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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: Mon, 21 Dec 2009 05:19:04 -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/21/t1261398010zhf2mdrbvonu167.htm/, Retrieved Mon, 21 Dec 2009 13:20:13 +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/2009/Dec/21/t1261398010zhf2mdrbvonu167.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 «

3030.29 2803.47 2767.63 2882.6 2863.36 2897.06 3012.61 3142.95 3032.93 3045.78 3110.52 3013.24 2987.1 2995.55 2833.18 2848.96 2794.83 2845.26 2915.02 2892.63 2604.42 2641.65 2659.81 2638.53 2720.25 2745.88 2735.7 2811.7 2799.43 2555.28 2304.98 2214.95 2065.81 1940.49 2042 1995.37 1946.81 1765.9 1635.25 1833.42 1910.43 1959.67 1969.6 2061.41 2093.48 2120.88 2174.56 2196.72 2350.44 2440.25 2408.64 2472.81 2407.6 2454.62 2448.05 2497.84 2645.64 2756.76 2849.27 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 etc...

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	0.980659	10.6977	0
2	0.951772	10.3826	0
3	0.919977	10.0358	0
4	0.879542	9.5947	0
5	0.831111	9.0664	0
6	0.775585	8.4606	0
7	0.719951	7.8537	0
8	0.663323	7.236	0
9	0.600915	6.5552	0
10	0.537189	5.86	0
11	0.477691	5.211	0
12	0.415448	4.532	7e-06
13	0.35299	3.8507	9.6e-05
14	0.292657	3.1925	0.000902
15	0.235994	2.5744	0.005634
16	0.179552	1.9587	0.026245
17	0.121021	1.3202	0.094654
18	0.067496	0.7363	0.231501
19	0.019253	0.21	0.417004
20	-0.028732	-0.3134	0.377252
21	-0.073658	-0.8035	0.211639
22	-0.114661	-1.2508	0.106731
23	-0.151651	-1.6543	0.050349
24	-0.18225	-1.9881	0.024548
25	-0.210553	-2.2969	0.011687
26	-0.234918	-2.5627	0.005817
27	-0.255925	-2.7918	0.003054
28	-0.276462	-3.0158	0.001567
29	-0.295439	-3.2229	0.000819
30	-0.312485	-3.4088	0.000446
31	-0.327879	-3.5767	0.000252
32	-0.342292	-3.734	0.000145
33	-0.358321	-3.9088	7.7e-05
34	-0.372107	-4.0592	4.4e-05
35	-0.383807	-4.1868	2.7e-05
36	-0.392013	-4.2764	1.9e-05
37	-0.399594	-4.3591	1.4e-05
38	-0.405615	-4.4247	1.1e-05
39	-0.409545	-4.4676	9e-06
40	-0.413786	-4.5139	8e-06
41	-0.417314	-4.5524	6e-06
42	-0.420514	-4.5873	6e-06
43	-0.420657	-4.5888	6e-06
44	-0.417242	-4.5516	6e-06
45	-0.413178	-4.5072	8e-06
46	-0.407918	-4.4499	1e-05
47	-0.400895	-4.3732	1.3e-05
48	-0.391748	-4.2735	1.9e-05
49	-0.381008	-4.1563	3.1e-05
50	-0.367273	-4.0065	5.4e-05
51	-0.350672	-3.8254	0.000105
52	-0.331393	-3.6151	0.000221
53	-0.308979	-3.3706	0.000506
54	-0.28651	-3.1255	0.001115
55	-0.263208	-2.8713	0.002421
56	-0.237915	-2.5953	0.005319
57	-0.212501	-2.3181	0.011076
58	-0.185621	-2.0249	0.022558
59	-0.15797	-1.7232	0.04372
60	-0.130236	-1.4207	0.079008

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.980659	10.6977	0
2	-0.258946	-2.8248	0.002775
3	-0.03192	-0.3482	0.364149
4	-0.235326	-2.5671	0.005747
5	-0.145525	-1.5875	0.057527
6	-0.15737	-1.7167	0.044317
7	0.074266	0.8101	0.209736
8	-0.02522	-0.2751	0.391851
9	-0.120966	-1.3196	0.094754
10	-0.011109	-0.1212	0.451874
11	0.087239	0.9517	0.171598
12	-0.156169	-1.7036	0.045532
13	0.024752	0.27	0.393808
14	-0.010646	-0.1161	0.453872
15	0.033816	0.3689	0.356432
16	-0.115432	-1.2592	0.105209
17	-0.06405	-0.6987	0.243051
18	0.062694	0.6839	0.24768
19	0.003513	0.0383	0.484749
20	-0.063797	-0.6959	0.24391
21	0.062175	0.6782	0.249465
22	-0.052777	-0.5757	0.282941
23	-0.009684	-0.1056	0.458024
24	0.094403	1.0298	0.152593
25	-0.021653	-0.2362	0.406841
26	-0.038651	-0.4216	0.337029
27	-0.061797	-0.6741	0.250769
28	-0.04284	-0.4673	0.320558
29	-0.073395	-0.8006	0.212467
30	-0.042728	-0.4661	0.320994
31	0.013153	0.1435	0.443077
32	-0.038512	-0.4201	0.33758
33	-0.113553	-1.2387	0.108944
34	0.04236	0.4621	0.322429
35	-0.034939	-0.3811	0.351888
36	0.108439	1.1829	0.119597
37	-0.090446	-0.9867	0.162907
38	0.045341	0.4946	0.310895
39	-0.080635	-0.8796	0.190419
40	-0.0972	-1.0603	0.145571
41	-0.000757	-0.0083	0.496712
42	-0.027698	-0.3021	0.381534
43	0.021904	0.2389	0.405782
44	0.092624	1.0104	0.157174
45	-0.063185	-0.6893	0.245999
46	0.006794	0.0741	0.47052
47	-0.069922	-0.7628	0.22356
48	0.058273	0.6357	0.2631
49	-0.015816	-0.1725	0.431655
50	0.038706	0.4222	0.336808
51	6.8e-05	7e-04	0.499705
52	-0.003042	-0.0332	0.486792
53	0.033762	0.3683	0.356651
54	-0.064434	-0.7029	0.241748
55	-0.03783	-0.4127	0.340293
56	0.036456	0.3977	0.345786
57	-0.042485	-0.4635	0.321941
58	0.054503	0.5946	0.276634
59	0.01463	0.1596	0.436733
60	-0.016354	-0.1784	0.429357

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/21/t1261398010zhf2mdrbvonu167/1yaoo1261397942.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t1261398010zhf2mdrbvonu167/1yaoo1261397942.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t1261398010zhf2mdrbvonu167/21ahc1261397942.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/21/t1261398010zhf2mdrbvonu167/21ahc1261397942.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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