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Identifying Integration Processes

*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 01:19:55 -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/t1259310417zshm8a2o005gmsm.htm/, Retrieved Fri, 27 Nov 2009 09:26:59 +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/t1259310417zshm8a2o005gmsm.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:

Integration

Dataseries X:

» Textbox « » Textfile « » CSV «

699.8 871.2 842.6 809.2 847.1 857 839.9 967.4 1037.2 1062.3 899.3 1129.6 845.7 1173.9 1073.8 1024.7 912.9 1055 936.4 920.6 1059.3 1164.1 823.9 1076.6 833.5 996 852.8 758.5 760.4 826.8 941.7 1097.8 802.8 839.7 791 1063.1 1138.4 888.6 931.1 863.2 936.2 701.7 873.8 696.8 658.1 706.7 458.5 685.7 660.1 774.9 787.4 486.9 310.8 619.5 550.2 463.4 630.4 729 485.6 453.7

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	0.620169	4.8038	5e-06
2	0.575029	4.4542	1.9e-05
3	0.526965	4.0819	6.7e-05
4	0.545276	4.2237	4.1e-05
5	0.478838	3.7091	0.000228
6	0.479381	3.7133	0.000225
7	0.405164	3.1384	0.001317
8	0.30329	2.3493	0.01106
9	0.207528	1.6075	0.056597
10	0.243372	1.8852	0.032127
11	0.15226	1.1794	0.121447
12	0.210964	1.6341	0.053735
13	0.111499	0.8637	0.195606
14	0.101327	0.7849	0.217808
15	0.031261	0.2421	0.404746
16	-0.039396	-0.3052	0.38065
17	-0.020912	-0.162	0.435931
18	-0.002485	-0.0193	0.492352
19	-0.04227	-0.3274	0.372245
20	-0.088323	-0.6841	0.248258
21	-0.120519	-0.9335	0.177143
22	-0.030877	-0.2392	0.405895
23	-0.125701	-0.9737	0.167064
24	-0.056006	-0.4338	0.332987
25	-0.052866	-0.4095	0.341815
26	-0.077855	-0.6031	0.274369
27	-0.0727	-0.5631	0.287722
28	-0.134664	-1.0431	0.150543
29	-0.124571	-0.9649	0.169228
30	-0.173333	-1.3426	0.092225
31	-0.220427	-1.7074	0.046457
32	-0.235212	-1.8219	0.036725
33	-0.270197	-2.0929	0.020296
34	-0.265169	-2.054	0.022171
35	-0.31159	-2.4136	0.009434
36	-0.268349	-2.0786	0.020968

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.620169	4.8038	5e-06
2	0.30943	2.3968	0.009835
3	0.159575	1.2361	0.110627
4	0.199182	1.5429	0.064062
5	0.030605	0.2371	0.406707
6	0.083809	0.6492	0.25935
7	-0.046234	-0.3581	0.360751
8	-0.168912	-1.3084	0.097866
9	-0.183127	-1.4185	0.08061
10	0.044591	0.3454	0.3655
11	-0.097475	-0.755	0.22659
12	0.167446	1.297	0.099794
13	-0.039861	-0.3088	0.379285
14	0.02596	0.2011	0.420655
15	-0.02691	-0.2084	0.417793
16	-0.193505	-1.4989	0.069574
17	0.014214	0.1101	0.456348
18	0.030704	0.2378	0.406411
19	-0.014355	-0.1112	0.455918
20	-0.027522	-0.2132	0.415953
21	0.001139	0.0088	0.496495
22	0.181451	1.4055	0.082513
23	-0.078503	-0.6081	0.272713
24	0.03332	0.2581	0.398607
25	0.027279	0.2113	0.416683
26	-0.072726	-0.5633	0.287653
27	0.021866	0.1694	0.433036
28	-0.192376	-1.4901	0.070713
29	-0.071122	-0.5509	0.291872
30	-0.11519	-0.8923	0.18791
31	-0.172321	-1.3348	0.093493
32	-0.092901	-0.7196	0.237279
33	0.005104	0.0395	0.484296
34	0.019846	0.1537	0.43917
35	0.042929	0.3325	0.370326
36	0.094864	0.7348	0.232658

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259310417zshm8a2o005gmsm/1wnog1259309993.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259310417zshm8a2o005gmsm/1wnog1259309993.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259310417zshm8a2o005gmsm/2fs7o1259309993.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259310417zshm8a2o005gmsm/2fs7o1259309993.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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