	-2.2953	0.013019
32	-0.301325	-2.1093	0.020027
33	-0.272496	-1.9075	0.031165
34	-0.242829	-1.6998	0.047754
35	-0.216875	-1.5181	0.067704
36	-0.187122	-1.3099	0.098177
37	-0.15944	-1.1161	0.134916
38	-0.135102	-0.9457	0.174467
39	-0.11219	-0.7853	0.218021
40	-0.091275	-0.6389	0.262923
41	-0.074101	-0.5187	0.303149
42	-0.059751	-0.4183	0.338793
43	-0.049803	-0.3486	0.364433
44	-0.044234	-0.3096	0.379075
45	-0.035293	-0.2471	0.40295
46	-0.024933	-0.1745	0.431082
47	-0.01405	-0.0983	0.461028
48	-0.005516	-0.0386	0.484677

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.970056	6.7904	0
2	-0.230515	-1.6136	0.056518
3	-0.03846	-0.2692	0.394446
4	-0.158037	-1.1063	0.137008
5	-0.176549	-1.2358	0.111204
6	-0.219649	-1.5375	0.065297
7	-0.035097	-0.2457	0.403478
8	0.000752	0.0053	0.497911
9	-0.126403	-0.8848	0.190287
10	-0.081867	-0.5731	0.284609
11	0.041006	0.287	0.387644
12	-0.142902	-1.0003	0.161036
13	0.007846	0.0549	0.478212
14	-0.02988	-0.2092	0.417595
15	-0.045502	-0.3185	0.375725
16	-0.035626	-0.2494	0.402053
17	0.138441	0.9691	0.168631
18	0.005435	0.038	0.484905
19	0.027431	0.192	0.424262
20	0.039257	0.2748	0.392314
21	0.007057	0.0494	0.480401
22	-0.064959	-0.4547	0.325661
23	-0.014445	-0.1011	0.459936
24	-0.002789	-0.0195	0.492253
25	-0.036016	-0.2521	0.401004
26	0.006182	0.0433	0.48283
27	0.004979	0.0349	0.486169
28	0.004435	0.031	0.487681
29	-0.222969	-1.5608	0.062506
30	-0.052798	-0.3696	0.356643
31	0.073384	0.5137	0.30489
32	-0.055582	-0.3891	0.349454
33	0.064655	0.4526	0.326424
34	0.069335	0.4853	0.314796
35	-0.102876	-0.7201	0.237432
36	0.049889	0.3492	0.364209
37	-0.029814	-0.2087	0.417774
38	-0.006676	-0.0467	0.481458
39	-0.073362	-0.5135	0.304942
40	0.05158	0.3611	0.359803
41	-0.055393	-0.3878	0.34994
42	-0.050171	-0.3512	0.363472
43	-0.0078	-0.0546	0.478339
44	-0.036171	-0.2532	0.400587
45	0.017026	0.1192	0.452809
46	0.060481	0.4234	0.33694
47	0.047004	0.329	0.371769
48	-0.049312	-0.3452	0.365716

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292838645wkqmqeu4p3ztxly/1o9901292838272.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292838645wkqmqeu4p3ztxly/1o9901292838272.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292838645wkqmqeu4p3ztxly/2hjql1292838272.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292838645wkqmqeu4p3ztxly/2hjql1292838272.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 48 ; 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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