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ACF d=1, D=1

*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, 08 Dec 2010 16:49:09 +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/08/t12918269093809diq2gkuzu3q.htm/, Retrieved Wed, 08 Dec 2010 17:48:31 +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/08/t12918269093809diq2gkuzu3q.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 «

31.514 27.071 29.462 26.105 22.397 23.843 21.705 18.089 20.764 25.316 17.704 15.548 28.029 29.383 36.438 32.034 22.679 24.319 18.004 17.537 20.366 22.782 19.169 13.807 29.743 25.591 29.096 26.482 22.405 27.044 17.970 18.730 19.684 19.785 18.479 10.698 31.956 29.506 34.506 27.165 26.736 23.691 18.157 17.328 18.205 20.995 17.382 9.367 31.124 26.551 30.651 25.859 25.100 25.778 20.418 18.688 20.424 24.776 19.814 12.738 31.566 30.111 30.019 31.934 25.826 26.835 20.205 17.789 20.520 22.518 15.572 11.509 25.447 24.090 27.786 26.195 20.516 22.759 19.028 16.971 20.036 22.485 18.730 14.538 27.561 25.985 34.670 32.066 27.186 29.586 21.359 21.553 19.573 24.256

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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.370752	-3.3368	0.000641
2	0.168272	1.5144	0.066903
3	-0.161982	-1.4578	0.074376
4	-0.110399	-0.9936	0.161691
5	0.025929	0.2334	0.408034
6	-0.008737	-0.0786	0.46876
7	-0.028594	-0.2574	0.39878
8	0.139598	1.2564	0.106294
9	0.078483	0.7063	0.241
10	-0.063258	-0.5693	0.285356
11	-0.065504	-0.5895	0.278571
12	-0.152153	-1.3694	0.087333
13	-0.148289	-1.3346	0.092873
14	0.050399	0.4536	0.325668
15	0.133705	1.2033	0.116174
16	-0.011602	-0.1044	0.458546
17	0.043281	0.3895	0.348952
18	-0.006554	-0.059	0.476556
19	-0.094668	-0.852	0.198359
20	-0.04626	-0.4163	0.339131
21	0.110963	0.9987	0.160466
22	-0.277767	-2.4999	0.007221
23	0.422107	3.799	0.00014
24	-0.190466	-1.7142	0.045159
25	0.181993	1.6379	0.052657
26	0.002896	0.0261	0.489637
27	-0.07523	-0.6771	0.250146
28	-0.048023	-0.4322	0.333371
29	0.059315	0.5338	0.297459
30	-0.042238	-0.3801	0.352419
31	0.021121	0.1901	0.424858
32	0.054224	0.488	0.313427
33	-0.101076	-0.9097	0.182845
34	0.114588	1.0313	0.152737
35	-0.03405	-0.3064	0.380026
36	-0.11262	-1.0136	0.1569
37	0.015598	0.1404	0.444352
38	-0.061452	-0.5531	0.29087
39	0.027433	0.2469	0.402807
40	0.030096	0.2709	0.393592
41	-0.017588	-0.1583	0.437311
42	0.019933	0.1794	0.429039
43	0.003016	0.0271	0.489205
44	0.097375	0.8764	0.191709
45	-0.157563	-1.4181	0.080004
46	0.147112	1.324	0.094613
47	-0.102253	-0.9203	0.180081
48	-0.033412	-0.3007	0.382204

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.370752	-3.3368	0.000641
2	0.035725	0.3215	0.37432
3	-0.102826	-0.9254	0.178746
4	-0.241293	-2.1716	0.016404
5	-0.092028	-0.8282	0.204981
6	-0.023313	-0.2098	0.41717
7	-0.112041	-1.0084	0.158141
8	0.068329	0.615	0.270153
9	0.201403	1.8126	0.036798
10	-0.002032	-0.0183	0.492727
11	-0.117613	-1.0585	0.146483
12	-0.154051	-1.3865	0.084706
13	-0.2995	-2.6955	0.004272
14	-0.227169	-2.0445	0.022075
15	0.064572	0.5812	0.281376
16	-0.046482	-0.4183	0.338405
17	-0.165075	-1.4857	0.070623
18	-0.013857	-0.1247	0.45053
19	-0.073179	-0.6586	0.256006
20	-0.196306	-1.7667	0.040519
21	0.199882	1.7989	0.037876
22	-0.237506	-2.1376	0.017784
23	0.039438	0.3549	0.361778
24	-0.043488	-0.3914	0.348266
25	-0.084161	-0.7574	0.22549
26	0.005421	0.0488	0.480603
27	0.10945	0.985	0.163767
28	-0.043284	-0.3896	0.348945
29	0.006355	0.0572	0.477266
30	0.064423	0.5798	0.281828
31	-0.117595	-1.0584	0.146521
32	-0.084635	-0.7617	0.22422
33	-0.072939	-0.6565	0.256696
34	0.015889	0.143	0.443323
35	0.014581	0.1312	0.447959
36	-0.051901	-0.4671	0.320838
37	0.004551	0.041	0.483714
38	-0.132855	-1.1957	0.117652
39	-0.013711	-0.1234	0.451047
40	0.029923	0.2693	0.394189
41	-0.118234	-1.0641	0.145221
42	0.004058	0.0365	0.485476
43	0.062776	0.565	0.286823
44	-0.046469	-0.4182	0.338445
45	0.028101	0.2529	0.400491
46	0.080018	0.7202	0.236749
47	0.0488	0.4392	0.330842
48	-0.184525	-1.6607	0.050317

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/08/t12918269093809diq2gkuzu3q/1amv51291826947.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t12918269093809diq2gkuzu3q/1amv51291826947.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t12918269093809diq2gkuzu3q/2amv51291826947.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t12918269093809diq2gkuzu3q/2amv51291826947.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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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