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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: Thu, 16 Dec 2010 13:50:41 +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/16/t12925075326itp3ni4e0jdcj3.htm/, Retrieved Thu, 16 Dec 2010 14:52:13 +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/16/t12925075326itp3ni4e0jdcj3.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 «

4143 4429 5219 4929 5761 5592 4163 4962 5208 4755 4491 5732 5731 5040 6102 4904 5369 5578 4619 4731 5011 5299 4146 4625 4736 4219 5116 4205 4121 5103 4300 4578 3809 5657 4248 3830 4736 4839 4411 4570 4104 4801 3953 3828 4440 4026 4109 4785 3224 3552 3940 3913 3681 4309 3830 4143 4087 3818 3380 3430 3458

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

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.444616	3.4726	0.000477
2	0.421613	3.2929	0.000826
3	0.547434	4.2756	3.4e-05
4	0.38581	3.0133	0.00188
5	0.344723	2.6924	0.004573
6	0.371944	2.905	0.002555
7	0.368838	2.8807	0.002734
8	0.338564	2.6443	0.005197
9	0.366219	2.8603	0.002894
10	0.346343	2.705	0.004421
11	0.113141	0.8837	0.190176
12	0.273146	2.1333	0.018464
13	0.149297	1.166	0.124067
14	0.094273	0.7363	0.232187
15	0.083406	0.6514	0.258612
16	0.094935	0.7415	0.230627
17	0.095852	0.7486	0.228479
18	0.030073	0.2349	0.407546
19	-0.000751	-0.0059	0.497671
20	-0.014188	-0.1108	0.456064
21	-0.004844	-0.0378	0.484973
22	0.027033	0.2111	0.416743
23	-0.09749	-0.7614	0.22467
24	-0.009818	-0.0767	0.469564
25	-0.011956	-0.0934	0.462954
26	-0.060893	-0.4756	0.318033
27	-0.104765	-0.8182	0.208203
28	-0.097247	-0.7595	0.225233
29	-0.088119	-0.6882	0.246959
30	-0.107318	-0.8382	0.2026
31	-0.188541	-1.4726	0.073006
32	-0.148225	-1.1577	0.125755
33	-0.145577	-1.137	0.129994
34	-0.20716	-1.618	0.055415
35	-0.193055	-1.5078	0.068383
36	-0.194583	-1.5197	0.066871
37	-0.258056	-2.0155	0.024133
38	-0.283903	-2.2174	0.015167
39	-0.219407	-1.7136	0.045838
40	-0.25981	-2.0292	0.023405
41	-0.278749	-2.1771	0.016676
42	-0.189021	-1.4763	0.072504
43	-0.254402	-1.9869	0.025712
44	-0.289112	-2.258	0.013766
45	-0.237986	-1.8587	0.033946
46	-0.269872	-2.1078	0.019584
47	-0.233451	-1.8233	0.036578
48	-0.157468	-1.2299	0.111735
49	-0.124947	-0.9759	0.166492
50	-0.103309	-0.8069	0.211439
51	-0.084454	-0.6596	0.255994
52	-0.08767	-0.6847	0.248056
53	-0.090446	-0.7064	0.241312
54	-0.091444	-0.7142	0.238914
55	-0.119637	-0.9344	0.176893
56	-0.085383	-0.6669	0.253687
57	-0.030133	-0.2353	0.407364
58	-0.007623	-0.0595	0.476358
59	0.018779	0.1467	0.44194
60	0.014772	0.1154	0.454265

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.444616	3.4726	0.000477
2	0.279104	2.1799	0.016568
3	0.389561	3.0426	0.001728
4	0.050405	0.3937	0.347596
5	0.013183	0.103	0.459167
6	0.030276	0.2365	0.406932
7	0.108795	0.8497	0.199403
8	0.070549	0.551	0.291821
9	0.09741	0.7608	0.224854
10	0.029646	0.2315	0.408833
11	-0.327248	-2.5559	0.00655
12	0.055502	0.4335	0.333097
13	-0.144641	-1.1297	0.131516
14	0.048121	0.3758	0.35417
15	-0.147109	-1.149	0.127529
16	0.027058	0.2113	0.416666
17	0.011983	0.0936	0.462872
18	-0.017517	-0.1368	0.445816
19	-0.073673	-0.5754	0.283567
20	-0.028284	-0.2209	0.412951
21	0.113651	0.8876	0.189109
22	0.062944	0.4916	0.312379
23	-0.015206	-0.1188	0.452926
24	-0.011991	-0.0937	0.462846
25	0.039817	0.311	0.378437
26	-0.043285	-0.3381	0.368236
27	-0.07521	-0.5874	0.279549
28	-0.042785	-0.3342	0.369701
29	-0.011124	-0.0869	0.465526
30	-0.020382	-0.1592	0.437023
31	-0.201423	-1.5732	0.060427
32	-0.028702	-0.2242	0.411689
33	-0.014048	-0.1097	0.456497
34	-0.11689	-0.9129	0.182433
35	0.023934	0.1869	0.426167
36	-0.007934	-0.062	0.475395
37	-0.036854	-0.2878	0.387224
38	-0.194323	-1.5177	0.067127
39	0.098808	0.7717	0.22163
40	0.057864	0.4519	0.326462
41	0.084214	0.6577	0.256593
42	-0.008555	-0.0668	0.473472
43	-0.011026	-0.0861	0.465827
44	-0.031976	-0.2497	0.401815
45	-0.06599	-0.5154	0.30407
46	-0.031399	-0.2452	0.40355
47	0.080463	0.6284	0.266032
48	0.210175	1.6415	0.052918
49	0.029032	0.2267	0.41069
50	0.068304	0.5335	0.297823
51	-0.076164	-0.5949	0.277069
52	-0.037241	-0.2909	0.386073
53	-0.007304	-0.057	0.477349
54	-0.046012	-0.3594	0.360282
55	-0.05149	-0.4022	0.344489
56	-0.071219	-0.5562	0.290041
57	-0.083624	-0.6531	0.258066
58	-0.011362	-0.0887	0.464791
59	0.090288	0.7052	0.241693
60	0.005857	0.0457	0.481831

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/16/t12925075326itp3ni4e0jdcj3/197xb1292507437.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t12925075326itp3ni4e0jdcj3/197xb1292507437.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t12925075326itp3ni4e0jdcj3/297xb1292507437.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t12925075326itp3ni4e0jdcj3/297xb1292507437.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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