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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: Tue, 09 Dec 2008 07:02:49 -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/09/t1228831393i5j1nfm3r9tehrg.htm/, Retrieved Tue, 09 Dec 2008 14:03:15 +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/09/t1228831393i5j1nfm3r9tehrg.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)

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

137.0 135.9 138.1 137.1 135.1 139.6 131.8 136.7 128.9 131.3 129.5 129.0 129.8 125.4 128.6 130.2 124.6 123.7 124.4 119.2 124.4 123.1 120.9 120.9 117.8 113.6 113.2 115.9 121.1 107.6 114.7 112.8 112.1 109.8 108.5 102.7 110.6 108.2 112.7 107.9 102.7 108.4 108.4 106.9 108.9 103.7 103.6 111.6 105.5 105.5 101.3 103.8 100.3 108.2 105.6 103.0 100.5 104.3 99.1 91.5

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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.875415	6.7809	0
2	0.835666	6.473	0
3	0.792501	6.1387	0
4	0.744932	5.7702	0
5	0.705387	5.4639	0
6	0.660612	5.1171	2e-06
7	0.618238	4.7889	6e-06
8	0.564143	4.3698	2.5e-05
9	0.525114	4.0675	7e-05
10	0.487558	3.7766	0.000184
11	0.437348	3.3877	0.000625
12	0.374508	2.9009	0.002597
13	0.360172	2.7899	0.003529
14	0.309732	2.3992	0.009778
15	0.267126	2.0691	0.021424
16	0.231972	1.7968	0.038697
17	0.179207	1.3881	0.085115
18	0.135677	1.0509	0.148749
19	0.107522	0.8329	0.204114
20	0.053974	0.4181	0.33869
21	0.022906	0.1774	0.429886
22	-0.026735	-0.2071	0.41832
23	-0.047306	-0.3664	0.357666
24	-0.089371	-0.6923	0.245722
25	-0.132286	-1.0247	0.154813
26	-0.154713	-1.1984	0.117736
27	-0.180351	-1.397	0.083781
28	-0.226699	-1.756	0.042095
29	-0.251143	-1.9453	0.028212
30	-0.261163	-2.023	0.02377
31	-0.301639	-2.3365	0.011412
32	-0.302237	-2.3411	0.011283
33	-0.313553	-2.4288	0.009082
34	-0.335366	-2.5977	0.005894
35	-0.355937	-2.7571	0.003858
36	-0.350062	-2.7116	0.004361
37	-0.355904	-2.7568	0.00386
38	-0.363145	-2.8129	0.003313
39	-0.367607	-2.8475	0.003013
40	-0.361873	-2.8031	0.003404
41	-0.365049	-2.8277	0.003182
42	-0.35387	-2.7411	0.004028
43	-0.364811	-2.8258	0.003198
44	-0.362669	-2.8092	0.003347
45	-0.356264	-2.7596	0.003831
46	-0.33187	-2.5707	0.006325
47	-0.32844	-2.5441	0.006775
48	-0.32236	-2.497	0.007644
49	-0.313314	-2.4269	0.009124
50	-0.299024	-2.3162	0.011989
51	-0.273947	-2.122	0.018989
52	-0.263835	-2.0437	0.022693
53	-0.225387	-1.7458	0.042979
54	-0.222104	-1.7204	0.045256
55	-0.187654	-1.4536	0.07564
56	-0.163224	-1.2643	0.105501
57	-0.126506	-0.9799	0.165533
58	-0.09461	-0.7328	0.233253
59	-0.057679	-0.4468	0.32832
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.875415	6.7809	0
2	0.296662	2.2979	0.012534
3	0.085733	0.6641	0.25459
4	-0.008105	-0.0628	0.475076
5	0.008352	0.0647	0.474316
6	-0.025542	-0.1979	0.421915
7	-0.021049	-0.163	0.435517
8	-0.078769	-0.6101	0.272037
9	0.001438	0.0111	0.495575
10	0.010218	0.0791	0.468589
11	-0.062958	-0.4877	0.313779
12	-0.129722	-1.0048	0.159509
13	0.132284	1.0247	0.154816
14	-0.057536	-0.4457	0.32872
15	-0.050252	-0.3893	0.349234
16	-0.012532	-0.0971	0.461495
17	-0.079863	-0.6186	0.269256
18	-0.044193	-0.3423	0.366654
19	0.04495	0.3482	0.36446
20	-0.123253	-0.9547	0.171776
21	0.026691	0.2067	0.418453
22	-0.073061	-0.5659	0.286777
23	0.043951	0.3404	0.367356
24	-0.079297	-0.6142	0.270692
25	-0.041481	-0.3213	0.374545
26	-0.003242	-0.0251	0.490023
27	0.034783	0.2694	0.394261
28	-0.135918	-1.0528	0.148324
29	-0.020713	-0.1604	0.436536
30	0.076159	0.5899	0.278728
31	-0.080494	-0.6235	0.26766
32	0.033648	0.2606	0.397633
33	0.043061	0.3335	0.369941
34	-0.100966	-0.7821	0.218622
35	-0.02238	-0.1734	0.431477
36	0.061688	0.4778	0.317253
37	-0.035555	-0.2754	0.391974
38	0.003502	0.0271	0.489226
39	-0.024788	-0.192	0.424192
40	-0.022664	-0.1756	0.430616
41	0.022645	0.1754	0.430675
42	0.016498	0.1278	0.449372
43	-0.150892	-1.1688	0.123553
44	0.061063	0.473	0.318966
45	0.002462	0.0191	0.492423
46	0.029352	0.2274	0.410459
47	-0.027286	-0.2114	0.416663
48	-0.024802	-0.1921	0.424149
49	-0.054424	-0.4216	0.337423
50	0.070455	0.5457	0.293633
51	0.00191	0.0148	0.494122
52	-0.025918	-0.2008	0.420781
53	0.098889	0.766	0.223343
54	-0.067023	-0.5192	0.302781
55	0.029324	0.2271	0.410543
56	0.02814	0.218	0.414097
57	0.036158	0.2801	0.39019
58	0.09595	0.7432	0.230123
59	0.015777	0.1222	0.451573
60	NA	NA	NA

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/09/t1228831393i5j1nfm3r9tehrg/110ko1228831368.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/09/t1228831393i5j1nfm3r9tehrg/110ko1228831368.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/09/t1228831393i5j1nfm3r9tehrg/2wyou1228831368.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/09/t1228831393i5j1nfm3r9tehrg/2wyou1228831368.ps (open in new window)

Parameters (Session):

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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