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workshop8, step2, ACF

*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: Sun, 07 Dec 2008 09:15:37 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/07/t122866660001xr9dz78x7xodf.htm/, Retrieved Sun, 07 Dec 2008 16:16:40 +0000

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/2008/Dec/07/t122866660001xr9dz78x7xodf.htm/},
    year = {2008},
}
@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 = {2008},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

Feedback Forum:

2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc] [reply] 
test

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

7.5 7.2 6.9 6.7 6.4 6.3 6.8 7.3 7.1 7.1 6.8 6.5 6.3 6.1 6.1 6.3 6.3 6 6.2 6.4 6.8 7.5 7.5 7.6 7.6 7.4 7.3 7.1 6.9 6.8 7.5 7.6 7.8 8 8.1 8.2 8.3 8.2 8 7.9 7.6 7.6 8.2 8.3 8.4 8.4 8.4 8.6 8.9 8.8 8.3 7.5 7.2 7.5 8.8 9.3 9.3 8.7 8.2 8.3 8.5 8.6 8.6 8.2 8.1 8 8.6 8.7 8.8 8.5 8.4 8.5 8.7 8.7 8.6 8.5 8.3 8.1 8.2 8.1 8.1 7.9 7.9 7.9 8 8 7.9 8 7.7 7.2 7.5 7.3 7 7 7 7.2 7.3 7.1 6.8 6.6 6.2 6.2 6.8 6.9 6.8 6.7

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.927418	9.5484	0
2	0.805919	8.2974	0
3	0.700009	7.207	0
4	0.643255	6.6227	0
5	0.628455	6.4703	0
6	0.622445	6.4085	0
7	0.593991	6.1155	0
8	0.554408	5.708	0
9	0.531096	5.468	0
10	0.5305	5.4618	0
11	0.543994	5.6008	0
12	0.53594	5.5178	0
13	0.462877	4.7656	3e-06
14	0.370658	3.8162	0.000114
15	0.283109	2.9148	0.002172
16	0.217781	2.2422	0.013515
17	0.169287	1.7429	0.042124
18	0.133398	1.3734	0.086261
19	0.091005	0.9369	0.175457
20	0.051924	0.5346	0.297026
21	0.03311	0.3409	0.366933
22	0.032643	0.3361	0.368738
23	0.039116	0.4027	0.343981
24	0.028254	0.2909	0.385849
25	-0.025896	-0.2666	0.395141
26	-0.085315	-0.8784	0.190864
27	-0.140358	-1.4451	0.075694
28	-0.180201	-1.8553	0.033167
29	-0.210332	-2.1655	0.016296
30	-0.234303	-2.4123	0.008785
31	-0.254802	-2.6233	0.004995
32	-0.266539	-2.7442	0.003563
33	-0.263355	-2.7114	0.003909
34	-0.256392	-2.6397	0.004775
35	-0.253597	-2.6109	0.005169
36	-0.261197	-2.6892	0.004161
37	-0.289085	-2.9763	0.001807
38	-0.303939	-3.1292	0.001132
39	-0.312783	-3.2203	0.00085
40	-0.320563	-3.3004	0.000658
41	-0.347478	-3.5775	0.000262
42	-0.38831	-3.9979	5.9e-05
43	-0.431158	-4.439	1.1e-05
44	-0.449894	-4.6319	5e-06
45	-0.429291	-4.4198	1.2e-05
46	-0.387082	-3.9853	6.2e-05
47	-0.342954	-3.5309	0.000307
48	-0.325132	-3.3474	0.000565
49	-0.343605	-3.5376	3e-04
50	-0.366447	-3.7728	0.000133
51	-0.378797	-3.9	8.5e-05
52	-0.379817	-3.9105	8.1e-05
53	-0.387563	-3.9902	6.1e-05
54	-0.397444	-4.0919	4.2e-05
55	-0.40772	-4.1977	2.8e-05
56	-0.404121	-4.1607	3.2e-05
57	-0.381538	-3.9282	7.6e-05
58	-0.352736	-3.6316	0.000218
59	-0.318396	-3.2781	0.000707
60	-0.28808	-2.966	0.001864

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.927418	9.5484	0
2	-0.387331	-3.9878	6.1e-05
3	0.187553	1.931	0.028078
4	0.213046	2.1934	0.01523
5	0.098129	1.0103	0.157325
6	-0.024789	-0.2552	0.399526
7	-0.08559	-0.8812	0.190101
8	0.105422	1.0854	0.140108
9	0.147596	1.5196	0.065795
10	0.03223	0.3318	0.370339
11	0.036375	0.3745	0.354388
12	-0.143104	-1.4733	0.071811
13	-0.357446	-3.6801	0.000184
14	0.162618	1.6743	0.048515
15	-0.176873	-1.821	0.035713
16	-0.118636	-1.2214	0.112316
17	-0.124486	-1.2817	0.101379
18	0.042709	0.4397	0.330518
19	-0.054972	-0.566	0.286304
20	0.012658	0.1303	0.448277
21	0.066755	0.6873	0.246702
22	0.040424	0.4162	0.339057
23	-0.006124	-0.0631	0.474921
24	-0.002838	-0.0292	0.488371
25	-0.098121	-1.0102	0.157347
26	0.121793	1.2539	0.106311
27	-0.107154	-1.1032	0.136214
28	-0.011377	-0.1171	0.453489
29	-0.03212	-0.3307	0.370762
30	-0.058687	-0.6042	0.273493
31	0.111227	1.1452	0.127363
32	-0.070582	-0.7267	0.23451
33	-0.01967	-0.2025	0.41995
34	-0.067592	-0.6959	0.244007
35	-0.034484	-0.355	0.361635
36	0.053777	0.5537	0.290487
37	-0.075545	-0.7778	0.219215
38	0.119199	1.2272	0.111228
39	-0.0561	-0.5776	0.282385
40	-0.063461	-0.6534	0.257466
41	-0.136939	-1.4099	0.080753
42	-0.121769	-1.2537	0.106357
43	-0.03766	-0.3877	0.349494
44	-0.003789	-0.039	0.484479
45	0.066235	0.6819	0.248386
46	0.064223	0.6612	0.254954
47	0.027506	0.2832	0.38879
48	-0.033094	-0.3407	0.366994
49	-0.085338	-0.8786	0.190801
50	-0.03993	-0.4111	0.340913
51	0.045045	0.4638	0.321883
52	-0.101037	-1.0402	0.150298
53	0.013145	0.1353	0.4463
54	0.031407	0.3234	0.373531
55	0.03291	0.3388	0.367704
56	-0.029775	-0.3065	0.379894
57	-0.101987	-1.05	0.148049
58	-0.059119	-0.6087	0.272025
59	0.062511	0.6436	0.260614
60	0.046472	0.4785	0.316654

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/07/t122866660001xr9dz78x7xodf/10gfh1228666532.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/07/t122866660001xr9dz78x7xodf/10gfh1228666532.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/07/t122866660001xr9dz78x7xodf/2xm491228666532.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/07/t122866660001xr9dz78x7xodf/2xm491228666532.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

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 (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='lags',ylab='ACF')

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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