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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: Mon, 28 Dec 2009 13:01:50 -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/28/t1262030584vcsdqu5jwpoauxj.htm/, Retrieved Mon, 28 Dec 2009 21:03:06 +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/28/t1262030584vcsdqu5jwpoauxj.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 «

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 2293.41 2443.27 2513.17 2466.92

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	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.966543	7.4868	0
2	0.921513	7.138	0
3	0.872421	6.7577	0
4	0.810399	6.2773	0
5	0.732893	5.677	0
6	0.642511	4.9769	3e-06
7	0.554557	4.2956	3.2e-05
8	0.46528	3.604	0.000319
9	0.366123	2.836	0.00311
10	0.268847	2.0825	0.020785
11	0.181044	1.4024	0.082981
12	0.087605	0.6786	0.250004
13	-0.001051	-0.0081	0.496766
14	-0.082668	-0.6403	0.262195
15	-0.149292	-1.1564	0.126049
16	-0.210744	-1.6324	0.053915
17	-0.274793	-2.1285	0.018704
18	-0.324712	-2.5152	0.007296
19	-0.363288	-2.814	0.003303
20	-0.400261	-3.1004	0.001471
21	-0.435169	-3.3708	0.000658
22	-0.460573	-3.5676	0.000358
23	-0.474081	-3.6722	0.000257
24	-0.474544	-3.6758	0.000254
25	-0.469263	-3.6349	0.000289
26	-0.452875	-3.508	0.000431
27	-0.433243	-3.3559	0.000688
28	-0.415587	-3.2191	0.001038
29	-0.391022	-3.0288	0.001809
30	-0.362813	-2.8103	0.003337
31	-0.33219	-2.5731	0.006284
32	-0.300695	-2.3292	0.011618
33	-0.276362	-2.1407	0.018186
34	-0.246505	-1.9094	0.030497
35	-0.212507	-1.6461	0.052489
36	-0.179565	-1.3909	0.084696
37	-0.146368	-1.1338	0.130702
38	-0.116667	-0.9037	0.184885
39	-0.090038	-0.6974	0.244114
40	-0.063634	-0.4929	0.311939
41	-0.036695	-0.2842	0.388602
42	-0.013608	-0.1054	0.458201
43	0.010572	0.0819	0.467503
44	0.031072	0.2407	0.405311
45	0.05257	0.4072	0.342652
46	0.071045	0.5503	0.292073
47	0.07857	0.6086	0.272543
48	0.080873	0.6264	0.266702
49	0.078856	0.6108	0.271814
50	0.075425	0.5842	0.280623
51	0.06978	0.5405	0.295422
52	0.061707	0.478	0.317199
53	0.053611	0.4153	0.339713
54	0.046018	0.3565	0.361376
55	0.036696	0.2842	0.388601
56	0.028283	0.2191	0.413667
57	0.021518	0.1667	0.434092
58	0.01575	0.122	0.451653
59	0.008728	0.0676	0.473162
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.966543	7.4868	0
2	-0.192909	-1.4943	0.070173
3	-0.057238	-0.4434	0.329548
4	-0.215277	-1.6675	0.050311
5	-0.227935	-1.7656	0.041278
6	-0.205385	-1.5909	0.058444
7	0.051343	0.3977	0.346132
8	-0.032222	-0.2496	0.401878
9	-0.144465	-1.119	0.133796
10	0.016409	0.1271	0.449641
11	0.069285	0.5367	0.296736
12	-0.212292	-1.6444	0.052661
13	0.048449	0.3753	0.354387
14	-0.005271	-0.0408	0.483785
15	0.10624	0.8229	0.206904
16	-0.069369	-0.5373	0.296515
17	-0.113558	-0.8796	0.191288
18	0.035772	0.2771	0.391332
19	-0.043734	-0.3388	0.367984
20	-0.091104	-0.7057	0.241557
21	-0.059775	-0.463	0.322513
22	-0.00278	-0.0215	0.491447
23	0.030396	0.2354	0.407333
24	0.139714	1.0822	0.141742
25	0.067567	0.5234	0.301321
26	0.003626	0.0281	0.488842
27	-0.146216	-1.1326	0.130947
28	-0.11423	-0.8848	0.189893
29	-0.011152	-0.0864	0.465724
30	-0.037748	-0.2924	0.385497
31	0.000557	0.0043	0.498287
32	0.064611	0.5005	0.309285
33	-0.169446	-1.3125	0.097171
34	0.020231	0.1567	0.437999
35	0.02867	0.2221	0.412503
36	0.081219	0.6291	0.265829
37	0.014604	0.1131	0.455156
38	-0.00933	-0.0723	0.471313
39	-0.079834	-0.6184	0.26933
40	-0.046829	-0.3627	0.359038
41	0.061188	0.474	0.318625
42	-0.084819	-0.657	0.256845
43	0.05658	0.4383	0.331383
44	-0.035831	-0.2775	0.391157
45	-0.014293	-0.1107	0.456106
46	-6.5e-05	-5e-04	0.499801
47	-0.142895	-1.1069	0.136387
48	-0.046259	-0.3583	0.36068
49	-0.007065	-0.0547	0.478271
50	-0.005686	-0.044	0.482507
51	0.008158	0.0632	0.474913
52	0.019573	0.1516	0.440002
53	0.057398	0.4446	0.329103
54	-0.029033	-0.2249	0.411416
55	-0.007903	-0.0612	0.475695
56	-0.09483	-0.7345	0.232738
57	0.018932	0.1466	0.441952
58	0.066549	0.5155	0.304053
59	-0.000732	-0.0057	0.497747
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/28/t1262030584vcsdqu5jwpoauxj/1hsk61262030506.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/28/t1262030584vcsdqu5jwpoauxj/1hsk61262030506.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/28/t1262030584vcsdqu5jwpoauxj/2ol831262030506.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/28/t1262030584vcsdqu5jwpoauxj/2ol831262030506.ps (open in new window)

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = 60 ; par2 = 0.9 ; 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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