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Autocorrelation

*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, 29 Dec 2010 19:44:32 +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/29/t1293651744pg4q77yc5yelgsm.htm/, Retrieved Wed, 29 Dec 2010 20:42:27 +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/29/t1293651744pg4q77yc5yelgsm.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 «

16198.90 16554.20 19554.20 15903.80 18003.80 18329.60 16260.70 14851.90 18174.10 18406.60 18466.50 16016.50 17428.50 17167.20 19630.00 17183.60 18344.70 19301.40 18147.50 16192.90 18374.40 20515.20 18957.20 16471.50 18746.80 19009.50 19211.20 20547.70 19325.80 20605.50 20056.90 16141.40 20359.80 19711.60 15638.60 14384.50 13721.40 14134.30 15021.70 14212.60 13635.00 15446.90 14762.10 12521.00 16236.80 16065.00 16032.10 15794.30 15160.00 15692.10 18908.90 17424.50 17014.20 19790.40 17681.20 16006.90 19601.70

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	6 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.516585	3.9001	0.000128
2	0.363097	2.7413	0.00408
3	0.509559	3.8471	0.000152
4	0.416402	3.1438	0.001324
5	0.281023	2.1217	0.019112
6	0.268144	2.0244	0.02381
7	0.08489	0.6409	0.262076
8	0.10237	0.7729	0.221395
9	-0.048526	-0.3664	0.357724
10	-0.243074	-1.8352	0.03585
11	-0.144031	-1.0874	0.140716
12	0.054738	0.4133	0.340482
13	-0.249805	-1.886	0.032198
14	-0.357951	-2.7025	0.004526
15	-0.260844	-1.9693	0.026892
16	-0.234957	-1.7739	0.040712
17	-0.249183	-1.8813	0.032521
18	-0.231057	-1.7444	0.043236
19	-0.237024	-1.7895	0.039424
20	-0.143095	-1.0803	0.142269
21	-0.209147	-1.579	0.059932
22	-0.253406	-1.9132	0.030377
23	-0.080409	-0.6071	0.273105
24	0.039935	0.3015	0.382064
25	-0.089737	-0.6775	0.250415
26	-0.139705	-1.0547	0.147996
27	-0.073034	-0.5514	0.29176
28	0.012447	0.094	0.462731
29	-0.024408	-0.1843	0.427226
30	-0.014008	-0.1058	0.458072
31	-0.015864	-0.1198	0.452544
32	0.009217	0.0696	0.472384
33	-0.028092	-0.2121	0.416396
34	-0.043715	-0.33	0.37129
35	0.005134	0.0388	0.484608
36	0.106913	0.8072	0.211461
37	0.017486	0.132	0.447719
38	-0.036451	-0.2752	0.392078
39	0.026277	0.1984	0.421723
40	0.04209	0.3178	0.375909
41	-0.014666	-0.1107	0.456112
42	0.053893	0.4069	0.342808
43	0.003419	0.0258	0.489748
44	0.003924	0.0296	0.488236
45	0.004242	0.032	0.48728
46	-0.012988	-0.0981	0.461115
47	-0.021211	-0.1601	0.436668
48	0.060858	0.4595	0.323822
49	-0.003523	-0.0266	0.489437
50	-0.039318	-0.2968	0.383831
51	0.02954	0.223	0.412159
52	0.012608	0.0952	0.462249
53	-0.038621	-0.2916	0.385832
54	0.025087	0.1894	0.425225
55	-0.001427	-0.0108	0.495722
56	-0.010601	-0.08	0.468246
57	NA	NA	NA
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.516585	3.9001	0.000128
2	0.131267	0.991	0.162927
3	0.38695	2.9214	0.002493
4	0.047508	0.3587	0.360581
5	-0.023963	-0.1809	0.428539
6	-0.034266	-0.2587	0.398397
7	-0.284141	-2.1452	0.018105
8	0.054256	0.4096	0.341809
9	-0.31051	-2.3443	0.011286
10	-0.218568	-1.6502	0.052206
11	0.056389	0.4257	0.335956
12	0.420688	3.1761	0.001205
13	-0.134714	-1.0171	0.15671
14	-0.210695	-1.5907	0.058603
15	-0.202957	-1.5323	0.065491
16	-0.018353	-0.1386	0.445142
17	0.085872	0.6483	0.25969
18	-0.001556	-0.0117	0.495334
19	0.064673	0.4883	0.313617
20	-0.024889	-0.1879	0.42581
21	0.005172	0.039	0.484494
22	-0.030763	-0.2323	0.408586
23	-0.012964	-0.0979	0.461186
24	-0.125742	-0.9493	0.173231
25	-0.061294	-0.4628	0.322648
26	-0.054358	-0.4104	0.341529
27	-0.008594	-0.0649	0.474246
28	0.079533	0.6005	0.27529
29	-0.081343	-0.6141	0.270788
30	0.073857	0.5576	0.289647
31	-0.138933	-1.0489	0.149321
32	-0.020423	-0.1542	0.439003
33	0.006827	0.0515	0.479537
34	0.058251	0.4398	0.330876
35	-0.096461	-0.7283	0.234715
36	0.002533	0.0191	0.492404
37	0.023762	0.1794	0.42913
38	0.050422	0.3807	0.352429
39	0.059812	0.4516	0.326646
40	-0.221161	-1.6697	0.050228
41	-0.131925	-0.996	0.161728
42	0.00574	0.0433	0.482793
43	0.066416	0.5014	0.308999
44	0.082108	0.6199	0.268898
45	-0.041942	-0.3167	0.37633
46	0.013213	0.0998	0.460445
47	-0.087589	-0.6613	0.255548
48	0.015164	0.1145	0.454628
49	-0.048103	-0.3632	0.358911
50	-0.068054	-0.5138	0.304691
51	0.026417	0.1994	0.421312
52	0.0356	0.2688	0.394537
53	0.041829	0.3158	0.376652
54	-0.076856	-0.5803	0.282015
55	0.026998	0.2038	0.419607
56	-0.089037	-0.6722	0.252082
57	NA	NA	NA
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293651744pg4q77yc5yelgsm/1dl7b1293651865.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293651744pg4q77yc5yelgsm/1dl7b1293651865.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293651744pg4q77yc5yelgsm/2od6w1293651865.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293651744pg4q77yc5yelgsm/2od6w1293651865.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293651744pg4q77yc5yelgsm/3hm5h1293651865.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293651744pg4q77yc5yelgsm/3hm5h1293651865.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 (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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