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WS 9.5

*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, 04 Dec 2009 05:24:35 -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/04/t1259929549xm68gdtswgwnb57.htm/, Retrieved Fri, 04 Dec 2009 13:25:54 +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/04/t1259929549xm68gdtswgwnb57.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 «

95.1 97.0 112.7 102.9 97.4 111.4 87.4 96.8 114.1 110.3 103.9 101.6 94.6 95.9 104.7 102.8 98.1 113.9 80.9 95.7 113.2 105.9 108.8 102.3 99.0 100.7 115.5 100.7 109.9 114.6 85.4 100.5 114.8 116.5 112.9 102.0 106.0 105.3 118.8 106.1 109.3 117.2 92.5 104.2 112.5 122.4 113.3 100.0 110.7 112.8 109.8 117.3 109.1 115.9 96.0 99.8 116.8 115.7 99.4 94.3

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	-0.629054	-4.3126	4.1e-05
2	0.07025	0.4816	0.31616
3	0.209657	1.4373	0.078624
4	-0.212046	-1.4537	0.076336
5	0.073488	0.5038	0.308376
6	0.08921	0.6116	0.271877
7	-0.15083	-1.034	0.153205
8	0.060691	0.4161	0.339623
9	0.085319	0.5849	0.280701
10	-0.157947	-1.0828	0.142205
11	0.126273	0.8657	0.19553
12	-0.052317	-0.3587	0.360726
13	0.009599	0.0658	0.473905
14	-0.034079	-0.2336	0.408141
15	0.099782	0.6841	0.248645
16	-0.137553	-0.943	0.175248
17	0.070706	0.4847	0.315058
18	0.068198	0.4675	0.321136
19	-0.140071	-0.9603	0.170914
20	0.078911	0.541	0.295536
21	0.086008	0.5896	0.279127
22	-0.290406	-1.9909	0.02616
23	0.387587	2.6572	0.005366
24	-0.263946	-1.8095	0.038384
25	0.004234	0.029	0.488483
26	0.151979	1.0419	0.151391
27	-0.117538	-0.8058	0.212208
28	0.017926	0.1229	0.451358
29	0.045632	0.3128	0.377893
30	-0.040397	-0.2769	0.391517
31	-0.027592	-0.1892	0.42539
32	0.092683	0.6354	0.264124
33	-0.123369	-0.8458	0.200982
34	0.088703	0.6081	0.273018
35	-0.075613	-0.5184	0.303314
36	0.043562	0.2986	0.383263

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.629054	-4.3126	4.1e-05
2	-0.538581	-3.6923	0.000289
3	-0.142536	-0.9772	0.166742
4	-0.083683	-0.5737	0.284453
5	-0.079852	-0.5474	0.293335
6	0.072462	0.4968	0.310832
7	0.025915	0.1777	0.429875
8	-0.073858	-0.5063	0.307491
9	0.044075	0.3022	0.38193
10	-0.019031	-0.1305	0.448375
11	0.016357	0.1121	0.455595
12	-0.03227	-0.2212	0.412935
13	0.050021	0.3429	0.36659
14	-0.074077	-0.5078	0.306969
15	0.062414	0.4279	0.335344
16	-0.028927	-0.1983	0.421826
17	-0.075997	-0.521	0.302404
18	0.054119	0.371	0.356145
19	0.029712	0.2037	0.419736
20	-0.045243	-0.3102	0.378902
21	0.140732	0.9648	0.169789
22	-0.223321	-1.531	0.066235
23	0.111774	0.7663	0.223669
24	-0.011142	-0.0764	0.469717
25	-0.022243	-0.1525	0.439727
26	-0.083762	-0.5742	0.284271
27	0.032958	0.2259	0.411112
28	0.0447	0.3064	0.38031
29	-0.004529	-0.0311	0.48768
30	0.026683	0.1829	0.42782
31	-0.004545	-0.0312	0.487638
32	-0.04606	-0.3158	0.376787
33	-0.045462	-0.3117	0.378335
34	-0.057185	-0.392	0.348401
35	-0.131638	-0.9025	0.185705
36	-0.177329	-1.2157	0.115084

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259929549xm68gdtswgwnb57/1jhos1259929474.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259929549xm68gdtswgwnb57/1jhos1259929474.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259929549xm68gdtswgwnb57/237401259929474.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259929549xm68gdtswgwnb57/237401259929474.ps (open in new window)

Parameters (Session):

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

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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