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Paper-ACF1-Xt

*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: Wed, 16 Dec 2009 13:22:54 -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/16/t1260995067agbdbxla0ue2kp5.htm/, Retrieved Wed, 16 Dec 2009 21:24:29 +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/16/t1260995067agbdbxla0ue2kp5.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 «

98,8 100,5 110,4 96,4 101,9 106,2 81 94,7 101 109,4 102,3 90,7 96,2 96,1 106 103,1 102 104,7 86 92,1 106,9 112,6 101,7 92 97,4 97 105,4 102,7 98,1 104,5 87,4 89,9 109,8 111,7 98,6 96,9 95,1 97 112,7 102,9 97,4 111,4 87,4 96,8 114,1 110,3 103,9 101,6 94,6 95,9 104,7 102,8 98,1 113,9 80,9 95,7 113,2 105,9 108,8 102,3 99 100,7 115,5 100,7 109,9 114,6 85,4 100,5 114,8 116,5 112,9 102 106 105,3 118,8 106,1 109,3 117,2 92,5 104,2 112,5 122,4 113,3 100 110,7 112,8 109,8 117,3 109,1 115,9 96 99,8 116,8 115,7 99,4 94,3 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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.191396	1.885	0.03121
2	-0.132432	-1.3043	0.097608
3	0.022368	0.2203	0.413052
4	0.015132	0.149	0.440919
5	0.338095	3.3298	0.000615
6	0.392249	3.8632	0.000101
7	0.245233	2.4153	0.008798
8	0.021253	0.2093	0.417319
9	-0.067191	-0.6618	0.254848
10	-0.174972	-1.7233	0.044013
11	0.151647	1.4935	0.06927
12	0.710062	6.9933	0
13	0.095612	0.9417	0.17435
14	-0.202912	-1.9984	0.024234
15	-0.061733	-0.608	0.272303
16	-0.051221	-0.5045	0.30754
17	0.228296	2.2485	0.013405
18	0.276957	2.7277	0.003786
19	0.142164	1.4001	0.08233
20	-0.038732	-0.3815	0.351845
21	-0.116944	-1.1518	0.126125
22	-0.221267	-2.1792	0.015868
23	0.105929	1.0433	0.149706
24	0.499454	4.9191	2e-06
25	0.028739	0.283	0.388871
26	-0.215309	-2.1205	0.018255
27	-0.146774	-1.4456	0.075763
28	-0.09189	-0.905	0.18385
29	0.132135	1.3014	0.098105
30	0.156874	1.545	0.062797
31	0.07777	0.7659	0.222784
32	-0.096879	-0.9541	0.17119
33	-0.17763	-1.7495	0.041687
34	-0.216997	-2.1372	0.017549
35	-0.005576	-0.0549	0.478159
36	0.363496	3.58	0.000269
37	-0.016462	-0.1621	0.435768
38	-0.224342	-2.2095	0.014746
39	-0.151124	-1.4884	0.069945
40	-0.117482	-1.1571	0.125044
41	0.065591	0.646	0.259904
42	0.108183	1.0655	0.144652
43	0.056233	0.5538	0.290486
44	-0.057934	-0.5706	0.284802
45	-0.181825	-1.7908	0.038225
46	-0.177457	-1.7477	0.041836
47	-0.016039	-0.158	0.437404
48	0.277298	2.7311	0.00375
49	-0.016708	-0.1646	0.434817
50	-0.224784	-2.2139	0.01459
51	-0.159763	-1.5735	0.059432
52	-0.136239	-1.3418	0.091397
53	-0.005965	-0.0588	0.476636
54	0.03454	0.3402	0.367227
55	0.003718	0.0366	0.485434
56	-0.113009	-1.113	0.134227
57	-0.183458	-1.8069	0.036943
58	-0.210239	-2.0706	0.020525
59	-0.048224	-0.475	0.317944
60	0.195928	1.9297	0.028285

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.191396	1.885	0.03121
2	-0.175493	-1.7284	0.043549
3	0.091841	0.9045	0.183979
4	-0.036526	-0.3597	0.359913
5	0.388566	3.8269	0.000115
6	0.270914	2.6682	0.004469
7	0.33656	3.3147	0.000645
8	0.054257	0.5344	0.297154
9	0.027739	0.2732	0.392642
10	-0.450849	-4.4403	1.2e-05
11	-0.104646	-1.0306	0.152636
12	0.524161	5.1624	1e-06
13	-0.104836	-1.0325	0.152199
14	-0.080599	-0.7938	0.214624
15	-0.027406	-0.2699	0.393897
16	0.048928	0.4819	0.315486
17	-0.131093	-1.2911	0.099865
18	-0.036475	-0.3592	0.360098
19	0.05065	0.4988	0.309509
20	-0.035725	-0.3518	0.362858
21	0.061549	0.6062	0.272904
22	-0.074676	-0.7355	0.231912
23	0.0196	0.193	0.423665
24	-0.093575	-0.9216	0.17951
25	0.033783	0.3327	0.370031
26	-0.0212	-0.2088	0.417523
27	-0.065694	-0.647	0.259578
28	0.008358	0.0823	0.46728
29	-0.03439	-0.3387	0.367781
30	-0.046363	-0.4566	0.324481
31	0.016927	0.1667	0.433971
32	-0.014336	-0.1412	0.444003
33	-0.029639	-0.2919	0.38549
34	0.053573	0.5276	0.299478
35	-0.156916	-1.5454	0.062748
36	0.065504	0.6451	0.260179
37	-0.065487	-0.645	0.260233
38	0.072744	0.7164	0.23772
39	0.019465	0.1917	0.424187
40	0.062581	0.6163	0.269555
41	-0.02712	-0.2671	0.39498
42	0.019531	0.1924	0.423933
43	0.020023	0.1972	0.42204
44	0.066099	0.651	0.258293
45	-0.067856	-0.6683	0.252762
46	0.023593	0.2324	0.408374
47	-0.012423	-0.1224	0.451435
48	-0.036999	-0.3644	0.358178
49	-0.126475	-1.2456	0.107949
50	-0.067209	-0.6619	0.254793
51	-0.116273	-1.1452	0.127481
52	-0.034813	-0.3429	0.36622
53	-0.047587	-0.4687	0.320174
54	-0.019358	-0.1907	0.424599
55	-0.023249	-0.229	0.409686
56	-0.034391	-0.3387	0.367781
57	0.086597	0.8529	0.197913
58	-0.03603	-0.3549	0.361735
59	0.043011	0.4236	0.336396
60	-0.002686	-0.0265	0.489475

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260995067agbdbxla0ue2kp5/1ofyc1260994972.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260995067agbdbxla0ue2kp5/1ofyc1260994972.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260995067agbdbxla0ue2kp5/21ndu1260994972.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260995067agbdbxla0ue2kp5/21ndu1260994972.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = MA ; 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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