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*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: Tue, 21 Dec 2010 15:20:18 +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/21/t1292944755c5k6wxdijim23d0.htm/, Retrieved Tue, 21 Dec 2010 16:19:15 +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/21/t1292944755c5k6wxdijim23d0.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 «

21.3 21.1 20.6 20.5 20.5 20.8 21.1 21.3 21.3 21.1 20.9 19.9 19.8 19.5 19.6 19.6 19.7 20.2 19.7 19.3 18.9 18.4 18 17.8 17.8 17.7 17.5 17.4 17.1 17.1 17.2 17.8 18.6 18.9 18.9 18.7 18.6 19.1 20.3 21.1 21.6 21.5 21.5 21.7 21.9 22.2 22.6 22.5 23.2 23.6 23.8 23.9 23.8 23.5 23.3 23.2 23.5 23.5 23.5 23.3

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	0.551818	4.2386	4e-05
2	0.276604	2.1246	0.018909
3	-0.032604	-0.2504	0.40156
4	-0.12495	-0.9598	0.170546
5	0.0356	0.2735	0.392731
6	0.171141	1.3146	0.096873
7	0.346426	2.661	0.005011
8	0.307748	2.3639	0.010699
9	0.189141	1.4528	0.075786
10	0.137353	1.055	0.147857
11	0.046174	0.3547	0.362051
12	-0.021558	-0.1656	0.434523
13	-0.110674	-0.8501	0.199352
14	-0.097664	-0.7502	0.228067
15	-0.095325	-0.7322	0.233471
16	-0.04011	-0.3081	0.379549
17	0.018002	0.1383	0.445246
18	-0.058004	-0.4455	0.328781
19	-0.149996	-1.1521	0.126955
20	-0.260392	-2.0001	0.025049
21	-0.238378	-1.831	0.036075
22	-0.160174	-1.2303	0.11173
23	-0.060691	-0.4662	0.321404
24	0.003924	0.0301	0.488027
25	-0.018372	-0.1411	0.444129
26	-0.08575	-0.6587	0.256339
27	-0.239997	-1.8435	0.035144
28	-0.242973	-1.8663	0.033485
29	-0.206182	-1.5837	0.059303
30	-0.168599	-1.295	0.100176
31	0.020672	0.1588	0.437191
32	0.101314	0.7782	0.219778
33	0.097088	0.7457	0.229391
34	0.044466	0.3416	0.366951
35	-0.100798	-0.7742	0.220939
36	-0.134557	-1.0336	0.152781
37	-0.192473	-1.4784	0.072308
38	-0.11058	-0.8494	0.199551
39	-2.9e-05	-2e-04	0.499911
40	0.02361	0.1814	0.428356
41	0.042289	0.3248	0.37323
42	0.044982	0.3455	0.365468
43	0.041611	0.3196	0.375194
44	0.018126	0.1392	0.444871
45	-0.031181	-0.2395	0.40577
46	-0.043995	-0.3379	0.368308
47	-0.064249	-0.4935	0.311745
48	-0.012702	-0.0976	0.461305
49	-0.004277	-0.0329	0.486952
50	0.023864	0.1833	0.427593
51	0.038062	0.2924	0.385517
52	0.019059	0.1464	0.442054
53	0.002515	0.0193	0.492326
54	-0.020573	-0.158	0.437488
55	-0.003895	-0.0299	0.488117
56	0.007052	0.0542	0.478493
57	0.016331	0.1254	0.450301
58	0.006727	0.0517	0.479482
59	NA	NA	NA
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.551818	4.2386	4e-05
2	-0.040114	-0.3081	0.379537
3	-0.243709	-1.872	0.033086
4	0.000508	0.0039	0.498449
5	0.270343	2.0765	0.021104
6	0.09217	0.708	0.240875
7	0.167089	1.2834	0.102179
8	0.012206	0.0938	0.462812
9	-0.010648	-0.0818	0.467546
10	0.155316	1.193	0.118822
11	0.00235	0.0181	0.49283
12	-0.164808	-1.2659	0.105259
13	-0.172619	-1.3259	0.09499
14	0.000188	0.0014	0.499426
15	-0.098508	-0.7567	0.226134
16	-0.052979	-0.4069	0.342763
17	-0.031623	-0.2429	0.404461
18	-0.183318	-1.4081	0.082176
19	-0.114518	-0.8796	0.191314
20	-0.047246	-0.3629	0.358988
21	0.019898	0.1528	0.439524
22	0.010266	0.0789	0.468706
23	0.062075	0.4768	0.317632
24	0.032907	0.2528	0.400666
25	0.066402	0.51	0.305961
26	0.061086	0.4692	0.320323
27	-0.160497	-1.2328	0.11127
28	-0.001436	-0.011	0.49562
29	0.031518	0.2421	0.404774
30	-0.13023	-1.0003	0.160622
31	0.134438	1.0326	0.152994
32	0.098384	0.7557	0.226418
33	-0.151134	-1.1609	0.125182
34	0.0397	0.3049	0.380741
35	-0.03382	-0.2598	0.397971
36	-0.075761	-0.5819	0.281416
37	-0.053753	-0.4129	0.340593
38	-0.009648	-0.0741	0.470588
39	-0.097093	-0.7458	0.229378
40	-0.095483	-0.7334	0.233103
41	-0.01213	-0.0932	0.46304
42	0.007124	0.0547	0.478274
43	0.035614	0.2736	0.392689
44	0.07418	0.5698	0.285493
45	-0.067818	-0.5209	0.302187
46	0.020976	0.1611	0.436275
47	0.071645	0.5503	0.29209
48	-0.000783	-0.006	0.497611
49	-0.103681	-0.7964	0.2145
50	-0.005186	-0.0398	0.484179
51	0.054275	0.4169	0.339134
52	0.037441	0.2876	0.387333
53	-0.032802	-0.252	0.400976
54	-0.103048	-0.7915	0.215905
55	-0.021846	-0.1678	0.433657
56	0.014619	0.1123	0.455486
57	-0.080961	-0.6219	0.268211
58	-0.029631	-0.2276	0.410372
59	NA	NA	NA
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292944755c5k6wxdijim23d0/12rmg1292944814.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292944755c5k6wxdijim23d0/12rmg1292944814.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292944755c5k6wxdijim23d0/2ci3j1292944814.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292944755c5k6wxdijim23d0/2ci3j1292944814.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292944755c5k6wxdijim23d0/3nakm1292944814.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292944755c5k6wxdijim23d0/3nakm1292944814.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; 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 (par8 != '') par8 <- as.numeric(par8)

ox <- x

if (par8 == '') {

if (par2 == 0) {

x <- log(x)

} else {

x <- (x ^ par2 - 1) / par2

}

} else {

x <- log(x,base=par8)

}

if (par3 > 0) x <- diff(x,lag=1,difference=par3)

if (par4 > 0) x <- diff(x,lag=par5,difference=par4)

bitmap(file='picts.png')

op <- par(mfrow=c(2,1))

plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')

if (par8=='') {

mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')

mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')

} else {

mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')

mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')

}

plot(x,type='l', main=mytitle,xlab='time',ylab='value')

par(op)

dev.off()

bitmap(file='pic1.png')

racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)

dev.off()

bitmap(file='pic2.png')

rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)

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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