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Workshop 8: Review

*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: Wed, 02 Dec 2009 10:40:29 -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/02/t1259775690cjzku6r5nm8lg4d.htm/, Retrieved Wed, 02 Dec 2009 18:41:32 +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/02/t1259775690cjzku6r5nm8lg4d.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:

RW8(2)

Dataseries X:

» Textbox « » Textfile « » CSV «

269645 267037 258113 262813 267413 267366 264777 258863 254844 254868 277267 285351 286602 283042 276687 277915 277128 277103 275037 270150 267140 264993 287259 291186 292300 288186 281477 282656 280190 280408 276836 275216 274352 271311 289802 290726 292300 278506 269826 265861 269034 264176 255198 253353 246057 235372 258556 260993 254663 250643 243422 247105 248541 245039 237080 237085 225554 226839 247934 248333 246969 245098 246263 255765 264319 268347 273046 273963 267430 271993 292710 295881

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	0.923799	7.1557	0
2	0.846636	6.558	0
3	0.750657	5.8146	0
4	0.646242	5.0058	3e-06
5	0.54266	4.2034	4.4e-05
6	0.434843	3.3683	0.000663
7	0.340071	2.6342	0.005357
8	0.253641	1.9647	0.027043
9	0.171842	1.3311	0.094099
10	0.097746	0.7571	0.225964
11	0.043391	0.3361	0.368982
12	-0.021354	-0.1654	0.434589
13	-0.069678	-0.5397	0.295692
14	-0.122877	-0.9518	0.172509
15	-0.184957	-1.4327	0.078571
16	-0.228008	-1.7661	0.041229
17	-0.274443	-2.1258	0.018821
18	-0.322382	-2.4972	0.00764
19	-0.36247	-2.8077	0.003361
20	-0.402384	-3.1169	0.001402
21	-0.442075	-3.4243	0.000559
22	-0.46022	-3.5648	0.000361
23	-0.473365	-3.6667	0.000261
24	-0.456423	-3.5354	0.000396
25	-0.446817	-3.461	0.000499
26	-0.42149	-3.2648	0.000906
27	-0.383749	-2.9725	0.002123
28	-0.346633	-2.685	0.004682
29	-0.319368	-2.4738	0.008107
30	-0.284497	-2.2037	0.015697
31	-0.25184	-1.9507	0.027881
32	-0.224837	-1.7416	0.043353
33	-0.181336	-1.4046	0.082644
34	-0.142129	-1.1009	0.137663
35	-0.104045	-0.8059	0.211732
36	-0.085752	-0.6642	0.254543
37	-0.058422	-0.4525	0.326258
38	-0.043492	-0.3369	0.368688
39	-0.034776	-0.2694	0.394284
40	-0.030428	-0.2357	0.407236
41	-0.020152	-0.1561	0.438239
42	-0.000343	-0.0027	0.498946
43	0.019034	0.1474	0.441642
44	0.037994	0.2943	0.384773
45	0.058335	0.4519	0.3265
46	0.073121	0.5664	0.28662
47	0.089885	0.6963	0.24448
48	0.109032	0.8446	0.200856

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.923799	7.1557	0
2	-0.046177	-0.3577	0.360917
3	-0.170373	-1.3197	0.095974
4	-0.114407	-0.8862	0.189526
5	-0.044626	-0.3457	0.365398
6	-0.08452	-0.6547	0.257584
7	0.017093	0.1324	0.447556
8	-0.004607	-0.0357	0.485826
9	-0.052018	-0.4029	0.344215
10	-0.03839	-0.2974	0.383607
11	0.063789	0.4941	0.311518
12	-0.14708	-1.1393	0.129558
13	0.016105	0.1248	0.450569
14	-0.085496	-0.6622	0.255174
15	-0.148302	-1.1487	0.12761
16	0.053121	0.4115	0.341095
17	-0.048011	-0.3719	0.355641
18	-0.123603	-0.9574	0.171097
19	-0.020795	-0.1611	0.436286
20	-0.063074	-0.4886	0.313464
21	-0.11834	-0.9167	0.181496
22	0.069436	0.5378	0.296336
23	-0.00518	-0.0401	0.484064
24	0.077034	0.5967	0.276477
25	-0.118167	-0.9153	0.181845
26	0.051986	0.4027	0.344306
27	-0.009963	-0.0772	0.46937
28	-0.019004	-0.1472	0.441732
29	-0.123049	-0.9531	0.172173
30	0.014893	0.1154	0.454274
31	-0.015733	-0.1219	0.451707
32	-0.036809	-0.2851	0.388265
33	0.091256	0.7069	0.241192
34	0.03038	0.2353	0.407379
35	-0.10733	-0.8314	0.204528
36	-0.150683	-1.1672	0.123877
37	0.068749	0.5325	0.298165
38	-0.125258	-0.9702	0.167909
39	-0.035833	-0.2776	0.391151
40	-0.050326	-0.3898	0.349025
41	0.017225	0.1334	0.447152
42	0.054411	0.4215	0.33746
43	0.029965	0.2321	0.408623
44	-0.111712	-0.8653	0.195156
45	0.054283	0.4205	0.33782
46	-0.103981	-0.8054	0.211874
47	0.02167	0.1679	0.43363
48	0.037045	0.2869	0.387571

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259775690cjzku6r5nm8lg4d/1lc9l1259775627.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259775690cjzku6r5nm8lg4d/1lc9l1259775627.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259775690cjzku6r5nm8lg4d/23e4s1259775627.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259775690cjzku6r5nm8lg4d/23e4s1259775627.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; 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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