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R Software Module: /rwasp_autocorrelation.wasp (opens new window with default values)

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Sun, 27 Dec 2009 07:07:34 -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/27/t1261922912sv434topzaabiud.htm/, Retrieved Sun, 27 Dec 2009 15:08:34 +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/27/t1261922912sv434topzaabiud.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 «

2921,44 2981,85 3080,58 3106,22 3119,31 3061,26 3097,31 3161,69 3257,16 3277,01 3295,32 3363,99 3494,17 3667,03 3813,06 3917,96 3895,51 3801,06 3570,12 3701,61 3862,27 3970,1 4138,52 4199,75 4290,89 4443,91 4502,64 4356,98 4591,27 4696,96 4621,4 4562,84 4202,52 4296,49 4435,23 4105,18 4116,68 3844,49 3720,98 3674,4 3857,62 3801,06 3504,37 3032,6 3047,03 2962,34 2197,82 2014,45 1862,83 1905,41 1810,99 1670,07 1864,44 2052,02 2029,6 2070,83 2293,41 2443,27 2513,17 2466,92

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	0.965158	7.4761	0
2	0.919736	7.1242	0
3	0.871062	6.7472	0
4	0.810548	6.2785	0
5	0.737101	5.7096	0
6	0.649998	5.0349	2e-06
7	0.562613	4.358	2.6e-05
8	0.473694	3.6692	0.000259
9	0.375781	2.9108	0.002527
10	0.278576	2.1578	0.017477
11	0.188709	1.4617	0.074516
12	0.091711	0.7104	0.240108
13	-0.000976	-0.0076	0.496998
14	-0.08629	-0.6684	0.253221
15	-0.158419	-1.2271	0.112287
16	-0.225258	-1.7448	0.043067
17	-0.294338	-2.2799	0.01309
18	-0.348593	-2.7002	0.004496
19	-0.390544	-3.0251	0.001828
20	-0.430354	-3.3335	0.000737
21	-0.468064	-3.6256	0.000298
22	-0.495516	-3.8382	0.00015
23	-0.509593	-3.9473	0.000105
24	-0.508826	-3.9413	0.000107
25	-0.501493	-3.8845	0.000129
26	-0.481535	-3.73	0.000213
27	-0.459048	-3.5558	0.000371
28	-0.439505	-3.4044	0.000594
29	-0.410437	-3.1792	0.001168
30	-0.376571	-2.9169	0.002484
31	-0.339565	-2.6303	0.005413
32	-0.30209	-2.34	0.011315
33	-0.273888	-2.1215	0.019008
34	-0.238993	-1.8512	0.03453
35	-0.19993	-1.5486	0.063362
36	-0.163828	-1.269	0.10467
37	-0.127906	-0.9908	0.162891
38	-0.096499	-0.7475	0.228847
39	-0.069269	-0.5366	0.296779
40	-0.042834	-0.3318	0.370602
41	-0.015828	-0.1226	0.451415
42	0.007193	0.0557	0.477876
43	0.031293	0.2424	0.404649
44	0.051319	0.3975	0.346201
45	0.07237	0.5606	0.288588
46	0.090059	0.6976	0.244064
47	0.096342	0.7463	0.229212
48	0.097167	0.7527	0.227301
49	0.093656	0.7255	0.235496
50	0.088634	0.6866	0.247503
51	0.081666	0.6326	0.264706
52	0.072631	0.5626	0.287902
53	0.063241	0.4899	0.313009
54	0.054145	0.4194	0.338209
55	0.043464	0.3367	0.36877
56	0.033791	0.2617	0.397208
57	0.025682	0.1989	0.421494
58	0.018534	0.1436	0.443162
59	0.010116	0.0784	0.468902
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.965158	7.4761	0
2	-0.172257	-1.3343	0.093574
3	-0.049419	-0.3828	0.351611
4	-0.194125	-1.5037	0.068954
5	-0.187287	-1.4507	0.076033
6	-0.21831	-1.691	0.048011
7	-0.002759	-0.0214	0.491511
8	-0.048374	-0.3747	0.354601
9	-0.138161	-1.0702	0.144411
10	-0.005566	-0.0431	0.482877
11	0.051922	0.4022	0.344489
12	-0.210097	-1.6274	0.054446
13	0.021197	0.1642	0.435067
14	0.004582	0.0355	0.485903
15	0.093308	0.7228	0.236317
16	-0.058321	-0.4518	0.326537
17	-0.107457	-0.8324	0.204253
18	0.061628	0.4774	0.317416
19	-0.021116	-0.1636	0.435313
20	-0.093211	-0.722	0.236546
21	-0.088376	-0.6846	0.248129
22	-0.00117	-0.0091	0.4964
23	0.04436	0.3436	0.366171
24	0.134732	1.0436	0.150422
25	0.050296	0.3896	0.349109
26	0.053027	0.4107	0.34136
27	-0.156907	-1.2154	0.114488
28	-0.127911	-0.9908	0.162882
29	0.01646	0.1275	0.449486
30	-0.037488	-0.2904	0.386263
31	0.001973	0.0153	0.493929
32	0.050417	0.3905	0.348764
33	-0.191245	-1.4814	0.071869
34	0.015568	0.1206	0.45221
35	0.006388	0.0495	0.480351
36	0.05971	0.4625	0.322692
37	0.012558	0.0973	0.461416
38	-0.021207	-0.1643	0.435036
39	-0.063223	-0.4897	0.313057
40	-0.031303	-0.2425	0.404619
41	0.082088	0.6359	0.263645
42	-0.084802	-0.6569	0.256888
43	0.070256	0.5442	0.29416
44	-0.01854	-0.1436	0.443143
45	-0.022176	-0.1718	0.432097
46	-0.026717	-0.207	0.418374
47	-0.118194	-0.9155	0.18179
48	-0.052555	-0.4071	0.342695
49	-0.019688	-0.1525	0.439651
50	-0.045858	-0.3552	0.361838
51	0.004509	0.0349	0.486128
52	0.024939	0.1932	0.423737
53	0.068327	0.5293	0.299291
54	0.002764	0.0214	0.491496
55	-0.021085	-0.1633	0.435405
56	-0.096213	-0.7453	0.229512
57	0.018901	0.1464	0.442046
58	0.056661	0.4389	0.331157
59	0.012296	0.0952	0.462219
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/27/t1261922912sv434topzaabiud/15uxk1261922852.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/27/t1261922912sv434topzaabiud/15uxk1261922852.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/27/t1261922912sv434topzaabiud/26gfr1261922852.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/27/t1261922912sv434topzaabiud/26gfr1261922852.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1.4 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 1.4 ; 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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