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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: Fri, 27 Nov 2009 05:19:35 -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/27/t12593245803tsa8iy6pc0gb68.htm/, Retrieved Fri, 27 Nov 2009 13:23:02 +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/27/t12593245803tsa8iy6pc0gb68.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 «

1.4 1.2 1 1.7 2.4 2 2.1 2 1.8 2.7 2.3 1.9 2 2.3 2.8 2.4 2.3 2.7 2.7 2.9 3 2.2 2.3 2.8 2.8 2.8 2.2 2.6 2.8 2.5 2.4 2.3 1.9 1.7 2 2.1 1.7 1.8 1.8 1.8 1.3 1.3 1.3 1.2 1.4 2.2 2.9 3.1 3.5 3.6 4.4 4.1 5.1 5.8 5.9 5.4 5.5 4.8 3.2 2.7 2.1 1.9 0.6 0.7 -0.2 -1 -1.7 -0.7 -1

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	0.162865	1.2188	0.11402
2	0.103663	0.7757	0.220583
3	0.141654	1.06	0.146839
4	0.264238	1.9774	0.026465
5	0.068917	0.5157	0.304036
6	0.092798	0.6944	0.245141
7	0.03933	0.2943	0.384803
8	-0.000713	-0.0053	0.497881
9	-0.134865	-1.0092	0.1586
10	-0.090703	-0.6788	0.250044
11	0.053237	0.3984	0.345929
12	-0.383352	-2.8687	0.002901
13	-0.203986	-1.5265	0.066258
14	-0.053163	-0.3978	0.346133
15	0.021814	0.1632	0.435457
16	-0.156749	-1.173	0.12288
17	-0.107203	-0.8022	0.212904
18	-0.054069	-0.4046	0.343651
19	0.000981	0.0073	0.497084
20	-0.103101	-0.7715	0.221816
21	-0.034521	-0.2583	0.398548
22	0.04692	0.3511	0.363408
23	-0.029224	-0.2187	0.413841
24	-0.062856	-0.4704	0.319958
25	0.095569	0.7152	0.238738
26	0.015989	0.1196	0.452595
27	-0.069042	-0.5167	0.303714
28	0.016913	0.1266	0.44987
29	0.042024	0.3145	0.377164
30	0.037529	0.2808	0.389934
31	-0.056946	-0.4261	0.335817
32	0.002513	0.0188	0.492531
33	0.07643	0.572	0.284821
34	0.016443	0.1231	0.451254
35	-0.068993	-0.5163	0.303841
36	0.07684	0.575	0.28379
37	-0.046429	-0.3474	0.36478
38	-0.056262	-0.421	0.337675
39	0.040549	0.3034	0.38134
40	0.020667	0.1547	0.438823
41	-0.04555	-0.3409	0.36724
42	-0.055653	-0.4165	0.339328
43	0.032307	0.2418	0.404923
44	0.02889	0.2162	0.414812
45	-0.056271	-0.4211	0.337649
46	-0.069363	-0.5191	0.30288
47	0.000803	0.006	0.497613
48	-0.044735	-0.3348	0.369527
49	0.029083	0.2176	0.41425
50	0.054384	0.407	0.342791
51	-0.074224	-0.5554	0.290403
52	-0.071108	-0.5321	0.298371
53	0.030016	0.2246	0.411546
54	0.020039	0.15	0.440667
55	-0.004323	-0.0324	0.487153
56	NA	NA	NA
57	NA	NA	NA
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.162865	1.2188	0.11402
2	0.07924	0.593	0.277793
3	0.117023	0.8757	0.192463
4	0.22938	1.7165	0.045797
5	-0.015535	-0.1163	0.453933
6	0.042332	0.3168	0.376294
7	-0.036773	-0.2752	0.392095
8	-0.08067	-0.6037	0.274248
9	-0.167537	-1.2537	0.107574
10	-0.099294	-0.743	0.23028
11	0.103888	0.7774	0.220089
12	-0.401286	-3.003	0.001996
13	-0.037241	-0.2787	0.390756
14	0.071707	0.5366	0.296833
15	0.111121	0.8316	0.204597
16	0.05931	0.4438	0.329437
17	-0.036819	-0.2755	0.391964
18	0.03393	0.2539	0.400248
19	-0.011828	-0.0885	0.464892
20	-0.078768	-0.5894	0.278967
21	-0.114287	-0.8552	0.198029
22	-0.04011	-0.3002	0.382586
23	0.057233	0.4283	0.33504
24	-0.18406	-1.3774	0.086938
25	0.080094	0.5994	0.275672
26	-0.01829	-0.1369	0.445811
27	0.020652	0.1545	0.438869
28	0.091823	0.6871	0.247415
29	-0.073005	-0.5463	0.293509
30	0.050109	0.375	0.354546
31	-0.075483	-0.5649	0.287212
32	-0.030762	-0.2302	0.409387
33	-0.006087	-0.0456	0.481915
34	-0.026843	-0.2009	0.420763
35	0.010988	0.0822	0.46738
36	-0.043981	-0.3291	0.371645
37	-0.028145	-0.2106	0.416975
38	-0.058759	-0.4397	0.330918
39	0.07741	0.5793	0.28236
40	0.010629	0.0795	0.468443
41	-0.077488	-0.5799	0.282165
42	0.033606	0.2515	0.40118
43	0.006068	0.0454	0.48197
44	-0.01028	-0.0769	0.469477
45	-0.045927	-0.3437	0.366186
46	-0.030397	-0.2275	0.410444
47	-0.070302	-0.5261	0.300452
48	-0.046986	-0.3516	0.363225
49	0.090757	0.6792	0.249916
50	0.001616	0.0121	0.495196
51	-0.068571	-0.5131	0.304935
52	-0.0084	-0.0629	0.475052
53	0.025384	0.19	0.425015
54	-0.022622	-0.1693	0.43309
55	-0.007207	-0.0539	0.478592
56	NA	NA	NA
57	NA	NA	NA
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/27/t12593245803tsa8iy6pc0gb68/1grxo1259324374.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t12593245803tsa8iy6pc0gb68/1grxo1259324374.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t12593245803tsa8iy6pc0gb68/2y9501259324374.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t12593245803tsa8iy6pc0gb68/2y9501259324374.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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