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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, 06 Dec 2009 13:57:50 -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/06/t1260133114vzkpx6eblvxn7vi.htm/, Retrieved Sun, 06 Dec 2009 21:58:37 +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/06/t1260133114vzkpx6eblvxn7vi.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 «

100.00 100.83 101.51 102.16 102.39 102.54 102.85 103.47 103.57 103.69 103.50 103.47 103.45 103.48 103.93 103.89 104.40 104.79 104.77 105.13 105.26 104.96 104.75 105.01 105.15 105.20 105.77 105.78 106.26 106.13 106.12 106.57 106.44 106.54 107.10 108.10 108.40 108.84 109.62 110.42 110.67 111.66 112.28 112.87 112.18 112.36 112.16 111.49 111.25 111.36 111.74 111.10 111.33 111.25 111.04 110.97 111.31 111.02 111.07 111.36

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
0	1	7.746	0
1	0.949945	7.3582	0
2	0.903482	6.9983	0
3	0.858452	6.6495	0
4	0.81264	6.2947	0
5	0.766092	5.9341	0
6	0.719129	5.5703	0
7	0.672302	5.2076	1e-06
8	0.627069	4.8573	4e-06
9	0.582926	4.5153	1.5e-05
10	0.536014	4.1519	5.3e-05
11	0.488294	3.7823	0.00018
12	0.438583	3.3973	0.000607
13	0.386668	2.9951	0.001991
14	0.330946	2.5635	0.006443
15	0.276773	2.1439	0.018053
16	0.220447	1.7076	0.046442
17	0.165011	1.2782	0.103056
18	0.114493	0.8869	0.189349
19	0.065838	0.51	0.305968
20	0.024359	0.1887	0.425488
21	-0.01459	-0.113	0.544802
22	-0.053566	-0.4149	0.660159
23	-0.092775	-0.7186	0.762422
24	-0.128738	-0.9972	0.838663
25	-0.164292	-1.2726	0.895966
26	-0.196217	-1.5199	0.933104
27	-0.221722	-1.7174	0.954472
28	-0.247873	-1.92	0.970193
29	-0.271113	-2.1	0.980031
30	-0.294261	-2.2793	0.986891
31	-0.318535	-2.4674	0.991759
32	-0.340309	-2.636	0.994669
33	-0.36292	-2.8112	0.996671
34	-0.387516	-3.0017	0.998046
35	-0.406826	-3.1513	0.998732
36	-0.418967	-3.2453	0.99904
37	-0.431016	-3.3386	0.999275
38	-0.43918	-3.4019	0.999402
39	-0.443107	-3.4323	0.999455
40	-0.443062	-3.4319	0.999454
41	-0.441359	-3.4188	0.999432
42	-0.428968	-3.3228	0.999239
43	-0.41138	-3.1865	0.998857
44	-0.38578	-2.9882	0.997969
45	-0.362772	-2.81	0.99666
46	-0.337549	-2.6146	0.994361
47	-0.310807	-2.4075	0.990423
48	-0.289844	-2.2451	0.985771
49	-0.270952	-2.0988	0.979974
50	-0.251347	-1.9469	0.971885
51	-0.22869	-1.7714	0.959216
52	-0.211146	-1.6355	0.946413
53	-0.190967	-1.4792	0.927845
54	-0.168218	-1.303	0.901225
55	-0.145741	-1.1289	0.868285
56	-0.123321	-0.9552	0.828356
57	-0.096589	-0.7482	0.771362
58	-0.069276	-0.5366	0.703239
59	-0.038168	-0.2956	0.61574

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.949945	7.3582	0
1	0.011126	0.0862	0.465806
2	-0.008472	-0.0656	0.526053
3	-0.031197	-0.2417	0.595062
4	-0.03312	-0.2565	0.600795
5	-0.03136	-0.2429	0.595548
6	-0.026413	-0.2046	0.580709
7	-0.011568	-0.0896	0.535549
8	-0.015313	-0.1186	0.547012
9	-0.055073	-0.4266	0.664398
10	-0.040667	-0.315	0.623075
11	-0.054516	-0.4223	0.662836
12	-0.059173	-0.4584	0.675823
13	-0.07909	-0.6126	0.728781
14	-0.029008	-0.2247	0.588509
15	-0.064783	-0.5018	0.691179
16	-0.03862	-0.2992	0.617071
17	0.002758	0.0214	0.491513
18	-0.022075	-0.171	0.567598
19	0.032045	0.2482	0.402407
20	-0.008966	-0.0695	0.52757
21	-0.035523	-0.2752	0.607932
22	-0.04202	-0.3255	0.627027
23	-0.010292	-0.0797	0.531637
24	-0.031946	-0.2475	0.597299
25	-0.000629	-0.0049	0.501934
26	0.031205	0.2417	0.404912
27	-0.037684	-0.2919	0.614313
28	-0.011285	-0.0874	0.534682
29	-0.044201	-0.3424	0.63337
30	-0.060577	-0.4692	0.679696
31	-0.024538	-0.1901	0.575052
32	-0.061596	-0.4771	0.682496
33	-0.068245	-0.5286	0.700491
34	0	0	0.500001
35	0.028121	0.2178	0.414154
36	-0.031403	-0.2432	0.595677
37	0.000599	0.0046	0.498155
38	0.005106	0.0396	0.48429
39	0.005826	0.0451	0.482078
40	-0.012596	-0.0976	0.5387
41	0.081555	0.6317	0.264985
42	0.056249	0.4357	0.332309
43	0.089297	0.6917	0.2459
44	-0.020258	-0.1569	0.562082
45	0.02957	0.229	0.409805
46	0.007572	0.0587	0.476713
47	-0.076875	-0.5955	0.723116
48	-0.046283	-0.3585	0.639389
49	-0.017986	-0.1393	0.555167
50	0.002494	0.0193	0.492325
51	-0.06986	-0.5411	0.704791
52	-0.001982	-0.0154	0.506101
53	0.007917	0.0613	0.475651
54	-0.015679	-0.1214	0.548129
55	-0.018718	-0.145	0.557397
56	0.034338	0.266	0.395582
57	0.024469	0.1895	0.425156
58	0.059872	0.4638	0.322245
59	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/06/t1260133114vzkpx6eblvxn7vi/1zkth1260133068.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/06/t1260133114vzkpx6eblvxn7vi/1zkth1260133068.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/06/t1260133114vzkpx6eblvxn7vi/2sesw1260133068.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/06/t1260133114vzkpx6eblvxn7vi/2sesw1260133068.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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

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 (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='lags',ylab='ACF')

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 1:par1) {

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(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-1,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(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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