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WS8:1.1 The Long Run Trend

*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, 27 Nov 2009 10:27:08 -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/Nov/27/t1259343137jzvhrlbftn5l0kv.htm/, Retrieved Fri, 27 Nov 2009 18:32:19 +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/Nov/27/t1259343137jzvhrlbftn5l0kv.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 «

14,3 14,2 15,9 15,3 15,5 15,1 15 12,1 15,8 16,9 15,1 13,7 14,8 14,7 16 15,4 15 15,5 15,1 11,7 16,3 16,7 15 14,9 14,6 15,3 17,9 16,4 15,4 17,9 15,9 13,9 17,8 17,9 17,4 16,7 16 16,6 19,1 17,8 17,2 18,6 16,3 15,1 19,2 17,7 19,1 18 17,5 17,8 21,1 17,2 19,4 19,8 17,6 16,2 19,5 19,9 20 17,3

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	0.514958	3.9888	9.1e-05
2	0.343228	2.6586	0.005022
3	0.474104	3.6724	0.000257
4	0.462995	3.5863	0.000337
5	0.445392	3.45	0.000516
6	0.608965	4.717	7e-06
7	0.37029	2.8683	0.002844
8	0.38359	2.9713	0.002131
9	0.329161	2.5497	0.006678
10	0.134601	1.0426	0.150656
11	0.306419	2.3735	0.01042
12	0.549114	4.2534	3.7e-05
13	0.182431	1.4131	0.081396
14	0.096017	0.7437	0.229968
15	0.123377	0.9557	0.171535
16	0.077896	0.6034	0.274266
17	0.155318	1.2031	0.116835
18	0.212583	1.6467	0.052428
19	0.033714	0.2612	0.397435
20	0.062034	0.4805	0.316306
21	-0.019609	-0.1519	0.439891
22	-0.198304	-1.5361	0.064891
23	-0.009822	-0.0761	0.469804
24	0.122772	0.951	0.172712
25	-0.14404	-1.1157	0.134493
26	-0.187193	-1.45	0.076134
27	-0.202197	-1.5662	0.06128
28	-0.215435	-1.6687	0.050189
29	-0.15702	-1.2163	0.114322
30	-0.126848	-0.9826	0.164884
31	-0.23573	-1.826	0.036417
32	-0.180751	-1.4001	0.083318
33	-0.293758	-2.2754	0.013232
34	-0.356681	-2.7628	0.003798
35	-0.223259	-1.7294	0.044444
36	-0.135702	-1.0511	0.148704

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.514958	3.9888	9.1e-05
2	0.106212	0.8227	0.206964
3	0.35984	2.7873	0.003554
4	0.154938	1.2001	0.117401
5	0.192383	1.4902	0.070706
6	0.397577	3.0796	0.001563
7	-0.190523	-1.4758	0.072615
8	0.207818	1.6098	0.05635
9	-0.323083	-2.5026	0.007535
10	-0.369053	-2.8587	0.002921
11	0.183044	1.4179	0.080703
12	0.202526	1.5688	0.060982
13	-0.188206	-1.4578	0.07505
14	-0.063964	-0.4955	0.311043
15	-0.192635	-1.4921	0.07045
16	0.024967	0.1934	0.423652
17	0.039176	0.3035	0.381297
18	-0.029242	-0.2265	0.41079
19	0.115729	0.8964	0.186802
20	-0.103013	-0.7979	0.214028
21	0.021482	0.1664	0.434201
22	-0.168899	-1.3083	0.097883
23	-0.073664	-0.5706	0.2852
24	0.032824	0.2543	0.400086
25	-0.193557	-1.4993	0.069522
26	0.047701	0.3695	0.356531
27	-0.081465	-0.631	0.265211
28	0.093224	0.7221	0.236516
29	-0.09758	-0.7559	0.226347
30	0.019834	0.1536	0.439206
31	0.064732	0.5014	0.308957
32	-0.035064	-0.2716	0.393429
33	0.028697	0.2223	0.412422
34	0.072705	0.5632	0.287708
35	-0.150251	-1.1638	0.124548
36	0.032761	0.2538	0.400274

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259343137jzvhrlbftn5l0kv/1880z1259342826.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259343137jzvhrlbftn5l0kv/1880z1259342826.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259343137jzvhrlbftn5l0kv/2i69w1259342826.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259343137jzvhrlbftn5l0kv/2i69w1259342826.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 0 ; 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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