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ACF (d=0; D=1)

*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: Wed, 16 Dec 2009 06:50:30 -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/16/t126097147820ad18cryowdl5q.htm/, Retrieved Wed, 16 Dec 2009 14:51:20 +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/16/t126097147820ad18cryowdl5q.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 «

8715.1 8919.9 10085.8 9511.7 8991.3 10311.2 8895.4 7449.8 10084.0 9859.4 9100.1 8920.8 8502.7 8599.6 10394.4 9290.4 8742.2 10217.3 8639.0 8139.6 10779.1 10427.7 10349.1 10036.4 9492.1 10638.8 12054.5 10324.7 11817.3 11008.9 9996.6 9419.5 11958.8 12594.6 11890.6 10871.7 11835.7 11542.2 13093.7 11180.2 12035.7 12112.0 10875.2 9897.3 11672.1 12385.7 11405.6 9830.9 11025.1 10853.8 12252.6 11839.4 11669.1 11601.4 11178.4 9516.4 12102.8 12989.0 11610.2 10205.5 11356.2 11307.1 12648.6 11947.2 11714.1 12192.5 11268.8 9097.4 12639.8 13040.1 11687.3 11191.7 11391.9 11793.1 13933.2 12778.1 11810.3 13698.4 11956.6 10723.8 13938.9 13979.8 13807.4 12973.9 12509.8 12934.1 14908.3 13772.1 13012.6 14049.9 11816.5 11593.2 14466.2 13615.9 14733.9 13880.7 13527.5 13584.0 16170.2 13260.6 14741.9 15486.5 13154.5 12621.2 15031.6 15452.4 15428.0 13105.9 14716.8 14180.0 16202.2 14392.4 15140.6 15960.1 14351.3 13230.2 15 etc...

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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.458543	5.0231	1e-06
2	0.445796	4.8835	2e-06
3	0.537995	5.8934	0
4	0.239414	2.6226	0.004928
5	0.292252	3.2015	0.000875
6	0.257462	2.8204	0.002807
7	-1.5e-05	-2e-04	0.499934
8	0.133674	1.4643	0.07286
9	0.06457	0.7073	0.240368
10	-0.130437	-1.4289	0.07782
11	-0.056225	-0.6159	0.269559
12	-0.108003	-1.1831	0.119551
13	-0.180916	-1.9818	0.024892
14	-0.09229	-1.011	0.157029
15	-0.152078	-1.6659	0.049168
16	-0.271266	-2.9716	0.00179
17	-0.094401	-1.0341	0.151582
18	-0.159813	-1.7507	0.04128
19	-0.243453	-2.6669	0.004356
20	-0.114443	-1.2537	0.106202
21	-0.18075	-1.98	0.024995
22	-0.232226	-2.5439	0.006116
23	-0.008926	-0.0978	0.461135
24	-0.233438	-2.5572	0.005899
25	-0.222302	-2.4352	0.008177
26	-0.098157	-1.0753	0.142209
27	-0.211756	-2.3197	0.011024
28	-0.195482	-2.1414	0.017132
29	-0.120404	-1.319	0.094847
30	-0.20196	-2.2124	0.014417
31	-0.102894	-1.1271	0.130965
32	-0.03448	-0.3777	0.353158
33	-0.178633	-1.9568	0.026345
34	-0.0957	-1.0483	0.148294
35	-0.071724	-0.7857	0.216798
36	-0.135295	-1.4821	0.07047

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.458543	5.0231	1e-06
2	0.298243	3.2671	0.000709
3	0.35829	3.9249	7.3e-05
4	-0.194643	-2.1322	0.017514
5	0.028826	0.3158	0.376363
6	-0.019243	-0.2108	0.416701
7	-0.215527	-2.361	0.009919
8	0.067839	0.7431	0.229425
9	0.015769	0.1727	0.431571
10	-0.139773	-1.5311	0.064184
11	-0.104885	-1.149	0.126429
12	0.017495	0.1916	0.424171
13	0.004323	0.0474	0.481154
14	0.005495	0.0602	0.47605
15	0.013886	0.1521	0.439675
16	-0.191726	-2.1003	0.0189
17	0.075205	0.8238	0.205836
18	0.016372	0.1793	0.428986
19	-0.087003	-0.9531	0.171235
20	-0.032576	-0.3569	0.360915
21	-0.007082	-0.0776	0.469147
22	-0.116677	-1.2781	0.101834
23	0.156071	1.7097	0.044956
24	-0.158805	-1.7396	0.042244
25	-0.116788	-1.2793	0.101622
26	-0.091866	-1.0063	0.158138
27	0.070006	0.7669	0.222329
28	-0.107767	-1.1805	0.120062
29	-0.017608	-0.1929	0.423688
30	0.039455	0.4322	0.333184
31	-0.029031	-0.318	0.375513
32	0.023657	0.2591	0.397983
33	-0.088916	-0.974	0.166002
34	-0.08839	-0.9683	0.167431
35	-0.098211	-1.0758	0.142077
36	-0.014752	-0.1616	0.435944

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/16/t126097147820ad18cryowdl5q/1qz5p1260971428.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t126097147820ad18cryowdl5q/1qz5p1260971428.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t126097147820ad18cryowdl5q/2ud1f1260971428.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t126097147820ad18cryowdl5q/2ud1f1260971428.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 0.0 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 36 ; par2 = 0.0 ; par3 = 0 ; par4 = 1 ; 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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