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paper autocorrelation

*Unverified author*

R Software Module: rwasp_autocorrelation.wasp (opens new window with default values)

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Sun, 14 Dec 2008 04:10:58 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/14/t1229253098gxb27zcwsqr4m7n.htm/, Retrieved Sun, 14 Dec 2008 12:11:40 +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/2008/Dec/14/t1229253098gxb27zcwsqr4m7n.htm/},
    year = {2008},
}
@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 = {2008},
    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 «

6340.5 7901.5 8191.1 7181.7 7594.4 7384.7 7876.7 8463.4 8317.2 7778.7 8532.8 7272.2 6680.1 8427.6 8752.8 7952.7 8694.3 7787 8474.2 9154.7 8557.2 7951.1 9156.7 7865.7 7337.4 9131.7 8814.6 8598.8 8439.6 7451.8 8016.2 9544.1 8270.7 8102.2 9369 7657.7 7816.6 9391.3 9445.4 9533.1 10068.7 8955.5 10423.9 11617.2 9391.1 10872 10230.4 9221 9428.6 10934.5 10986 11724.6 11180.9 11163.2 11240.9 12107.1 10762.3 11340.4 11266.8 9542.7 9227.7 10571.9 10774.4 10392.8 9920.2 9884.9 10174.5 11395.4 10760.2 10570.1 10536 9902.6 8889 10837.3 11624.1 10509 10984.9 10649.1 10855.7 11677.4 10760.2 10046.2 10772.8 9987.7 8638.7 11063.7 11855.7 10684.5 11337.4 10478 11123.9 12909.3 11339.9 10462.2 12733.5 10519.2 10414.9 12476.8 12384.6 12266.7 12919.9 11497.3 12142 13919.4 12656.8 12034.1 13199.7 10881.3 11301.2 13643.9 12517 13981.1 14275.7 13435 13565.7 16216.3 12970 14079.9 14235 12213.4 12581

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	0.808707	8.8958	0
2	0.752772	8.2805	0
3	0.802896	8.8319	0
4	0.687505	7.5626	0
5	0.675461	7.4301	0
6	0.70868	7.7955	0
7	0.579926	6.3792	0
8	0.57274	6.3001	0
9	0.601018	6.6112	0
10	0.47514	5.2265	0
11	0.53707	5.9078	0
12	0.609198	6.7012	0
13	0.457671	5.0344	1e-06
14	0.423941	4.6633	4e-06
15	0.449093	4.94	1e-06
16	0.361533	3.9769	6e-05
17	0.380482	4.1853	2.7e-05
18	0.38995	4.2895	1.8e-05
19	0.289375	3.1831	0.000926
20	0.306825	3.3751	0.000496
21	0.310178	3.412	0.000439
22	0.212777	2.3405	0.010446
23	0.280023	3.0802	0.00128
24	0.321303	3.5343	0.00029
25	0.212825	2.3411	0.010432
26	0.188635	2.075	0.020054
27	0.184875	2.0336	0.022088
28	0.136295	1.4992	0.068208
29	0.154055	1.6946	0.046362
30	0.140017	1.5402	0.063063
31	0.077034	0.8474	0.19923
32	0.092908	1.022	0.154412
33	0.086474	0.9512	0.171697
34	0.035679	0.3925	0.3477
35	0.082246	0.9047	0.18371
36	0.109756	1.2073	0.114833
37	0.048233	0.5306	0.298347
38	0.006139	0.0675	0.473135
39	0.015667	0.1723	0.43173
40	-0.006498	-0.0715	0.471569
41	0.001532	0.0169	0.493292
42	0.004645	0.0511	0.479667
43	-0.022124	-0.2434	0.404066
44	-0.021934	-0.2413	0.404876
45	-0.017993	-0.1979	0.42172
46	-0.035309	-0.3884	0.3492
47	-0.021478	-0.2363	0.406818
48	0.024775	0.2725	0.392843
49	-0.021249	-0.2337	0.40779
50	-0.071446	-0.7859	0.216728
51	-0.033276	-0.366	0.357487
52	-0.044965	-0.4946	0.310883
53	-0.056554	-0.6221	0.267526
54	-0.017348	-0.1908	0.424489
55	-0.043326	-0.4766	0.317257
56	-0.048059	-0.5286	0.29901
57	-0.011571	-0.1273	0.449463
58	-0.03497	-0.3847	0.35058
59	-0.024658	-0.2712	0.393333
60	0.037503	0.4125	0.340339

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.808707	8.8958	0
2	0.285453	3.14	0.001062
3	0.431252	4.7438	3e-06
4	-0.207434	-2.2818	0.012125
5	0.154615	1.7008	0.045777
6	0.095575	1.0513	0.147602
7	-0.230084	-2.5309	0.00633
8	0.067298	0.7403	0.230284
9	0.052447	0.5769	0.282532
10	-0.166479	-1.8313	0.034761
11	0.330146	3.6316	0.000207
12	0.215883	2.3747	0.009567
13	-0.321351	-3.5349	0.000289
14	-0.313277	-3.4461	0.000391
15	0.055099	0.6061	0.272794
16	0.146772	1.6145	0.054513
17	-0.016685	-0.1835	0.427341
18	-0.008184	-0.09	0.464209
19	0.072832	0.8012	0.212306
20	-0.046738	-0.5141	0.304055
21	-0.016582	-0.1824	0.427787
22	-0.010019	-0.1102	0.456214
23	0.047229	0.5195	0.302173
24	-0.004124	-0.0454	0.481945
25	-0.004326	-0.0476	0.481061
26	-0.147692	-1.6246	0.053424
27	-0.098089	-1.079	0.141373
28	0.114748	1.2622	0.104647
29	-0.01543	-0.1697	0.432754
30	-0.058182	-0.64	0.26169
31	0.092516	1.0177	0.155431
32	0.004844	0.0533	0.478797
33	0.011307	0.1244	0.450613
34	0.037946	0.4174	0.338559
35	-0.028433	-0.3128	0.377501
36	-0.084782	-0.9326	0.17644
37	0.010515	0.1157	0.454054
38	-0.090347	-0.9938	0.161146
39	0.066254	0.7288	0.233769
40	-0.021633	-0.238	0.406158
41	0.044377	0.4881	0.313166
42	0.04786	0.5265	0.299767
43	0.103075	1.1338	0.129554
44	-0.080396	-0.8844	0.18913
45	-0.087759	-0.9653	0.168148
46	0.070428	0.7747	0.220013
47	-0.050232	-0.5526	0.290795
48	-0.02556	-0.2812	0.389534
49	-0.010965	-0.1206	0.452097
50	-0.006647	-0.0731	0.470918
51	0.132835	1.4612	0.073279
52	-0.04642	-0.5106	0.305274
53	-0.029255	-0.3218	0.374077
54	0.068891	0.7578	0.225022
55	0.011224	0.1235	0.450973
56	0.040233	0.4426	0.329436
57	-0.057379	-0.6312	0.264559
58	-0.004016	-0.0442	0.482419
59	-0.005635	-0.062	0.47534
60	-0.059993	-0.6599	0.255279

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/14/t1229253098gxb27zcwsqr4m7n/1v6s21229253056.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/14/t1229253098gxb27zcwsqr4m7n/1v6s21229253056.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/14/t1229253098gxb27zcwsqr4m7n/2mtu31229253056.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/14/t1229253098gxb27zcwsqr4m7n/2mtu31229253056.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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

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 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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