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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, 18 Dec 2009 04:02:34 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/18/t1261134337srox6l59m5r6asb.htm/, Retrieved Fri, 18 Dec 2009 12:05:39 +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/2009/Dec/18/t1261134337srox6l59m5r6asb.htm/},
    year = {2009},
}
@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 = {2009},
    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 «

80.2 74.8 77.8 73 72 75.8 72.6 71.9 74.8 72.9 72.9 79.9 74 76 69.6 77.3 75.2 75.8 77.6 76.7 77 77.9 76.7 71.9 73.4 72.5 73.7 69.5 74.7 72.5 72.1 70.7 71.4 69.5 73.5 72.4 74.5 72.2 73 73.3 71.3 73.6 71.3 71.2 81.4 76.1 71.1 75.7 70 68.5 56.7 57.9 58.8 59.3 61.3 62.9 61.4 64.5 63.8 61.6

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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.409873	-3.1483	0.001288
2	0.100754	0.7739	0.221038
3	0.029023	0.2229	0.41218
4	-0.0197	-0.1513	0.440121
5	-0.062612	-0.4809	0.316171
6	-0.042847	-0.3291	0.371618
7	-0.134587	-1.0338	0.152729
8	0.071924	0.5525	0.291361
9	-0.065893	-0.5061	0.307326
10	0.108486	0.8333	0.204019
11	0.08756	0.6726	0.251926
12	-0.307347	-2.3608	0.01078
13	0.337338	2.5911	0.006018
14	-0.230707	-1.7721	0.040771
15	0.032747	0.2515	0.401138
16	-0.041393	-0.3179	0.375824
17	0.042122	0.3235	0.373713
18	-0.086787	-0.6666	0.253805
19	0.150769	1.1581	0.125749
20	-0.076526	-0.5878	0.279452
21	0.061533	0.4726	0.319105
22	-0.187412	-1.4395	0.077642
23	0.232052	1.7824	0.039912
24	-0.071137	-0.5464	0.29342
25	-0.052122	-0.4004	0.345171
26	0.118844	0.9129	0.182517
27	-0.01041	-0.08	0.46827
28	-0.013509	-0.1038	0.458853
29	0.100382	0.771	0.221878
30	-0.107791	-0.828	0.205515
31	-0.031201	-0.2397	0.405714
32	-0.02677	-0.2056	0.418898
33	0.008176	0.0628	0.475069
34	0.076967	0.5912	0.278324
35	-0.277083	-2.1283	0.018749
36	0.287035	2.2048	0.015691

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.409873	-3.1483	0.001288
2	-0.080819	-0.6208	0.268566
3	0.049036	0.3766	0.353893
4	0.023157	0.1779	0.429716
5	-0.080183	-0.6159	0.270167
6	-0.127693	-0.9808	0.165342
7	-0.240945	-1.8507	0.034608
8	-0.083706	-0.643	0.261371
9	-0.059105	-0.454	0.32575
10	0.09239	0.7097	0.240356
11	0.197692	1.5185	0.067115
12	-0.320499	-2.4618	0.008383
13	0.019572	0.1503	0.440506
14	-0.154647	-1.1879	0.119824
15	-0.073847	-0.5672	0.286356
16	-0.046137	-0.3544	0.362156
17	0.046604	0.358	0.360822
18	-0.085873	-0.6596	0.256038
19	0.001481	0.0114	0.495482
20	-0.012229	-0.0939	0.462741
21	-0.090653	-0.6963	0.24448
22	-0.242886	-1.8656	0.033533
23	0.093224	0.7161	0.238388
24	0.010577	0.0812	0.467762
25	0.107347	0.8245	0.206475
26	0.05183	0.3981	0.345993
27	0.040948	0.3145	0.377114
28	-0.097788	-0.7511	0.227781
29	0.087666	0.6734	0.251669
30	-0.085913	-0.6599	0.25594
31	0.016111	0.1237	0.450968
32	-0.069071	-0.5305	0.298863
33	0.062085	0.4769	0.317604
34	0.049838	0.3828	0.351617
35	-0.149611	-1.1492	0.127558
36	-0.020811	-0.1599	0.436771

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/18/t1261134337srox6l59m5r6asb/1jqhe1261134153.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/18/t1261134337srox6l59m5r6asb/1jqhe1261134153.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/18/t1261134337srox6l59m5r6asb/2ai9j1261134153.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/18/t1261134337srox6l59m5r6asb/2ai9j1261134153.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

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