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WS 8 review

*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: Fri, 04 Dec 2009 02:19:05 -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/04/t1259918465219kndzdyqy5njl.htm/, Retrieved Fri, 04 Dec 2009 10:21:07 +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/04/t1259918465219kndzdyqy5njl.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 «

11.1 10.9 10 9.2 9.2 9.5 9.6 9.5 9.1 8.9 9 10.1 10.3 10.2 9.6 9.2 9.3 9.4 9.4 9.2 9 9 9 9.8 10 9.8 9.3 9 9 9.1 9.1 9.1 9.2 8.8 8.3 8.4 8.1 7.7 7.9 7.9 8 7.9 7.6 7.1 6.8 6.5 6.9 8.2 8.7 8.3 7.9 7.5 7.8 8.3 8.4 8.2 7.7 7.2 7.3 8.1

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	0.888865	5.3332	3e-06
2	0.643929	3.8636	0.000224
3	0.394391	2.3663	0.011733
4	0.242376	1.4543	0.077269
5	0.216634	1.2998	0.100965
6	0.267206	1.6032	0.058811
7	0.304913	1.8295	0.03781
8	0.251626	1.5098	0.069917
9	0.086716	0.5203	0.303021
10	-0.140693	-0.8442	0.202078
11	-0.335702	-2.0142	0.025753
12	-0.434891	-2.6093	0.006566
13	-0.418051	-2.5083	0.008388
14	-0.331729	-1.9904	0.027092
15	-0.242666	-1.456	0.07703
16	-0.197342	-1.1841	0.122076
17	-0.200809	-1.2049	0.11806
18	-0.237362	-1.4242	0.081504
19	-0.273444	-1.6407	0.054788
20	-0.274209	-1.6453	0.054311
21	-0.229237	-1.3754	0.08875
22	-0.152394	-0.9144	0.183305
23	-0.081935	-0.4916	0.31299
24	-0.040772	-0.2446	0.404065
25	-0.029748	-0.1785	0.429671
26	-0.040754	-0.2445	0.404107
27	-0.055374	-0.3322	0.370817
28	-0.054258	-0.3255	0.373325
29	-0.03869	-0.2321	0.408871
30	-0.017904	-0.1074	0.457525
31	0.002824	0.0169	0.493287
32	0.012096	0.0726	0.471273
33	0.011419	0.0685	0.472877
34	0.005338	0.032	0.487313
35	-0.000371	-0.0022	0.499117
36	NA	NA	NA
37	NA	NA	NA
38	NA	NA	NA
39	NA	NA	NA
40	NA	NA	NA
41	NA	NA	NA
42	NA	NA	NA
43	NA	NA	NA
44	NA	NA	NA
45	NA	NA	NA
46	NA	NA	NA
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	0.888865	5.3332	3e-06
2	-0.696233	-4.1774	9e-05
3	0.391835	2.351	0.012159
4	0.225074	1.3504	0.092651
5	0.062965	0.3778	0.353902
6	-0.095637	-0.5738	0.284829
7	-0.16286	-0.9772	0.167506
8	-0.24229	-1.4537	0.07734
9	-0.197836	-1.187	0.121498
10	-0.104086	-0.6245	0.268114
11	0.06257	0.3754	0.354776
12	-0.149905	-0.8994	0.1872
13	0.127331	0.764	0.224928
14	-0.084612	-0.5077	0.30739
15	0.109482	0.6569	0.257714
16	0.103562	0.6214	0.269134
17	0.120322	0.7219	0.2375
18	-0.179786	-1.0787	0.143944
19	-0.050188	-0.3011	0.382525
20	-0.057234	-0.3434	0.366647
21	-0.066794	-0.4008	0.345482
22	-0.102541	-0.6152	0.271131
23	-0.110255	-0.6615	0.256243
24	-0.026209	-0.1573	0.437962
25	0.066443	0.3987	0.346251
26	-0.064163	-0.385	0.351259
27	0.136935	0.8216	0.208353
28	0.039901	0.2394	0.406074
29	-0.04909	-0.2945	0.385018
30	-0.039031	-0.2342	0.408083
31	0.066594	0.3996	0.345919
32	-0.135443	-0.8127	0.210879
33	-0.002298	-0.0138	0.494537
34	-0.104167	-0.625	0.267956
35	-0.047987	-0.2879	0.387528
36	NA	NA	NA
37	NA	NA	NA
38	NA	NA	NA
39	NA	NA	NA
40	NA	NA	NA
41	NA	NA	NA
42	NA	NA	NA
43	NA	NA	NA
44	NA	NA	NA
45	NA	NA	NA
46	NA	NA	NA
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/Dec/04/t1259918465219kndzdyqy5njl/1y0iw1259918343.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259918465219kndzdyqy5njl/1y0iw1259918343.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259918465219kndzdyqy5njl/2wb5u1259918343.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259918465219kndzdyqy5njl/2wb5u1259918343.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 2 ; 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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