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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: Fri, 17 Dec 2010 14:09:32 +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/17/t12925948607jcaxbd2xgmznv1.htm/, Retrieved Fri, 17 Dec 2010 15:07:41 +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/17/t12925948607jcaxbd2xgmznv1.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 «

101.76 102.37 102.38 102.86 102.87 102.92 102.95 103.02 104.08 104.16 104.24 104.33 104.73 104.86 105.03 105.62 105.63 105.63 105.94 106.61 107.69 107.78 107.93 108.48 108.14 108.48 108.48 108.89 108.93 109.21 109.47 109.80 111.73 111.85 112.12 112.15 112.17 112.67 112.80 113.44 113.53 114.53 114.51 115.05 116.67 117.07 116.92 117.00 117.02 117.35 117.36 117.82 117.88 118.24 118.50 118.80 119.76 120.09

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.085651	-0.6466	0.260228
2	-0.038335	-0.2894	0.386654
3	-0.06786	-0.5123	0.305199
4	-0.145992	-1.1022	0.137501
5	0.07478	0.5646	0.287288
6	-0.232557	-1.7558	0.04225
7	0.161358	1.2182	0.114078
8	-0.236061	-1.7822	0.04002
9	0.010702	0.0808	0.467944
10	-0.096398	-0.7278	0.234861
11	-9e-04	-0.0068	0.497302
12	0.610873	4.612	1.2e-05
13	-0.016346	-0.1234	0.451108
14	-0.061554	-0.4647	0.321951
15	-0.108155	-0.8166	0.208792
16	-0.209846	-1.5843	0.059329
17	0.083165	0.6279	0.266294
18	-0.104474	-0.7888	0.21676
19	0.089134	0.6729	0.25185
20	-0.117726	-0.8888	0.188921
21	0.012765	0.0964	0.46178
22	0.027257	0.2058	0.418846
23	-0.108413	-0.8185	0.208241
24	0.421616	3.1831	0.00118
25	-0.018754	-0.1416	0.443951
26	-0.001498	-0.0113	0.495508
27	-0.179903	-1.3582	0.08987
28	-0.141332	-1.067	0.145227
29	0.119151	0.8996	0.186067
30	-0.117955	-0.8905	0.188459
31	0.080705	0.6093	0.272369
32	-0.080898	-0.6108	0.27189
33	0.049613	0.3746	0.354684
34	-0.080301	-0.6063	0.273375
35	-0.061521	-0.4645	0.32204
36	0.193096	1.4578	0.075186
37	-0.020726	-0.1565	0.438104
38	-0.0297	-0.2242	0.41169
39	-0.091087	-0.6877	0.247217
40	-0.031871	-0.2406	0.405355
41	0.062442	0.4714	0.319567
42	-0.035809	-0.2704	0.393932
43	0.059135	0.4465	0.328478
44	0.015476	0.1168	0.453697
45	-0.010661	-0.0805	0.468064
46	-0.004777	-0.0361	0.485677
47	-0.029801	-0.225	0.411395
48	0.073206	0.5527	0.291317

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.085651	-0.6466	0.260228
2	-0.046009	-0.3474	0.364801
3	-0.075952	-0.5734	0.284307
4	-0.163313	-1.233	0.111321
5	0.039358	0.2971	0.383716
6	-0.25321	-1.9117	0.030473
7	0.11031	0.8328	0.204211
8	-0.29866	-2.2548	0.014001
9	-0.01619	-0.1222	0.451573
10	-0.26968	-2.036	0.023202
11	0.018427	0.1391	0.444922
12	0.505564	3.8169	0.000168
13	0.163914	1.2375	0.110483
14	-0.161131	-1.2165	0.114402
15	0.018803	0.142	0.443808
16	-0.344694	-2.6024	0.005889
17	0.147734	1.1154	0.134687
18	0.02679	0.2023	0.420217
19	-0.021734	-0.1641	0.435122
20	0.059774	0.4513	0.326749
21	0.057345	0.4329	0.333344
22	0.054404	0.4107	0.341402
23	-0.068656	-0.5183	0.303114
24	-0.160069	-1.2085	0.115923
25	0.010331	0.078	0.469051
26	0.063895	0.4824	0.315686
27	-0.060369	-0.4558	0.325142
28	0.183364	1.3844	0.085821
29	-0.006615	-0.0499	0.480172
30	-0.089796	-0.6779	0.250275
31	-0.066809	-0.5044	0.307962
32	-0.05904	-0.4457	0.328736
33	-0.058932	-0.4449	0.32903
34	-0.108014	-0.8155	0.209095
35	-0.023262	-0.1756	0.430607
36	-0.065183	-0.4921	0.312263
37	-0.068865	-0.5199	0.302567
38	-0.098824	-0.7461	0.229335
39	0.050518	0.3814	0.352161
40	0.045342	0.3423	0.366682
41	-0.043489	-0.3283	0.37193
42	-0.019035	-0.1437	0.443117
43	-0.013831	-0.1044	0.458601
44	-0.007519	-0.0568	0.477466
45	0.038045	0.2872	0.387489
46	0.031992	0.2415	0.405005
47	0.092322	0.697	0.244313
48	0.013359	0.1009	0.460009

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/17/t12925948607jcaxbd2xgmznv1/12v8q1292594968.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t12925948607jcaxbd2xgmznv1/12v8q1292594968.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t12925948607jcaxbd2xgmznv1/22v8q1292594968.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t12925948607jcaxbd2xgmznv1/22v8q1292594968.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 48 ; 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 (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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