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Autocorrelation function

*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, 19 Dec 2008 09:25:44 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/19/t12297041373pyp5gx7x7ssgsk.htm/, Retrieved Fri, 19 Dec 2008 17:28:57 +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/2008/Dec/19/t12297041373pyp5gx7x7ssgsk.htm/},
    year = {2008},
}
@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 = {2008},
    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:

paper: tijdsreeks 2

Dataseries X:

» Textbox « » Textfile « » CSV «

99.4 102.7 109.3 93.9 95.3 101.8 85.6 81.1 109.5 104.0 94.5 79.0 92.8 95.6 101.7 90.8 89.5 91.8 83.8 77.4 112.7 98.8 85.7 72.8 96.9 95.0 94.2 87.3 80.6 87.9 79.6 71.9 94.6 91.4 86.6 68.5 90.1 91.6 95.4 85.4 81.6 88.9 84.1 74.7 97.1 95.3 85.1 67.3 80.6 87.9 89.2 81.3 79.7 83.7 82.1 69.3 91.2 85.7 85.2 70.0 85.8 91.4 97.5 87.1 85.1 94.1 85.8 74.7 99.9 90.7 86.8 74.8 91.8 97.6 100.8 85.4 84.0 90.6 80.5 73.9 93.6

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	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.218154	1.9634	0.026516
2	-0.14527	-1.3074	0.097383
3	-0.03339	-0.3005	0.38228
4	0.354679	3.1921	0.001006
5	0.163229	1.4691	0.072845
6	0.095852	0.8627	0.195434
7	0.161803	1.4562	0.074598
8	0.315723	2.8415	0.002839
9	-0.079249	-0.7132	0.238873
10	-0.192443	-1.732	0.043541
11	0.053685	0.4832	0.315142
12	0.670894	6.038	0
13	0.046483	0.4183	0.338399
14	-0.244703	-2.2023	0.015243
15	-0.1378	-1.2402	0.109241
16	0.215295	1.9377	0.028075
17	0.067166	0.6045	0.273603
18	0.006589	0.0593	0.476428
19	0.05529	0.4976	0.310052
20	0.205618	1.8506	0.033939
21	-0.124351	-1.1192	0.13319
22	-0.214002	-1.926	0.028805
23	-0.042262	-0.3804	0.352337
24	0.471046	4.2394	3e-05
25	0.022568	0.2031	0.419778
26	-0.255336	-2.298	0.01207
27	-0.213913	-1.9252	0.028856
28	0.086982	0.7828	0.218004
29	0.024018	0.2162	0.414704
30	-0.082357	-0.7412	0.230353
31	-0.067094	-0.6038	0.273817
32	0.085919	0.7733	0.220806
33	-0.169998	-1.53	0.064958
34	-0.246834	-2.2215	0.014554
35	-0.118087	-1.0628	0.14552
36	0.3188	2.8692	0.002623
37	-0.019012	-0.1711	0.432282
38	-0.22792	-2.0513	0.021736
39	-0.211118	-1.9001	0.030491
40	0.020381	0.1834	0.427461
41	-0.01242	-0.1118	0.455638
42	-0.095039	-0.8554	0.19744
43	-0.107462	-0.9672	0.168173
44	0.038925	0.3503	0.363502
45	-0.146845	-1.3216	0.095011
46	-0.230024	-2.0702	0.020809
47	-0.140101	-1.2609	0.105481
48	0.197005	1.773	0.039991

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.218154	1.9634	0.026516
2	-0.202498	-1.8225	0.036036
3	0.053533	0.4818	0.315624
4	0.352094	3.1688	0.00108
5	-0.018381	-0.1654	0.434509
6	0.197664	1.779	0.039498
7	0.187148	1.6843	0.047984
8	0.211576	1.9042	0.030218
9	-0.225	-2.025	0.023081
10	-0.166282	-1.4965	0.0692
11	-0.021619	-0.1946	0.423108
12	0.567209	5.1049	1e-06
13	-0.402845	-3.6256	0.000251
14	-0.001328	-0.012	0.495246
15	-0.106831	-0.9615	0.169588
16	-0.065905	-0.5931	0.277368
17	0.111936	1.0074	0.158366
18	-0.023022	-0.2072	0.418186
19	-0.002757	-0.0248	0.490133
20	0.015137	0.1362	0.445987
21	0.023778	0.214	0.415542
22	-0.014567	-0.1311	0.448008
23	-0.03109	-0.2798	0.390167
24	-0.011711	-0.1054	0.45816
25	0.070373	0.6334	0.264142
26	-0.114893	-1.034	0.152097
27	-0.096514	-0.8686	0.19381
28	-0.091528	-0.8237	0.20625
29	0.045345	0.4081	0.342138
30	-0.140401	-1.2636	0.104998
31	-0.003788	-0.0341	0.486445
32	-0.045985	-0.4139	0.340034
33	-0.021755	-0.1958	0.422629
34	0.049899	0.4491	0.327282
35	0.018733	0.1686	0.433266
36	0.025265	0.2274	0.410347
37	-0.063309	-0.5698	0.285201
38	0.150695	1.3563	0.089393
39	-0.034985	-0.3149	0.376839
40	-0.063026	-0.5672	0.286061
41	-0.114294	-1.0286	0.153353
42	0.017677	0.1591	0.436996
43	-0.122882	-1.1059	0.136013
44	-0.011428	-0.1029	0.459166
45	-0.017999	-0.162	0.435857
46	-0.07403	-0.6663	0.253566
47	0.051422	0.4628	0.322375
48	-0.078419	-0.7058	0.241179

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/19/t12297041373pyp5gx7x7ssgsk/1ftwh1229703939.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/19/t12297041373pyp5gx7x7ssgsk/1ftwh1229703939.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/19/t12297041373pyp5gx7x7ssgsk/2b2vn1229703939.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/19/t12297041373pyp5gx7x7ssgsk/2b2vn1229703939.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

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 (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='lags',ylab='ACF')

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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