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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: Wed, 02 Dec 2009 09:06:40 -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/02/t1259770036ucxjeax6n686h7k.htm/, Retrieved Wed, 02 Dec 2009 17:07:18 +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/02/t1259770036ucxjeax6n686h7k.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 «

1111.92 1131.13 1144.94 1113.89 1107.30 1120.68 1140.84 1101.72 1104.24 1114.58 1130.20 1173.78 1211.92 1181.27 1203.60 1180.59 1156.85 1191.50 1191.33 1234.18 1220.33 1228.81 1207.01 1249.48 1248.29 1280.08 1280.66 1302.88 1310.61 1270.05 1270.06 1278.53 1303.80 1335.83 1377.76 1400.63 1418.03 1437.90 1406.80 1420.83 1482.37 1530.63 1504.66 1455.18 1473.96 1527.29 1545.79 1479.63 1467.97 1378.60 1330.45 1326.41 1385.97 1399.62 1276.69 1269.42 1287.83 1164.17 968.67 888.61

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	-0.248033	-1.889	0.03195
2	-0.345733	-2.633	0.005415
3	-0.046834	-0.3567	0.361314
4	0.266849	2.0323	0.023358
5	-0.077447	-0.5898	0.278802
6	-0.147386	-1.1225	0.133146
7	0.11578	0.8818	0.190776
8	0.036584	0.2786	0.390764
9	-0.016145	-0.123	0.451283
10	-0.180473	-1.3744	0.087296
11	0.281851	2.1465	0.018013
12	-0.056433	-0.4298	0.334475
13	-0.085816	-0.6536	0.25799
14	-0.059273	-0.4514	0.326688
15	0.095315	0.7259	0.235411
16	0.081373	0.6197	0.268935
17	-0.110905	-0.8446	0.200894
18	-0.039457	-0.3005	0.382438
19	0.034047	0.2593	0.398164
20	0.032586	0.2482	0.40244
21	-0.012068	-0.0919	0.463543
22	0.032292	0.2459	0.403304
23	0.03433	0.2614	0.397336
24	-0.160004	-1.2186	0.113974
25	0.130533	0.9941	0.162149
26	-0.078477	-0.5977	0.276197
27	-0.006744	-0.0514	0.479608
28	0.018911	0.144	0.442992
29	0.110298	0.84	0.202178
30	-0.085283	-0.6495	0.259291
31	-0.018225	-0.1388	0.445047
32	-0.00365	-0.0278	0.488959
33	-0.035965	-0.2739	0.392566
34	0.104333	0.7946	0.21505
35	-0.086643	-0.6599	0.25598
36	0.1102	0.8393	0.202385

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.248033	-1.889	0.03195
2	-0.43395	-3.3049	0.000816
3	-0.364204	-2.7737	0.003721
4	-0.064113	-0.4883	0.313599
5	-0.175413	-1.3359	0.093399
6	-0.208587	-1.5886	0.058799
7	-0.047034	-0.3582	0.360746
8	-0.114142	-0.8693	0.194139
9	-0.018628	-0.1419	0.443837
10	-0.229275	-1.7461	0.043043
11	0.144742	1.1023	0.137438
12	-0.011328	-0.0863	0.465774
13	0.053659	0.4087	0.342148
14	0.029542	0.225	0.41139
15	-0.021532	-0.164	0.435157
16	0.131111	0.9985	0.161089
17	0.055245	0.4207	0.337753
18	0.001686	0.0128	0.494898
19	0.021337	0.1625	0.43574
20	-0.100146	-0.7627	0.224369
21	0.062171	0.4735	0.318824
22	-0.011131	-0.0848	0.466368
23	0.116925	0.8905	0.188444
24	-0.137516	-1.0473	0.149655
25	0.13269	1.0105	0.158218
26	-0.140844	-1.0726	0.143939
27	-0.144795	-1.1027	0.137351
28	-0.070108	-0.5339	0.297717
29	0.011541	0.0879	0.465132
30	-0.055508	-0.4227	0.337027
31	0.08515	0.6485	0.259615
32	-0.12322	-0.9384	0.17596
33	-0.087287	-0.6648	0.254419
34	-0.041232	-0.314	0.377318
35	0.000481	0.0037	0.498546
36	0.057473	0.4377	0.331616

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259770036ucxjeax6n686h7k/1rh1t1259769999.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259770036ucxjeax6n686h7k/1rh1t1259769999.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259770036ucxjeax6n686h7k/223nr1259769999.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259770036ucxjeax6n686h7k/223nr1259769999.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 2 ; 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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