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ACF

*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: Thu, 03 Dec 2009 12:08:25 -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/03/t12598677023559xqlphci8def.htm/, Retrieved Thu, 03 Dec 2009 20:15:05 +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/03/t12598677023559xqlphci8def.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:

d=1 D=0 lambda =1

Dataseries X:

» Textbox « » Textfile « » CSV «

1954 1828 2251 2277 2085 2282 2266 1878 2267 2069 1746 2299 2360 2214 2825 2355 2333 3016 2155 2172 2150 2533 2058 2160 2260 2498 2695 2799 2947 2930 2318 2540 2570 2669 2450 2842 3440 2678 2981 2260 2844 2546 2456 2295 2379 2479 2057 2280 2351 2276 2548 2311 2201 2725 2408 2139 1898 2537 2069 2063 2524

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	-0.524425	-3.6333	0.00034
2	0.178155	1.2343	0.111552
3	-0.233147	-1.6153	0.056402
4	0.23854	1.6527	0.052464
5	-0.187512	-1.2991	0.100054
6	0.040555	0.281	0.38997
7	-0.03089	-0.214	0.415722
8	0.084877	0.588	0.279628
9	0.089204	0.618	0.269741
10	-0.183819	-1.2735	0.104481
11	0.320628	2.2214	0.015538
12	-0.432367	-2.9955	0.002162
13	0.144866	1.0037	0.160287
14	-0.12782	-0.8856	0.190134
15	0.291288	2.0181	0.024594
16	-0.295212	-2.0453	0.023164
17	0.18003	1.2473	0.109173
18	-0.144745	-1.0028	0.160488
19	0.251965	1.7457	0.043634
20	-0.257572	-1.7845	0.040331
21	0.083571	0.579	0.282648
22	-0.021517	-0.1491	0.441061
23	0.051192	0.3547	0.362195
24	-0.045435	-0.3148	0.377146
25	0.004542	0.0315	0.487513
26	0.111594	0.7731	0.221614
27	-0.138896	-0.9623	0.170361
28	0.072009	0.4989	0.310068
29	-0.042142	-0.292	0.385784
30	0.141257	0.9787	0.166328
31	-0.228237	-1.5813	0.060192
32	0.164588	1.1403	0.12991
33	-0.036751	-0.2546	0.400053
34	0.0326	0.2259	0.411135
35	-0.103359	-0.7161	0.238701
36	0.081352	0.5636	0.287818

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.524425	-3.6333	0.00034
2	-0.133613	-0.9257	0.179617
3	-0.277099	-1.9198	0.030419
4	-0.001312	-0.0091	0.496393
5	-0.087633	-0.6071	0.273311
6	-0.165014	-1.1432	0.129302
7	-0.095328	-0.6605	0.25606
8	-0.027366	-0.1896	0.425212
9	0.20444	1.4164	0.081558
10	-0.039922	-0.2766	0.391643
11	0.356986	2.4733	0.00849
12	-0.178325	-1.2355	0.111334
13	-0.305166	-2.1143	0.019857
14	-0.19975	-1.3839	0.086395
15	0.015315	0.1061	0.457969
16	-0.085629	-0.5933	0.277899
17	-0.097931	-0.6785	0.250362
18	-0.207615	-1.4384	0.078405
19	-0.016954	-0.1175	0.453493
20	-0.09849	-0.6824	0.249145
21	0.126958	0.8796	0.191732
22	0.055088	0.3817	0.352199
23	0.153572	1.064	0.146331
24	-0.028516	-0.1976	0.422111
25	-0.142003	-0.9838	0.165068
26	-0.027577	-0.1911	0.424644
27	0.035377	0.2451	0.403712
28	-0.083773	-0.5804	0.282182
29	-0.024636	-0.1707	0.432596
30	-0.102384	-0.7093	0.240774
31	-0.088922	-0.6161	0.27038
32	-0.064212	-0.4449	0.329205
33	0.188553	1.3063	0.098832
34	-0.006803	-0.0471	0.481301
35	0.047202	0.327	0.372536
36	-0.02273	-0.1575	0.437763

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/03/t12598677023559xqlphci8def/11cxg1259867303.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t12598677023559xqlphci8def/11cxg1259867303.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t12598677023559xqlphci8def/2q5041259867303.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t12598677023559xqlphci8def/2q5041259867303.ps (open in new window)

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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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