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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, 24 Dec 2010 13:07:49 +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/24/t1293195949yupc6zam7v54k0q.htm/, Retrieved Fri, 24 Dec 2010 14:05:49 +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/24/t1293195949yupc6zam7v54k0q.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 «

3494,17 3667,03 3813,06 3917,96 3895,51 3801,06 3570,12 3701,61 3862,27 3970,1 4138,52 4199,75 4290,89 4443,91 4502,64 4356,98 4591,27 4696,96 4621,4 4562,84 4202,52 4296,49 4435,23 4105,18 4116,68 3844,49 3720,98 3674,4 3857,62 3801,06 3504,37 3032,6 3047,03 2962,34 2197,82 2014,45 1862,83 1905,41 1810,99 1670,07 1864,44 2052,02 2029,6 2070,83 2293,41 2443,27 2513,17 2466,92 2502,66 2539,91 2482,6 2626,15 2656,32 2446,66 2467,38 2462,32 2504,58 2579,39 2649,24 2636,87

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

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.975976	7.5599	0
2	0.941156	7.2902	0
3	0.902985	6.9945	0
4	0.854881	6.6219	0
5	0.798178	6.1827	0
6	0.732561	5.6744	0
7	0.668155	5.1755	1e-06
8	0.607097	4.7026	8e-06
9	0.539716	4.1806	4.8e-05
10	0.470178	3.642	0.000283
11	0.406877	3.1517	0.001267
12	0.337748	2.6162	0.005616
13	0.269873	2.0904	0.020412
14	0.205728	1.5936	0.058145
15	0.138518	1.073	0.143793
16	0.072431	0.561	0.288428
17	0.000577	0.0045	0.498225
18	-0.065126	-0.5045	0.307892
19	-0.121881	-0.9441	0.174455
20	-0.184177	-1.4266	0.079435
21	-0.24266	-1.8796	0.032508
22	-0.291542	-2.2583	0.013789
23	-0.332207	-2.5733	0.006282
24	-0.366087	-2.8357	0.003112
25	-0.393567	-3.0486	0.001709
26	-0.414457	-3.2104	0.001065
27	-0.419426	-3.2489	0.00095
28	-0.421707	-3.2665	0.000901
29	-0.427034	-3.3078	0.000796
30	-0.426067	-3.3003	0.000814
31	-0.422338	-3.2714	0.000888
32	-0.412588	-3.1959	0.001112
33	-0.40344	-3.125	0.001369
34	-0.393141	-3.0453	0.001725
35	-0.377029	-2.9205	0.002459
36	-0.357189	-2.7668	0.003758

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.975976	7.5599	0
2	-0.239571	-1.8557	0.034204
3	-0.040262	-0.3119	0.37811
4	-0.221752	-1.7177	0.045506
5	-0.135693	-1.0511	0.148719
6	-0.178918	-1.3859	0.085455
7	0.090295	0.6994	0.243495
8	0.061894	0.4794	0.316688
9	-0.144249	-1.1173	0.13415
10	-0.041222	-0.3193	0.375303
11	0.082146	0.6363	0.263501
12	-0.2566	-1.9876	0.025712
13	0.057041	0.4418	0.330096
14	0.029015	0.2247	0.411469
15	-0.158972	-1.2314	0.11149
16	-0.058074	-0.4498	0.327225
17	-0.172683	-1.3376	0.093038
18	0.137652	1.0662	0.145292
19	0.015154	0.1174	0.453475
20	-0.172392	-1.3353	0.093404
21	0.106057	0.8215	0.207304
22	-0.019079	-0.1478	0.441502
23	0.068335	0.5293	0.299268
24	0.022227	0.1722	0.431943
25	0.062501	0.4841	0.315029
26	-0.002629	-0.0204	0.491911
27	0.115403	0.8939	0.187471
28	-0.061849	-0.4791	0.316811
29	-0.191287	-1.4817	0.071826
30	-0.045421	-0.3518	0.3631
31	0.079305	0.6143	0.270671
32	0.039099	0.3029	0.381523
33	-0.098963	-0.7666	0.223174
34	0.063329	0.4905	0.312768
35	-0.022866	-0.1771	0.430005
36	0.047965	0.3715	0.355775

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293195949yupc6zam7v54k0q/1goe11293196066.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293195949yupc6zam7v54k0q/1goe11293196066.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293195949yupc6zam7v54k0q/2goe11293196066.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293195949yupc6zam7v54k0q/2goe11293196066.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = MA ;

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = MA ;

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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