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WS 8 03

*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: Sat, 21 Nov 2009 04:02:54 -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/Nov/21/t1258801409dijjzasqe4z3w08.htm/, Retrieved Sat, 21 Nov 2009 12:03:31 +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/Nov/21/t1258801409dijjzasqe4z3w08.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 «

103.63 103.64 103.66 103.77 103.88 103.91 103.91 103.92 104.05 104.23 104.30 104.31 104.31 104.34 104.55 104.65 104.73 104.75 104.75 104.76 104.94 105.29 105.38 105.43 105.43 105.42 105.52 105.69 105.72 105.74 105.74 105.74 105.95 106.17 106.34 106.37 106.37 106.36 106.44 106.29 106.23 106.23 106.23 106.23 106.34 106.44 106.44 106.48 106.50 106.57 106.40 106.37 106.25 106.21 106.21 106.24 106.19 106.08 106.13 106.09

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	-0.198391	-1.5109	0.068122
2	-0.149249	-1.1367	0.13018
3	-0.246446	-1.8769	0.032784
4	-0.058306	-0.444	0.32933
5	0.026686	0.2032	0.419833
6	0.243482	1.8543	0.034391
7	0.149755	1.1405	0.129382
8	-0.296049	-2.2546	0.013974
9	-0.086071	-0.6555	0.25737
10	-0.221537	-1.6872	0.048471
11	0.343852	2.6187	0.005622
12	0.086398	0.658	0.256576
13	0.166666	1.2693	0.104703
14	-0.178258	-1.3576	0.089929
15	-0.080577	-0.6137	0.27092
16	-0.173725	-1.3231	0.095505
17	0.238626	1.8173	0.037167
18	0.06195	0.4718	0.31942
19	-0.140522	-1.0702	0.144486
20	0.019236	0.1465	0.442018
21	-0.058519	-0.4457	0.328747
22	0.004622	0.0352	0.486021
23	0.001726	0.0131	0.494779
24	0.189684	1.4446	0.076977
25	-0.13848	-1.0546	0.147984
26	0.0169	0.1287	0.449018
27	-0.086336	-0.6575	0.256724
28	0.142701	1.0868	0.140816
29	-0.036388	-0.2771	0.391335
30	-0.020028	-0.1525	0.43965
31	-0.032624	-0.2485	0.402328
32	-0.03717	-0.2831	0.389061
33	0.036026	0.2744	0.39239
34	0.041514	0.3162	0.376509
35	0.092323	0.7031	0.2424
36	-0.220342	-1.6781	0.049357
37	0.105155	0.8008	0.213248
38	-0.02739	-0.2086	0.417748
39	0.002771	0.0211	0.491618
40	0.053698	0.409	0.34204
41	0.014873	0.1133	0.455104
42	-0.041643	-0.3171	0.376136
43	-0.069641	-0.5304	0.298939
44	0.055961	0.4262	0.335775
45	0.0266	0.2026	0.420086
46	0.019241	0.1465	0.442002
47	-0.032403	-0.2468	0.402977
48	-0.038611	-0.2941	0.384883
49	-0.001281	-0.0098	0.496125
50	0.036076	0.2747	0.392243
51	0.006283	0.0478	0.481002
52	0.003871	0.0295	0.488291
53	-0.029922	-0.2279	0.41027
54	0.001686	0.0128	0.494901
55	0.024404	0.1859	0.426603
56	-0.011154	-0.0849	0.466297
57	-0.0017	-0.0129	0.494857
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.198391	-1.5109	0.068122
2	-0.196336	-1.4952	0.070135
3	-0.347354	-2.6454	0.005242
4	-0.300582	-2.2892	0.012864
5	-0.286621	-2.1828	0.016555
6	-0.036675	-0.2793	0.390502
7	0.138076	1.0516	0.148683
8	-0.213181	-1.6235	0.054949
9	-0.134343	-1.0231	0.155248
10	-0.432956	-3.2973	0.000835
11	-0.07806	-0.5945	0.277248
12	-0.162079	-1.2344	0.111023
13	0.018843	0.1435	0.443195
14	0.014242	0.1085	0.457001
15	0.167859	1.2784	0.103105
16	-0.010935	-0.0833	0.46696
17	0.303204	2.3091	0.012259
18	0.037088	0.2825	0.389301
19	-0.08022	-0.6109	0.271814
20	-0.066234	-0.5044	0.307939
21	0.177465	1.3515	0.090887
22	0.089247	0.6797	0.249703
23	0.131483	1.0013	0.160409
24	0.059504	0.4532	0.326059
25	0.058772	0.4476	0.328056
26	-0.088032	-0.6704	0.252621
27	-0.139625	-1.0634	0.146014
28	-0.105121	-0.8006	0.213322
29	-0.085808	-0.6535	0.258011
30	-0.090836	-0.6918	0.245915
31	0.004096	0.0312	0.48761
32	-0.05717	-0.4354	0.332445
33	-0.017214	-0.1311	0.448077
34	-0.06414	-0.4885	0.313529
35	-0.025292	-0.1926	0.423964
36	-0.21234	-1.6171	0.055638
37	-0.003848	-0.0293	0.488361
38	0.002555	0.0195	0.492272
39	-0.048356	-0.3683	0.357007
40	0.055457	0.4223	0.337167
41	-0.065707	-0.5004	0.309341
42	0.022043	0.1679	0.433632
43	-0.021016	-0.1601	0.436698
44	-0.029187	-0.2223	0.412437
45	0.01749	0.1332	0.447249
46	-0.06912	-0.5264	0.300309
47	0.091716	0.6985	0.243832
48	-0.035292	-0.2688	0.394528
49	0.002423	0.0185	0.49267
50	0.073743	0.5616	0.288273
51	0.028825	0.2195	0.413506
52	-0.00648	-0.0494	0.480404
53	0.058496	0.4455	0.328812
54	0.023616	0.1799	0.428946
55	0.033185	0.2527	0.400685
56	-0.011134	-0.0848	0.466359
57	-0.015784	-0.1202	0.452366
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/21/t1258801409dijjzasqe4z3w08/1bo3g1258801368.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/21/t1258801409dijjzasqe4z3w08/1bo3g1258801368.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/21/t1258801409dijjzasqe4z3w08/2y9f61258801368.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/21/t1258801409dijjzasqe4z3w08/2y9f61258801368.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 12 ; par6 = MA ; 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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