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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: Tue, 21 Dec 2010 18:57:45 +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/21/t1292957730jsl3q6i9ea34a91.htm/, Retrieved Tue, 21 Dec 2010 19:55:32 +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/21/t1292957730jsl3q6i9ea34a91.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 «

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 3970,10 4138,52 4199,75 4290,89 4443,91 4502,64 4356,98 4591,27 4696,96 4621,40 4562,84 4202,52 4296,49 4435,23 4105,18 4116,68 3844,49 3720,98 3674,40 3857,62 3801,06 3504,37 3032,60 3047,03 2962,34 2197,82 2014,45 1862,83 1905,41 1810,99 1670,07 1864,44 2052,02 2029,60 2070,83 2293,41 2443,27 2513,17 2466,92 2502,66 2539,91

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	5 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.96971	7.5737	0
2	0.927114	7.241	0
3	0.880727	6.8787	0
4	0.8255	6.4474	0
5	0.757929	5.9196	0
6	0.676521	5.2838	1e-06
7	0.592703	4.6292	1e-05
8	0.510667	3.9884	9e-05
9	0.422414	3.2992	0.000811
10	0.329463	2.5732	0.006262
11	0.240564	1.8789	0.032522
12	0.149835	1.1702	0.123226
13	0.06275	0.4901	0.312913
14	-0.021915	-0.1712	0.432332
15	-0.104585	-0.8168	0.208601
16	-0.181137	-1.4147	0.081116
17	-0.246774	-1.9274	0.029297
18	-0.307296	-2.4001	0.00973
19	-0.358635	-2.801	0.003408
20	-0.40048	-3.1279	0.001349
21	-0.431993	-3.374	0.000646
22	-0.45361	-3.5428	0.000383
23	-0.47005	-3.6712	0.000255
24	-0.477471	-3.7292	0.000212
25	-0.475934	-3.7172	0.00022
26	-0.465714	-3.6373	0.000284
27	-0.451672	-3.5277	0.000402
28	-0.428501	-3.3467	0.000702
29	-0.408919	-3.1938	0.001111
30	-0.389829	-3.0447	0.001718
31	-0.362995	-2.8351	0.003103
32	-0.335038	-2.6167	0.005588
33	-0.304253	-2.3763	0.010321
34	-0.27237	-2.1273	0.018724
35	-0.243857	-1.9046	0.030776
36	-0.207872	-1.6235	0.054816
37	-0.173818	-1.3576	0.089801
38	-0.143488	-1.1207	0.133409
39	-0.114035	-0.8906	0.188309
40	-0.081902	-0.6397	0.26239
41	-0.051593	-0.403	0.344196
42	-0.026828	-0.2095	0.417365
43	-0.009929	-0.0776	0.46922
44	0.004094	0.032	0.487297
45	0.021947	0.1714	0.432233
46	0.034178	0.2669	0.395207
47	0.044547	0.3479	0.364547
48	0.051473	0.402	0.344538
49	0.05581	0.4359	0.332226
50	0.055558	0.4339	0.332939
51	0.050767	0.3965	0.346559
52	0.046026	0.3595	0.36024
53	0.042535	0.3322	0.370435
54	0.038242	0.2987	0.383099
55	0.031828	0.2486	0.402259
56	0.025703	0.2007	0.420781
57	0.020045	0.1566	0.438056
58	0.016058	0.1254	0.450302
59	0.011366	0.0888	0.464777
60	0.006418	0.0501	0.480092

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.96971	7.5737	0
2	-0.221624	-1.7309	0.044259
3	-0.046544	-0.3635	0.358735
4	-0.163511	-1.2771	0.10321
5	-0.197454	-1.5422	0.064103
6	-0.227153	-1.7741	0.040517
7	-0.018451	-0.1441	0.442945
8	0.016018	0.1251	0.450425
9	-0.12069	-0.9426	0.174797
10	-0.071446	-0.558	0.28944
11	0.04001	0.3125	0.377867
12	-0.148194	-1.1574	0.125804
13	0.006088	0.0476	0.481115
14	-0.034916	-0.2727	0.393002
15	-0.062647	-0.4893	0.313196
16	-0.030467	-0.238	0.406358
17	0.100892	0.788	0.216875
18	-0.06179	-0.4826	0.315555
19	0.033197	0.2593	0.398149
20	0.028541	0.2229	0.412175
21	0.025764	0.2012	0.420598
22	-0.031592	-0.2467	0.402969
23	-0.027103	-0.2117	0.416532
24	0.015142	0.1183	0.453124
25	-0.027833	-0.2174	0.414317
26	0.031226	0.2439	0.40407
27	-0.038156	-0.298	0.383355
28	0.056881	0.4443	0.329215
29	-0.213054	-1.664	0.05062
30	-0.084069	-0.6566	0.256954
31	0.072696	0.5678	0.286136
32	-0.063805	-0.4983	0.31002
33	0.037545	0.2932	0.385168
34	0.05139	0.4014	0.344776
35	-0.09818	-0.7668	0.223076
36	0.107477	0.8394	0.202255
37	-0.06931	-0.5413	0.295126
38	0.005851	0.0457	0.481851
39	-0.072787	-0.5685	0.285898
40	0.144788	1.1308	0.131277
41	-0.063918	-0.4992	0.309712
42	-0.071443	-0.558	0.289447
43	-0.066752	-0.5213	0.302006
44	-0.008873	-0.0693	0.472489
45	0.01402	0.1095	0.456583
46	-0.021504	-0.1679	0.433589
47	0.058788	0.4591	0.32388
48	-0.071023	-0.5547	0.290562
49	-0.051233	-0.4001	0.345225
50	-0.095115	-0.7429	0.230206
51	-0.030286	-0.2365	0.406903
52	0.060535	0.4728	0.319023
53	0.007134	0.0557	0.477874
54	0.029541	0.2307	0.409153
55	-0.012866	-0.1005	0.460144
56	-0.003815	-0.0298	0.488162
57	0.008969	0.07	0.472192
58	0.027083	0.2115	0.41659
59	-0.031434	-0.2455	0.403444
60	-0.020894	-0.1632	0.435456

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292957730jsl3q6i9ea34a91/1rzdw1292957859.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292957730jsl3q6i9ea34a91/1rzdw1292957859.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292957730jsl3q6i9ea34a91/2rzdw1292957859.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292957730jsl3q6i9ea34a91/2rzdw1292957859.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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