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paper ACF WLH

*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, 27 Dec 2009 06:56:04 -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/27/t1261922235jse40686s9r1duh.htm/, Retrieved Sun, 27 Dec 2009 14:57:17 +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/27/t1261922235jse40686s9r1duh.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 «

401 394 372 334 320 334 400 427 423 395 373 377 391 398 393 375 371 364 400 406 407 397 389 394 399 401 396 392 384 370 380 376 378 376 373 374 379 376 371 375 360 338 352 344 330 334 333 343 350 341 320 302 287 304 370 385 365 333 313 330 367

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	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.798155	6.2338	0
2	0.448936	3.5063	0.000429
3	0.213944	1.671	0.049927
4	0.230063	1.7968	0.038656
5	0.418665	3.2699	0.000886
6	0.566074	4.4212	2.1e-05
7	0.51988	4.0604	7.1e-05
8	0.36699	2.8663	0.002846
9	0.239728	1.8723	0.032978
10	0.202901	1.5847	0.059102
11	0.24883	1.9434	0.028291
12	0.290176	2.2663	0.013495
13	0.213437	1.667	0.050321
14	0.111332	0.8695	0.193984
15	0.032429	0.2533	0.400452
16	0.005147	0.0402	0.484033
17	0.016253	0.1269	0.449703
18	0.016399	0.1281	0.449252
19	-0.042832	-0.3345	0.369565
20	-0.109753	-0.8572	0.197345
21	-0.15739	-1.2293	0.111848
22	-0.178744	-1.396	0.083882
23	-0.168895	-1.3191	0.096031
24	-0.154857	-1.2095	0.115574
25	-0.186423	-1.456	0.075259
26	-0.212251	-1.6577	0.051253
27	-0.219614	-1.7152	0.045688
28	-0.209965	-1.6399	0.053089
29	-0.194187	-1.5167	0.06726
30	-0.199084	-1.5549	0.062572
31	-0.244777	-1.9118	0.030303
32	-0.288433	-2.2527	0.013942
33	-0.29508	-2.3046	0.012303
34	-0.256828	-2.0059	0.024654
35	-0.193457	-1.5109	0.067983
36	-0.157237	-1.2281	0.112071
37	-0.19652	-1.5349	0.064993
38	-0.236381	-1.8462	0.034859
39	-0.22378	-1.7478	0.042767
40	-0.159952	-1.2493	0.10817
41	-0.091729	-0.7164	0.238232
42	-0.087639	-0.6845	0.248133
43	-0.170731	-1.3334	0.093671
44	-0.240903	-1.8815	0.032338
45	-0.213861	-1.6703	0.049991
46	-0.086888	-0.6786	0.249975
47	0.059754	0.4667	0.321192
48	0.105312	0.8225	0.206995
49	0.001061	0.0083	0.496707
50	-0.145123	-1.1334	0.130732
51	-0.204932	-1.6006	0.05732
52	-0.132577	-1.0355	0.152271
53	0.006194	0.0484	0.480787
54	0.096203	0.7514	0.22766
55	0.069872	0.5457	0.293624
56	0.00141	0.011	0.495625
57	-0.047108	-0.3679	0.357103
58	-0.048673	-0.3801	0.352578
59	-0.022078	-0.1724	0.431832
60	-0.000461	-0.0036	0.498568

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.798155	6.2338	0
2	-0.518301	-4.0481	7.4e-05
3	0.314906	2.4595	0.008382
4	0.37026	2.8918	0.002651
5	0.203806	1.5918	0.058303
6	-0.024466	-0.1911	0.424547
7	-0.106614	-0.8327	0.204136
8	0.219658	1.7156	0.045657
9	-0.006655	-0.052	0.479357
10	-0.147189	-1.1496	0.127401
11	0.029607	0.2312	0.408951
12	-0.006917	-0.054	0.478548
13	-0.33047	-2.581	0.006135
14	0.185497	1.4488	0.07626
15	-0.156871	-1.2252	0.112605
16	-0.128104	-1.0005	0.160505
17	-0.055814	-0.4359	0.332216
18	-3e-06	0	0.49999
19	-0.097821	-0.764	0.223905
20	-0.058748	-0.4588	0.323992
21	-0.024826	-0.1939	0.42345
22	0.007919	0.0619	0.475441
23	-0.029118	-0.2274	0.410429
24	0.011969	0.0935	0.462914
25	-0.004048	-0.0316	0.48744
26	0.049954	0.3902	0.34889
27	0.075667	0.591	0.27836
28	-0.00129	-0.0101	0.495998
29	-0.003983	-0.0311	0.487641
30	-0.016093	-0.1257	0.450194
31	-0.034416	-0.2688	0.394497
32	-0.104576	-0.8168	0.20862
33	0.03505	0.2737	0.392601
34	0.022958	0.1793	0.429147
35	-0.064118	-0.5008	0.309166
36	-0.067668	-0.5285	0.299533
37	-0.043957	-0.3433	0.36627
38	0.117118	0.9147	0.18197
39	0.02741	0.2141	0.4156
40	-0.046006	-0.3593	0.360299
41	0.007415	0.0579	0.477004
42	-0.065623	-0.5125	0.305065
43	-0.137079	-1.0706	0.144278
44	0.078168	0.6105	0.271895
45	0.079011	0.6171	0.269733
46	0.075544	0.59	0.278678
47	0.02014	0.1573	0.437764
48	-0.040078	-0.313	0.377666
49	-0.021582	-0.1686	0.433351
50	-0.119682	-0.9347	0.176802
51	-0.012324	-0.0963	0.461817
52	0.007025	0.0549	0.478212
53	-0.103888	-0.8114	0.210148
54	-0.002311	-0.018	0.492831
55	0.039126	0.3056	0.380482
56	0.06392	0.4992	0.309708
57	-0.116195	-0.9075	0.183853
58	-0.072024	-0.5625	0.287911
59	-0.009689	-0.0757	0.469962
60	0.047047	0.3674	0.357278

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/27/t1261922235jse40686s9r1duh/1su5z1261922160.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/27/t1261922235jse40686s9r1duh/1su5z1261922160.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/27/t1261922235jse40686s9r1duh/2677k1261922160.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/27/t1261922235jse40686s9r1duh/2677k1261922160.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; 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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