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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: Sat, 19 Dec 2009 09:09:18 -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/19/t1261239070vsup2py77kjxkhr.htm/, Retrieved Sat, 19 Dec 2009 17:11:12 +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/19/t1261239070vsup2py77kjxkhr.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 «

104.7 86 92.1 106.9 112.6 101.7 92 97.4 97 105.4 102.7 98.1 104.5 87.4 89.9 109.8 111.7 98.6 96.9 95.1 97 112.7 102.9 97.4 111.4 87.4 96.8 114.1 110.3 103.9 101.6 94.6 95.9 104.7 102.8 98.1 113.9 80.9 95.7 113.2 105.9 108.8 102.3 99 100.7 115.5 100.7 109.9 114.6 85.4 100.5 114.8 116.5 112.9 102 106 105.3 118.8 106.1 109.3 117.2 92.5 104.2 112.5 122.4 113.3 100 110.7 112.8 109.8 117.3 109.1 115.9 96 99.8 116.8 115.7 99.4 94.3 91 93.2 103.1 94.1 91.8 102.7 82.6 89.1

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	0.238183	2.2216	0.014452
2	-0.072717	-0.6783	0.249705
3	0.096201	0.8973	0.186017
4	0.052235	0.4872	0.313664
5	0.31157	2.9061	0.00232
6	0.387882	3.6179	0.000249
7	0.201265	1.8773	0.031916
8	0.005874	0.0548	0.478216
9	-0.05348	-0.4988	0.30958
10	-0.254099	-2.3701	0.009997
11	0.067317	0.6279	0.265861
12	0.593022	5.5313	0
13	0.000922	0.0086	0.496577
14	-0.235596	-2.1975	0.015321
15	-0.14613	-1.363	0.088198
16	-0.136179	-1.2702	0.103702
17	0.124569	1.1619	0.124226
18	0.145955	1.3614	0.088454
19	0.049281	0.4597	0.323451
20	-0.10241	-0.9552	0.171057
21	-0.156839	-1.4629	0.07355
22	-0.290997	-2.7142	0.004004
23	-0.000875	-0.0082	0.496752
24	0.410729	3.831	0.00012
25	-0.051699	-0.4822	0.315433
26	-0.24446	-2.2802	0.012521
27	-0.179984	-1.6788	0.048392
28	-0.170108	-1.5867	0.058108
29	0.039701	0.3703	0.356028
30	0.069355	0.6469	0.2597
31	0.023378	0.2181	0.413949
32	-0.123367	-1.1507	0.126506
33	-0.188632	-1.7594	0.041009
34	-0.251589	-2.3467	0.010607
35	-0.059623	-0.5561	0.289775
36	0.320195	2.9866	0.001832
37	-0.041159	-0.3839	0.350993
38	-0.23373	-2.1801	0.015976
39	-0.167799	-1.5651	0.060592
40	-0.117134	-1.0926	0.138803
41	0.013712	0.1279	0.449261
42	0.06236	0.5817	0.281151
43	0.027147	0.2532	0.400351
44	-0.096524	-0.9003	0.185218
45	-0.122827	-1.1457	0.12754
46	-0.177788	-1.6583	0.05043
47	-0.017402	-0.1623	0.435715
48	0.273046	2.5468	0.006315
49	-0.001151	-0.0107	0.495731
50	-0.175625	-1.6381	0.052504
51	-0.131362	-1.2253	0.111892
52	-0.079938	-0.7456	0.228957
53	0.00069	0.0064	0.497439
54	0.037317	0.3481	0.364313
55	-0.000516	-0.0048	0.498085
56	-0.092915	-0.8667	0.194259
57	-0.115921	-1.0812	0.14129
58	-0.170857	-1.5936	0.057321
59	-0.038719	-0.3611	0.359434
60	0.183778	1.7142	0.045029

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.238183	2.2216	0.014452
2	-0.137233	-1.28	0.101969
3	0.160544	1.4975	0.068947
4	-0.030303	-0.2826	0.389061
5	0.370179	3.4528	0.000429
6	0.235786	2.1993	0.015256
7	0.199302	1.859	0.033207
8	-0.063189	-0.5894	0.278566
9	-0.075042	-0.6999	0.242914
10	-0.533266	-4.974	2e-06
11	-0.062407	-0.5821	0.281003
12	0.494689	4.6142	7e-06
13	-0.162046	-1.5115	0.067148
14	-0.051744	-0.4826	0.315283
15	-0.078032	-0.7278	0.234334
16	0.105604	0.985	0.163676
17	-0.092673	-0.8644	0.194872
18	-0.092875	-0.8663	0.194359
19	0.093029	0.8677	0.193969
20	-0.076232	-0.711	0.239479
21	0.052257	0.4874	0.313592
22	-0.012885	-0.1202	0.452306
23	0.013333	0.1244	0.450658
24	-0.011811	-0.1102	0.456264
25	-0.058956	-0.5499	0.291896
26	-0.039783	-0.3711	0.355742
27	-0.026905	-0.2509	0.401222
28	-0.097258	-0.9072	0.183413
29	-0.104402	-0.9738	0.16643
30	0.007439	0.0694	0.47242
31	0.086313	0.8051	0.211487
32	-0.009787	-0.0913	0.463739
33	-0.004628	-0.0432	0.482834
34	0.119133	1.1112	0.134772
35	-0.137346	-1.2811	0.101786
36	0.040081	0.3739	0.354711
37	-0.064204	-0.5989	0.275414
38	-0.060883	-0.5679	0.28579
39	-0.121766	-1.1358	0.12959
40	0.108714	1.014	0.156693
41	-0.033356	-0.3111	0.378225
42	-0.000275	-0.0026	0.498979
43	-0.071743	-0.6692	0.252578
44	0.096132	0.8967	0.186186
45	0.006865	0.064	0.474544
46	0.016794	0.1566	0.437945
47	0.050878	0.4746	0.318147
48	-0.127485	-1.1891	0.118817
49	0.01879	0.1753	0.430641
50	-0.101667	-0.9483	0.172804
51	-0.056956	-0.5313	0.2983
52	-0.102347	-0.9546	0.171205
53	-0.085266	-0.7953	0.2143
54	-0.015487	-0.1445	0.442739
55	-0.044562	-0.4156	0.339345
56	0.113064	1.0546	0.147265
57	-0.046009	-0.4291	0.334442
58	0.069655	0.6497	0.258801
59	-0.004117	-0.0384	0.484728
60	0.014334	0.1337	0.446975

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261239070vsup2py77kjxkhr/1n2on1261238956.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261239070vsup2py77kjxkhr/1n2on1261238956.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261239070vsup2py77kjxkhr/28xi11261238956.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261239070vsup2py77kjxkhr/28xi11261238956.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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