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paper - time-series (2)

*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, 10 Dec 2010 14:01:10 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/10/t1291989608d4bcve9zz8clc2p.htm/, Retrieved Fri, 10 Dec 2010 15:00:10 +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/2010/Dec/10/t1291989608d4bcve9zz8clc2p.htm/},
    year = {2010},
}
@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 = {2010},
    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 «

296.95 296.84 287.54 287.81 283.99 275.79 269.52 278.35 283.43 289.46 282.30 293.55 304.78 300.99 315.29 316.21 331.79 329.38 317.27 317.98 340.28 339.21 336.71 340.11 347.72 328.68 303.05 299.83 320.04 317.94 303.31 308.85 319.19 314.52 312.39 315.77 320.23 309.45 296.54 297.28 301.39 306.68 305.91 314.76 323.34 341.58 330.12 318.16 317.84 325.39 327.56 329.77 333.29 346.10 358.00 344.82 313.30 301.26 306.38 319.31

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	7 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.847945	6.5682	0
2	0.636007	4.9265	3e-06
3	0.525772	4.0726	6.9e-05
4	0.473922	3.671	0.000258
5	0.34665	2.6851	0.00468
6	0.210829	1.6331	0.053845
7	0.16237	1.2577	0.106685
8	0.154135	1.1939	0.118603
9	0.05515	0.4272	0.335386
10	-0.086959	-0.6736	0.251581
11	-0.178826	-1.3852	0.085562
12	-0.225736	-1.7485	0.042742
13	-0.284194	-2.2014	0.015784
14	-0.354481	-2.7458	0.003977
15	-0.366352	-2.8378	0.003095
16	-0.328943	-2.548	0.006707
17	-0.290604	-2.251	0.01403
18	-0.267162	-2.0694	0.02141
19	-0.205962	-1.5954	0.057941
20	-0.122843	-0.9515	0.172574
21	-0.060514	-0.4687	0.320477
22	-0.039889	-0.309	0.379205
23	-0.015509	-0.1201	0.45239
24	0.024253	0.1879	0.425809
25	0.075709	0.5864	0.27989
26	0.087932	0.6811	0.249209
27	0.096806	0.7499	0.228136
28	0.132984	1.0301	0.153552
29	0.213574	1.6543	0.051641
30	0.267651	2.0732	0.021227
31	0.262539	2.0336	0.02321
32	0.213859	1.6565	0.051416
33	0.180086	1.3949	0.084088
34	0.140077	1.085	0.141124
35	0.081464	0.631	0.265214
36	0.03772	0.2922	0.385578
37	0.022751	0.1762	0.430353
38	-0.008615	-0.0667	0.473509
39	-0.081496	-0.6313	0.265132
40	-0.156406	-1.2115	0.115224
41	-0.199841	-1.548	0.063446
42	-0.222606	-1.7243	0.044902
43	-0.251224	-1.946	0.028173
44	-0.270981	-2.099	0.020016
45	-0.266787	-2.0665	0.021551
46	-0.248942	-1.9283	0.029277
47	-0.242037	-1.8748	0.032844
48	-0.24245	-1.878	0.032621
49	-0.220337	-1.7067	0.046522
50	-0.16874	-1.3071	0.098091
51	-0.12745	-0.9872	0.163748
52	-0.099519	-0.7709	0.221905
53	-0.075835	-0.5874	0.279565
54	-0.042268	-0.3274	0.372249
55	-0.009125	-0.0707	0.471944
56	0.009543	0.0739	0.470659
57	0.006659	0.0516	0.479518
58	0.000553	0.0043	0.498297
59	-0.004305	-0.0333	0.486754
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.847945	6.5682	0
2	-0.2954	-2.2882	0.012833
3	0.302755	2.3451	0.011173
4	-0.034168	-0.2647	0.396088
5	-0.297214	-2.3022	0.012405
6	0.125464	0.9718	0.167516
7	0.083989	0.6506	0.258902
8	-0.08716	-0.6751	0.25109
9	-0.244069	-1.8905	0.031758
10	-0.02425	-0.1878	0.425818
11	-0.103218	-0.7995	0.213571
12	-0.110731	-0.8577	0.197231
13	0.034881	0.2702	0.393972
14	-0.08656	-0.6705	0.252558
15	0.044756	0.3467	0.365024
16	-0.008081	-0.0626	0.475149
17	0.069354	0.5372	0.296553
18	0.030201	0.2339	0.407917
19	0.127318	0.9862	0.163998
20	0.00688	0.0533	0.478838
21	-0.004682	-0.0363	0.485594
22	-0.021692	-0.168	0.433564
23	-0.036621	-0.2837	0.388821
24	-0.02869	-0.2222	0.412444
25	0.077654	0.6015	0.274884
26	-0.153926	-1.1923	0.118918
27	0.038305	0.2967	0.383858
28	0.06059	0.4693	0.320269
29	0.188353	1.459	0.074894
30	0.002623	0.0203	0.491929
31	-0.014071	-0.109	0.456787
32	-0.098185	-0.7605	0.224955
33	-0.005561	-0.0431	0.482892
34	-0.039587	-0.3066	0.380089
35	0.012588	0.0975	0.461324
36	0.063963	0.4955	0.311044
37	-0.113848	-0.8819	0.190686
38	-0.168402	-1.3044	0.098534
39	-0.046941	-0.3636	0.358716
40	-0.032553	-0.2522	0.400893
41	0.001885	0.0146	0.494201
42	0.050845	0.3938	0.347545
43	0.058262	0.4513	0.326701
44	-0.080023	-0.6199	0.268849
45	0.033046	0.256	0.399425
46	0.029712	0.2301	0.409379
47	0.02409	0.1866	0.426303
48	-0.078294	-0.6065	0.273248
49	0.004835	0.0374	0.485126
50	-0.057577	-0.446	0.328606
51	-0.060269	-0.4668	0.321152
52	0.009472	0.0734	0.470879
53	-0.062774	-0.4862	0.314281
54	-0.055285	-0.4282	0.335007
55	0.024192	0.1874	0.425993
56	-0.050065	-0.3878	0.349769
57	-0.017716	-0.1372	0.445654
58	-0.031561	-0.2445	0.40385
59	-0.039347	-0.3048	0.380795
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/10/t1291989608d4bcve9zz8clc2p/1ebb71291989662.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t1291989608d4bcve9zz8clc2p/1ebb71291989662.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t1291989608d4bcve9zz8clc2p/2ebb71291989662.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t1291989608d4bcve9zz8clc2p/2ebb71291989662.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 4 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 4 ; 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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