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

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Fri, 18 Dec 2009 05:57:48 -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/18/t12611411044jrsa584v5i8eyx.htm/, Retrieved Fri, 18 Dec 2009 13:58:26 +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/18/t12611411044jrsa584v5i8eyx.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 «

100.00 110.08 123.28 106.30 114.60 110.22 117.82 138.84 131.13 153.26 148.76 110.75 132.00 138.55 126.50 119.47 152.49 152.46 134.08 162.33 130.46 142.83 148.39 122.88 125.86 133.31 140.97 110.30 123.04 125.99 112.24 136.10 111.86 109.63 135.75 114.39 121.79 101.33 147.01 113.01 101.89 117.85 128.68 117.27 121.55 109.18 127.88 104.92 100.93 116.79 107.50 109.18 128.31 83.80 93.16 103.99 106.33 97.55 111.71 105.43 103.62

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	0.38452	3.0032	0.001935
2	0.371872	2.9044	0.002559
3	0.527502	4.1199	5.8e-05
4	0.355104	2.7735	0.003674
5	0.294685	2.3016	0.012395
6	0.280497	2.1908	0.01615
7	0.271968	2.1241	0.01886
8	0.208866	1.6313	0.05399
9	0.212474	1.6595	0.051077
10	0.219262	1.7125	0.045943
11	0.012176	0.0951	0.462273
12	0.201326	1.5724	0.060515
13	0.070399	0.5498	0.29222
14	-0.001933	-0.0151	0.494002
15	-0.017721	-0.1384	0.445189
16	-0.056295	-0.4397	0.330862
17	-0.009324	-0.0728	0.471092
18	-0.060765	-0.4746	0.318388
19	-0.103943	-0.8118	0.210025
20	-0.065338	-0.5103	0.305838
21	-0.051451	-0.4018	0.344601
22	-0.069553	-0.5432	0.294477
23	-0.128234	-1.0015	0.160262
24	-0.055164	-0.4308	0.334051
25	-0.0699	-0.5459	0.293551
26	-0.098193	-0.7669	0.223046
27	-0.08649	-0.6755	0.250952
28	-0.170029	-1.328	0.094568
29	-0.115123	-0.8991	0.186058
30	-0.115612	-0.903	0.185051
31	-0.257316	-2.0097	0.024446
32	-0.183463	-1.4329	0.078497
33	-0.15191	-1.1865	0.120022
34	-0.242578	-1.8946	0.031444
35	-0.237142	-1.8521	0.034423
36	-0.172932	-1.3506	0.090899
37	-0.228516	-1.7848	0.039636
38	-0.314631	-2.4573	0.008427
39	-0.159551	-1.2461	0.10874
40	-0.180871	-1.4126	0.081421
41	-0.242056	-1.8905	0.031721
42	-0.082506	-0.6444	0.260868
43	-0.127498	-0.9958	0.161642
44	-0.145171	-1.1338	0.130652
45	-0.075225	-0.5875	0.279509
46	-0.10982	-0.8577	0.197202
47	-0.075733	-0.5915	0.278188
48	-0.024888	-0.1944	0.423262
49	-0.019939	-0.1557	0.438379
50	-0.005611	-0.0438	0.482596
51	-0.001822	-0.0142	0.494347
52	0.022386	0.1748	0.430892
53	0.074591	0.5826	0.281164
54	0.08105	0.633	0.264542
55	0.052952	0.4136	0.34032
56	0.052516	0.4102	0.341561
57	0.048333	0.3775	0.353559
58	0.019506	0.1523	0.439707
59	0.030656	0.2394	0.405786
60	0.021605	0.1687	0.43328

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.38452	3.0032	0.001935
2	0.262885	2.0532	0.022174
3	0.404682	3.1607	0.001225
4	0.076877	0.6004	0.275224
5	-0.006501	-0.0508	0.479837
6	-0.068755	-0.537	0.296614
7	0.028385	0.2217	0.412646
8	-0.00759	-0.0593	0.47646
9	0.048831	0.3814	0.352124
10	0.046363	0.3621	0.359263
11	-0.236468	-1.8469	0.034809
12	0.131625	1.028	0.153999
13	-0.109047	-0.8517	0.19886
14	0.008905	0.0696	0.47239
15	-0.171137	-1.3366	0.093155
16	-0.064232	-0.5017	0.308854
17	0.057541	0.4494	0.327364
18	0.055361	0.4324	0.333493
19	-0.038512	-0.3008	0.382301
20	-0.02106	-0.1645	0.434948
21	0.060988	0.4763	0.31777
22	-0.032161	-0.2512	0.401256
23	0.023154	0.1808	0.428547
24	-0.026544	-0.2073	0.418226
25	0.038523	0.3009	0.382267
26	-0.034457	-0.2691	0.394373
27	-0.019058	-0.1489	0.441081
28	-0.140244	-1.0953	0.138836
29	-0.024072	-0.188	0.425748
30	-0.04743	-0.3704	0.35617
31	-0.178256	-1.3922	0.084455
32	-0.004142	-0.0323	0.48715
33	-0.008217	-0.0642	0.474519
34	-0.056024	-0.4376	0.331625
35	-0.058603	-0.4577	0.324397
36	0.050712	0.3961	0.346715
37	-0.045192	-0.353	0.362666
38	-0.143079	-1.1175	0.134085
39	0.068567	0.5355	0.297117
40	0.123561	0.965	0.169166
41	0.055457	0.4331	0.333222
42	0.066759	0.5214	0.301987
43	0.011714	0.0915	0.463703
44	-0.007364	-0.0575	0.477162
45	-0.026317	-0.2055	0.418915
46	-0.112433	-0.8781	0.19166
47	0.011542	0.0901	0.464233
48	0.073965	0.5777	0.282801
49	-0.026956	-0.2105	0.416976
50	0.029353	0.2293	0.409718
51	-0.081574	-0.6371	0.263216
52	-0.050299	-0.3928	0.347902
53	0.068775	0.5371	0.296559
54	0.015902	0.1242	0.450783
55	0.042593	0.3327	0.370265
56	-0.039064	-0.3051	0.380663
57	-0.105375	-0.823	0.206855
58	-0.020272	-0.1583	0.437359
59	0.042626	0.3329	0.370168
60	-0.04602	-0.3594	0.36026

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/18/t12611411044jrsa584v5i8eyx/1q8gf1261141067.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/18/t12611411044jrsa584v5i8eyx/1q8gf1261141067.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/18/t12611411044jrsa584v5i8eyx/2zvek1261141067.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/18/t12611411044jrsa584v5i8eyx/2zvek1261141067.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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