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Workshop 8

*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 04:54:35 -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/t125906371877sa2ka5hbyu7wi.htm/, Retrieved Tue, 24 Nov 2009 12:55:20 +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/t125906371877sa2ka5hbyu7wi.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:

JSSHWWS8P3

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	0.883299	6.1197	0
2	0.624826	4.3289	3.8e-05
3	0.366994	2.5426	0.007141
4	0.222647	1.5425	0.064755
5	0.203534	1.4101	0.082475
6	0.242521	1.6802	0.049705
7	0.246074	1.7049	0.047344
8	0.1649	1.1425	0.129464
9	-0.001962	-0.0136	0.494604
10	-0.209218	-1.4495	0.07685
11	-0.391299	-2.711	0.004639
12	-0.491934	-3.4082	0.000666
13	-0.485306	-3.3623	0.000762
14	-0.404437	-2.802	0.003651
15	-0.317382	-2.1989	0.016369
16	-0.271059	-1.878	0.033235
17	-0.276916	-1.9185	0.030501
18	-0.310399	-2.1505	0.01829
19	-0.32757	-2.2695	0.013886
20	-0.302575	-2.0963	0.020676
21	-0.237338	-1.6443	0.053322
22	-0.154847	-1.0728	0.14436
23	-0.076957	-0.5332	0.298187
24	-0.023336	-0.1617	0.436119
25	0.007957	0.0551	0.478134
26	0.017356	0.1202	0.452395
27	0.012348	0.0856	0.46609
28	0.001249	0.0087	0.496565
29	0.003615	0.025	0.490062
30	0.031702	0.2196	0.413542
31	0.080589	0.5583	0.289604
32	0.118784	0.823	0.2073
33	0.124072	0.8596	0.197141
34	0.09768	0.6767	0.250907
35	0.065102	0.451	0.326995
36	0.051213	0.3548	0.362143
37	0.058594	0.406	0.343291
38	0.068408	0.4739	0.318843
39	0.066927	0.4637	0.322486
40	0.051528	0.357	0.361329
41	0.028285	0.196	0.422732
42	0.006494	0.045	0.48215
43	-0.010639	-0.0737	0.470773
44	-0.018891	-0.1309	0.448209
45	-0.019014	-0.1317	0.447872
46	-0.011935	-0.0827	0.467223
47	-0.003685	-0.0255	0.489868
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	0.883299	6.1197	0
2	-0.707017	-4.8984	6e-06
3	0.449283	3.1127	0.00156
4	0.238265	1.6507	0.05266
5	-0.138477	-0.9594	0.171083
6	-0.080097	-0.5549	0.290761
7	-0.149428	-1.0353	0.152865
8	-0.068684	-0.4759	0.318167
9	-0.287662	-1.993	0.025983
10	-0.194025	-1.3442	0.092594
11	-0.050794	-0.3519	0.363222
12	-0.012466	-0.0864	0.465766
13	0.118497	0.821	0.20786
14	-0.112725	-0.781	0.219325
15	-0.028224	-0.1955	0.422896
16	0.200239	1.3873	0.08588
17	-0.067082	-0.4648	0.322103
18	-0.092122	-0.6382	0.263175
19	0.011899	0.0824	0.467321
20	-0.09062	-0.6278	0.266545
21	-0.102755	-0.7119	0.239983
22	-0.138322	-0.9583	0.171352
23	0.046812	0.3243	0.373551
24	-0.091115	-0.6313	0.265431
25	0.091718	0.6354	0.264079
26	-0.119416	-0.8273	0.206069
27	-0.0914	-0.6332	0.264793
28	0.06186	0.4286	0.335072
29	0.083207	0.5765	0.283495
30	-0.038819	-0.2689	0.394562
31	-0.05372	-0.3722	0.355699
32	-0.110719	-0.7671	0.223393
33	0.018193	0.126	0.450111
34	-0.002583	-0.0179	0.492897
35	0.003802	0.0263	0.489548
36	-0.063613	-0.4407	0.330697
37	-0.063178	-0.4377	0.33178
38	-0.020327	-0.1408	0.444297
39	-0.060684	-0.4204	0.338023
40	-0.049799	-0.345	0.365794
41	-0.018662	-0.1293	0.448832
42	0.018551	0.1285	0.449134
43	-0.038947	-0.2698	0.394222
44	-0.015863	-0.1099	0.456472
45	-0.039893	-0.2764	0.391718
46	0.057577	0.3989	0.345866
47	0.030678	0.2125	0.416292
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/t125906371877sa2ka5hbyu7wi/1hiox1259063673.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t125906371877sa2ka5hbyu7wi/1hiox1259063673.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t125906371877sa2ka5hbyu7wi/2v8bq1259063673.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t125906371877sa2ka5hbyu7wi/2v8bq1259063673.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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