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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: Sun, 19 Dec 2010 07:00:10 +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/19/t1292742100yzesnw4uuhzyv3a.htm/, Retrieved Sun, 19 Dec 2010 08:01:41 +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/19/t1292742100yzesnw4uuhzyv3a.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 «

5 4 5 6 6 6 7 8 7 8 7 8 8 9 9 8 9 9 10 11 12 13 13 13 14 14 15 15 16 16 17 18 19 20 22 20 22 25 24 25 28 26 27 26 25 27 28 30 31 32 34 34 33 32 34 36 37 40 38 38 36 40 40 42 44 45 47 49 47 49 52 50 50 57 58 58 58 61 61 64 68 40 34 46 36 34 45 55 50 56 72 76 78 77 90 88 97 93 84 67 72 75 71 75 90 78 73 62 65 61 58 33 39 56 79 82 79 73 87 85 83 82 83 92 95 97 87 84 84 89 103 106 109 106 105 115 120 124 121 131 139 133 119 123 120 128 134 126 115 106 99 100 99 99 100 100 108 109 115 114 108 113 118 122 118 121 118 121 121 112 119 116 110 111 106 108

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	22 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.977846	12.9726	0
2	0.953	12.643	0
3	0.930981	12.3509	0
4	0.911983	12.0988	0
5	0.890114	11.8087	0
6	0.868584	11.5231	0
7	0.847036	11.2372	0
8	0.825742	10.9547	0
9	0.806707	10.7022	0
10	0.789928	10.4796	0
11	0.768803	10.1993	0
12	0.749302	9.9406	0
13	0.730982	9.6976	0
14	0.716867	9.5103	0
15	0.702932	9.3254	0
16	0.692844	9.1916	0
17	0.681445	9.0404	0
18	0.666756	8.8455	0
19	0.651133	8.6383	0
20	0.639606	8.4853	0
21	0.632263	8.3879	0
22	0.622938	8.2642	0
23	0.610927	8.1049	0
24	0.598112	7.9349	0
25	0.58492	7.7598	0
26	0.572209	7.5912	0
27	0.556545	7.3834	0
28	0.535003	7.0976	0
29	0.512336	6.7969	0
30	0.489824	6.4983	0
31	0.468136	6.2105	0
32	0.445779	5.9139	0
33	0.425614	5.6464	0
34	0.407564	5.4069	0
35	0.390947	5.1865	0
36	0.372403	4.9405	1e-06
37	0.35574	4.7194	2e-06
38	0.342853	4.5485	5e-06
39	0.329245	4.3679	1.1e-05
40	0.315067	4.1798	2.3e-05
41	0.300189	3.9825	5e-05
42	0.286075	3.7952	0.000101
43	0.271847	3.6065	0.000202
44	0.25331	3.3605	0.000477
45	0.234385	3.1095	0.001093
46	0.214311	2.8432	0.002498
47	0.197766	2.6237	0.004731
48	0.182911	2.4266	0.008125
49	0.169176	2.2444	0.013027
50	0.15283	2.0275	0.022059
51	0.134091	1.7789	0.038489
52	0.117063	1.553	0.061107
53	0.099917	1.3256	0.093353
54	0.082975	1.1008	0.136247
55	0.068028	0.9025	0.184014
56	0.055061	0.7305	0.233038
57	0.043548	0.5777	0.282094
58	0.031336	0.4157	0.339063
59	0.022063	0.2927	0.385048
60	0.013923	0.1847	0.426836

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.977846	12.9726	0
2	-0.072642	-0.9637	0.168258
3	0.055807	0.7404	0.230032
4	0.049795	0.6606	0.254866
5	-0.080197	-1.0639	0.144407
6	0.013196	0.1751	0.430614
7	-0.017913	-0.2376	0.406217
8	-0.012553	-0.1665	0.433964
9	0.047001	0.6235	0.266871
10	0.032048	0.4252	0.33562
11	-0.10982	-1.4569	0.07346
12	0.052984	0.7029	0.24152
13	-0.002881	-0.0382	0.484777
14	0.072204	0.9579	0.169714
15	0.007754	0.1029	0.459092
16	0.08368	1.1101	0.134228
17	-0.037374	-0.4958	0.310317
18	-0.074507	-0.9884	0.162146
19	-0.018838	-0.2499	0.401474
20	0.062118	0.8241	0.205504
21	0.092826	1.2315	0.109895
22	-0.048771	-0.647	0.259229
23	-0.035887	-0.4761	0.317298
24	-0.034251	-0.4544	0.325052
25	-0.021631	-0.287	0.387237
26	-0.016521	-0.2192	0.413383
27	-0.060829	-0.807	0.21038
28	-0.123862	-1.6432	0.051062
29	-0.001669	-0.0221	0.491181
30	-0.05208	-0.6909	0.245261
31	-0.026011	-0.3451	0.365223
32	-0.012537	-0.1663	0.434047
33	0.042785	0.5676	0.285512
34	0.047108	0.625	0.266405
35	0.026234	0.348	0.364117
36	-0.064487	-0.8555	0.196714
37	0.015429	0.2047	0.419024
38	0.066812	0.8864	0.188317
39	-0.049845	-0.6613	0.254651
40	0.008826	0.1171	0.453461
41	-0.042742	-0.567	0.285707
42	-0.016962	-0.225	0.411111
43	-0.04626	-0.6137	0.2701
44	-0.117759	-1.5622	0.060013
45	-0.000993	-0.0132	0.49475
46	-0.019381	-0.2571	0.398695
47	0.039767	0.5276	0.29923
48	0.007283	0.0966	0.461569
49	0.034089	0.4522	0.325827
50	-0.058869	-0.781	0.217931
51	-0.058086	-0.7706	0.220988
52	0.027443	0.3641	0.358122
53	-0.002038	-0.027	0.48923
54	0.030316	0.4022	0.344019
55	0.038328	0.5085	0.305877
56	0.015067	0.1999	0.420903
57	0.022666	0.3007	0.381998
58	-0.015854	-0.2103	0.41683
59	0.018661	0.2476	0.40238
60	0.023218	0.308	0.379213

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292742100yzesnw4uuhzyv3a/1ldib1292741985.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292742100yzesnw4uuhzyv3a/1ldib1292741985.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292742100yzesnw4uuhzyv3a/2emze1292741985.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292742100yzesnw4uuhzyv3a/2emze1292741985.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292742100yzesnw4uuhzyv3a/3ovyh1292741985.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292742100yzesnw4uuhzyv3a/3ovyh1292741985.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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