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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: Sun, 19 Dec 2010 16:55:52 +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/19/t1292777629h6pijgf8rvfpmm8.htm/, Retrieved Sun, 19 Dec 2010 17:53:49 +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/19/t1292777629h6pijgf8rvfpmm8.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 «

14.36 14.62 13.51 14.95 16.72 16.33 15.21 16.69 15.81 16.02 16.7 15.99 17.68 18.89 18.72 21.14 20.97 23.75 23.05 23.45 21.74 19.37 21.1 21.2 22.67 22.24 23.78 23.27 25.74 26.1 27.49 31.41 28.79 26.76 26.41 27.05 29.43 32.1 36.84 34.22 36.53 40.99 45.97 43.6 47.84 51.47 51.31 48.47 48.28 46.56 43.83 51.17 49.59 49.11 49.97 50.07 53.3 57.08 68.54 71.62 67.64 64.79 80.97 88.42 110.22 99 95.95 107.94 97.82 111.64 114.73 117.58 99.19 90.19 59.74 44.51 23.94 21.29 20.77 25.07 32.95 40.05 44.59 40.28 41.19 38.14 41.85 43.76 50.16 52.94 47.69 51.52 58.69 50.44 45.72 43.24 51.49 50.43 58.73 65.12 64.13

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

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.957675	9.6245	0
2	0.897589	9.0207	0
3	0.817532	8.2161	0
4	0.738489	7.4217	0
5	0.660657	6.6395	0
6	0.592007	5.9496	0
7	0.525772	5.2839	0
8	0.459861	4.6215	6e-06
9	0.396537	3.9851	6.4e-05
10	0.337541	3.3922	0.000495
11	0.290567	2.9202	0.002157
12	0.240986	2.4219	0.008612
13	0.208076	2.0911	0.019512
14	0.181575	1.8248	0.035493
15	0.167654	1.6849	0.047548
16	0.161063	1.6187	0.05432
17	0.158213	1.59	0.057478
18	0.15711	1.5789	0.058739
19	0.149833	1.5058	0.06762
20	0.139718	1.4041	0.081671
21	0.129987	1.3064	0.0972
22	0.12241	1.2302	0.110738
23	0.113778	1.1435	0.127777
24	0.109345	1.0989	0.137212
25	0.109899	1.1045	0.136006
26	0.101168	1.0167	0.155856
27	0.089346	0.8979	0.185684
28	0.06508	0.654	0.257285
29	0.036211	0.3639	0.358342
30	-0.003826	-0.0385	0.484701
31	-0.038287	-0.3848	0.350605
32	-0.064222	-0.6454	0.260059
33	-0.084829	-0.8525	0.197972
34	-0.109255	-1.098	0.137409
35	-0.131342	-1.32	0.094915
36	-0.154055	-1.5482	0.062348
37	-0.17894	-1.7983	0.037556
38	-0.193992	-1.9496	0.026999
39	-0.203685	-2.047	0.021627
40	-0.209126	-2.1017	0.019034
41	-0.218574	-2.1966	0.015166
42	-0.23088	-2.3203	0.011167
43	-0.240967	-2.4217	0.008616
44	-0.248386	-2.4963	0.007085
45	-0.252727	-2.5399	0.006306
46	-0.25549	-2.5676	0.005852
47	-0.256018	-2.5729	0.005769
48	-0.260504	-2.618	0.005102
49	-0.263397	-2.6471	0.00471
50	-0.265644	-2.6697	0.004424
51	-0.267326	-2.6866	0.004221
52	-0.268146	-2.6948	0.004125
53	-0.270734	-2.7208	0.003835
54	-0.273101	-2.7446	0.003585
55	-0.279884	-2.8128	0.002951
56	-0.287934	-2.8937	0.002332
57	-0.293751	-2.9522	0.001962
58	-0.296364	-2.9784	0.001814
59	-0.295453	-2.9693	0.001864
60	-0.289219	-2.9066	0.002246

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.957675	9.6245	0
2	-0.235965	-2.3714	0.009808
3	-0.241857	-2.4306	0.008418
4	0.053416	0.5368	0.296286
5	0.002209	0.0222	0.491166
6	0.038267	0.3846	0.35068
7	-0.058933	-0.5923	0.277496
8	-0.087708	-0.8815	0.190082
9	0.003801	0.0382	0.484801
10	0.016907	0.1699	0.432708
11	0.092058	0.9252	0.178541
12	-0.15043	-1.5118	0.066853
13	0.145746	1.4647	0.07305
14	0.037422	0.3761	0.353822
15	0.040246	0.4045	0.343363
16	0.043657	0.4387	0.330891
17	-0.061277	-0.6158	0.269698
18	0.01977	0.1987	0.421454
19	-0.081364	-0.8177	0.207728
20	-0.011862	-0.1192	0.452674
21	0.051462	0.5172	0.303077
22	-0.016508	-0.1659	0.434283
23	0.007485	0.0752	0.470095
24	0.001859	0.0187	0.492565
25	0.102707	1.0322	0.152225
26	-0.173057	-1.7392	0.042523
27	-0.008299	-0.0834	0.466847
28	-0.091354	-0.9181	0.180378
29	-0.045478	-0.457	0.324309
30	-0.06071	-0.6101	0.271574
31	0.050267	0.5052	0.307268
32	0.096782	0.9727	0.166525
33	-0.070819	-0.7117	0.239139
34	-0.123554	-1.2417	0.108612
35	0.034453	0.3462	0.36494
36	-0.027059	-0.2719	0.393112
37	0.007938	0.0798	0.468286
38	0.047816	0.4805	0.315939
39	0.017573	0.1766	0.430086
40	-0.103536	-1.0405	0.150291
41	-0.069095	-0.6944	0.244514
42	-0.082004	-0.8241	0.205903
43	0.02732	0.2746	0.392105
44	0.040831	0.4103	0.341211
45	0.016009	0.1609	0.43625
46	-0.04779	-0.4803	0.316033
47	0.016562	0.1664	0.43407
48	-0.044764	-0.4499	0.326884
49	-0.014817	-0.1489	0.440962
50	-0.034718	-0.3489	0.363942
51	-0.029167	-0.2931	0.385015
52	0.02254	0.2265	0.410625
53	-0.016837	-0.1692	0.432985
54	-0.054141	-0.5441	0.293783
55	-0.011185	-0.1124	0.455362
56	-0.048224	-0.4846	0.314489
57	0.031877	0.3204	0.37468
58	-0.016335	-0.1642	0.434966
59	0.073678	0.7405	0.230371
60	-0.021005	-0.2111	0.416617

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292777629h6pijgf8rvfpmm8/1678t1292777749.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292777629h6pijgf8rvfpmm8/1678t1292777749.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292777629h6pijgf8rvfpmm8/2678t1292777749.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292777629h6pijgf8rvfpmm8/2678t1292777749.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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