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SHW WS8

*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: Tue, 24 Nov 2009 04:57:54 -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/24/t1259063950fqn76pn7wroq85g.htm/, Retrieved Tue, 24 Nov 2009 12:59:15 +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/24/t1259063950fqn76pn7wroq85g.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 «

8.6 8.5 8.3 7.8 7.8 8 8.6 8.9 8.9 8.6 8.3 8.3 8.3 8.4 8.5 8.4 8.6 8.5 8.5 8.5 8.5 8.5 8.5 8.5 8.5 8.5 8.5 8.5 8.6 8.4 8.1 8 8 8 8 7.9 7.8 7.8 7.9 8.1 8 7.6 7.3 7 6.8 7 7.1 7.2 7.1 6.9 6.7 6.7 6.6 6.9 7.3 7.5 7.3 7.1 6.9 7.1

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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.575754	3.9472	0.000131
2	-0.04706	-0.3226	0.374204
3	-0.48429	-3.3201	0.000873
4	-0.543792	-3.7281	0.000259
5	-0.222689	-1.5267	0.066771
6	0.136025	0.9325	0.177911
7	0.240356	1.6478	0.053032
8	0.212041	1.4537	0.07634
9	0.02344	0.1607	0.436512
10	-0.06464	-0.4431	0.329845
11	-0.061768	-0.4235	0.336946
12	-0.042901	-0.2941	0.384984
13	-0.039627	-0.2717	0.393533
14	0.004404	0.0302	0.48802
15	-0.001491	-0.0102	0.495944
16	0.035848	0.2458	0.403469
17	0.038586	0.2645	0.396263
18	-0.01844	-0.1264	0.44997
19	-0.094339	-0.6468	0.260468
20	-0.056867	-0.3899	0.349201
21	-0.028295	-0.194	0.423513
22	-0.006149	-0.0422	0.483278
23	-0.003143	-0.0215	0.491451
24	-0.009707	-0.0665	0.473612
25	-0.003556	-0.0244	0.490328
26	0.028028	0.1921	0.424227
27	-0.059784	-0.4099	0.341885
28	-0.144986	-0.994	0.162663
29	-0.151684	-1.0399	0.151854
30	-0.041999	-0.2879	0.387332
31	0.162051	1.111	0.136118
32	0.2969	2.0354	0.023733
33	0.19664	1.3481	0.092045
34	-0.036133	-0.2477	0.402718
35	-0.306517	-2.1014	0.020498
36	-0.378869	-2.5974	0.006251
37	-0.174685	-1.1976	0.118542
38	0.11784	0.8079	0.211618
39	0.287825	1.9732	0.027183
40	0.256364	1.7575	0.042668
41	0.074455	0.5104	0.306066
42	-0.048091	-0.3297	0.371548
43	-0.069847	-0.4788	0.317133
44	-0.041276	-0.283	0.38922
45	-0.009827	-0.0674	0.473287
46	0.005895	0.0404	0.483967
47	NA	NA	NA
48	NA	NA	NA
49	NA	NA	NA
50	NA	NA	NA
51	NA	NA	NA
52	NA	NA	NA
53	NA	NA	NA
54	NA	NA	NA
55	NA	NA	NA
56	NA	NA	NA
57	NA	NA	NA
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	0.575754	3.9472	0.000131
2	-0.566265	-3.8821	0.000161
3	-0.255033	-1.7484	0.043461
4	-0.108326	-0.7426	0.230695
5	0.11407	0.782	0.21906
6	-0.068916	-0.4725	0.319392
7	-0.184726	-1.2664	0.105802
8	0.165867	1.1371	0.130625
9	-0.140117	-0.9606	0.170837
10	0.168425	1.1547	0.127033
11	-0.083806	-0.5745	0.28417
12	0.000527	0.0036	0.498567
13	-0.063827	-0.4376	0.331848
14	0.115988	0.7952	0.215256
15	-0.071594	-0.4908	0.312918
16	0.023357	0.1601	0.436734
17	-0.008073	-0.0553	0.478048
18	-0.101535	-0.6961	0.2449
19	-0.046276	-0.3173	0.376228
20	0.112947	0.7743	0.221309
21	-0.13091	-0.8975	0.18702
22	-0.14117	-0.9678	0.169046
23	0.045791	0.3139	0.377482
24	-0.02454	-0.1682	0.433558
25	-0.020506	-0.1406	0.444402
26	-0.048397	-0.3318	0.37076
27	-0.223409	-1.5316	0.066161
28	-0.140794	-0.9652	0.169683
29	0.061745	0.4233	0.337002
30	0.00292	0.02	0.492058
31	0.03124	0.2142	0.41567
32	0.044194	0.303	0.381621
33	-0.025935	-0.1778	0.429822
34	-0.106306	-0.7288	0.234871
35	-0.090443	-0.62	0.269112
36	-0.062997	-0.4319	0.333901
37	-0.052473	-0.3597	0.360329
38	-0.013219	-0.0906	0.464087
39	-0.017305	-0.1186	0.453033
40	-0.090842	-0.6228	0.268219
41	0.058032	0.3978	0.346272
42	0.091705	0.6287	0.266295
43	-0.014699	-0.1008	0.460081
44	-0.009199	-0.0631	0.474991
45	0.038389	0.2632	0.396781
46	-0.015205	-0.1042	0.458711
47	NA	NA	NA
48	NA	NA	NA
49	NA	NA	NA
50	NA	NA	NA
51	NA	NA	NA
52	NA	NA	NA
53	NA	NA	NA
54	NA	NA	NA
55	NA	NA	NA
56	NA	NA	NA
57	NA	NA	NA
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259063950fqn76pn7wroq85g/1xf611259063872.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259063950fqn76pn7wroq85g/1xf611259063872.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259063950fqn76pn7wroq85g/2pfpk1259063872.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259063950fqn76pn7wroq85g/2pfpk1259063872.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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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