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*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: Tue, 24 Nov 2009 09:20:41 -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/24/t1259079756oojz2t3gbsbgf0c.htm/, Retrieved Tue, 24 Nov 2009 17:22:38 +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/24/t1259079756oojz2t3gbsbgf0c.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:

ws8ma1.3

Dataseries X:

» Textbox « » Textfile « » CSV «

2756.76 2849.27 2921.44 2981.85 3080.58 3106.22 3119.31 3061.26 3097.31 3161.69 3257.16 3277.01 3295.32 3363.99 3494.17 3667.03 3813.06 3917.96 3895.51 3801.06 3570.12 3701.61 3862.27 3970.1 4138.52 4199.75 4290.89 4443.91 4502.64 4356.98 4591.27 4696.96 4621.4 4562.84 4202.52 4296.49 4435.23 4105.18 4116.68 3844.49 3720.98 3674.4 3857.62 3801.06 3504.37 3032.6 3047.03 2962.34 2197.82 2014.45 1862.83 1905.41 1810.99 1670.07 1864.44 2052.02 2029.6 2070.83 2293.41 2443.27

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	0.967005	6.6996	0
2	0.923853	6.4006	0
3	0.875881	6.0683	0
4	0.817314	5.6625	0
5	0.755884	5.2369	2e-06
6	0.675855	4.6825	1.2e-05
7	0.589124	4.0816	8.4e-05
8	0.51221	3.5487	0.000439
9	0.43367	3.0046	0.002109
10	0.354174	2.4538	0.008908
11	0.274296	1.9004	0.031699
12	0.185847	1.2876	0.102031
13	0.113496	0.7863	0.217772
14	0.047186	0.3269	0.372576
15	-0.025105	-0.1739	0.431326
16	-0.093862	-0.6503	0.2593
17	-0.159399	-1.1044	0.137473
18	-0.210307	-1.4571	0.075807
19	-0.252554	-1.7497	0.043277
20	-0.299672	-2.0762	0.021627
21	-0.342845	-2.3753	0.010788
22	-0.376828	-2.6107	0.006009
23	-0.395469	-2.7399	0.004302
24	-0.404723	-2.804	0.003632
25	-0.409286	-2.8356	0.003338
26	-0.409319	-2.8358	0.003336
27	-0.404514	-2.8026	0.003646
28	-0.395053	-2.737	0.004334
29	-0.386266	-2.6761	0.005079
30	-0.378469	-2.6221	0.005837
31	-0.369964	-2.5632	0.006781
32	-0.355133	-2.4604	0.008763
33	-0.336813	-2.3335	0.011929
34	-0.312276	-2.1635	0.017755
35	-0.294705	-2.0418	0.023345
36	-0.275815	-1.9109	0.031

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.967005	6.6996	0
2	-0.173263	-1.2004	0.117938
3	-0.075165	-0.5208	0.302465
4	-0.176376	-1.222	0.113843
5	-0.033223	-0.2302	0.409466
6	-0.322369	-2.2334	0.015108
7	-0.073153	-0.5068	0.307302
8	0.141899	0.9831	0.165243
9	-0.042242	-0.2927	0.385521
10	-0.06576	-0.4556	0.325367
11	-0.032323	-0.2239	0.411877
12	-0.186176	-1.2899	0.101639
13	0.154283	1.0689	0.14523
14	-0.035745	-0.2476	0.402732
15	-0.14101	-0.9769	0.166748
16	-0.058049	-0.4022	0.344669
17	0.038958	0.2699	0.394193
18	0.094971	0.658	0.256848
19	-0.085285	-0.5909	0.278689
20	-0.09715	-0.6731	0.252064
21	-0.012604	-0.0873	0.465388
22	0.008894	0.0616	0.47556
23	0.153521	1.0636	0.14641
24	-0.06896	-0.4778	0.317493
25	0.090252	0.6253	0.267373
26	0.020686	0.1433	0.44332
27	-0.127542	-0.8836	0.190648
28	-0.113666	-0.7875	0.217431
29	-0.14157	-0.9808	0.165798
30	0.039508	0.2737	0.392736
31	0.018927	0.1311	0.448112
32	0.031014	0.2149	0.41539
33	0.008343	0.0578	0.477074
34	0.104969	0.7272	0.235304
35	-0.108376	-0.7509	0.228203
36	-0.048404	-0.3354	0.36941

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259079756oojz2t3gbsbgf0c/1degb1259079639.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259079756oojz2t3gbsbgf0c/1degb1259079639.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259079756oojz2t3gbsbgf0c/26mz71259079639.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t1259079756oojz2t3gbsbgf0c/26mz71259079639.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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