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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 08:51:35 -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/t1259769167uypkprwe1wosb7d.htm/, Retrieved Wed, 02 Dec 2009 16:52:50 +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/t1259769167uypkprwe1wosb7d.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	0.87365	6.7673	0
2	0.736194	5.7025	0
3	0.667816	5.1729	1e-06
4	0.632592	4.9	4e-06
5	0.566279	4.3864	2.4e-05
6	0.494899	3.8335	0.000153
7	0.469009	3.6329	0.000291
8	0.420485	3.2571	0.000927
9	0.336488	2.6064	0.005762
10	0.24372	1.8878	0.031942
11	0.163307	1.265	0.105386
12	0.097893	0.7583	0.225627
13	0.040142	0.3109	0.378463
14	0.011393	0.0882	0.464986
15	-0.011111	-0.0861	0.465849
16	-0.058399	-0.4524	0.326321
17	-0.118551	-0.9183	0.181072
18	-0.144609	-1.1201	0.133559
19	-0.148041	-1.1467	0.128024
20	-0.155465	-1.2042	0.116616
21	-0.184761	-1.4312	0.078787
22	-0.216042	-1.6735	0.049722
23	-0.236248	-1.83	0.036112
24	-0.248217	-1.9227	0.029636
25	-0.248164	-1.9223	0.029662
26	-0.245602	-1.9024	0.030959
27	-0.247365	-1.9161	0.030061
28	-0.253384	-1.9627	0.027161
29	-0.270061	-2.0919	0.020344
30	-0.30227	-2.3414	0.011276
31	-0.329725	-2.554	0.006603
32	-0.334595	-2.5918	0.005987
33	-0.331445	-2.5674	0.006379
34	-0.326676	-2.5304	0.007017
35	-0.317829	-2.4619	0.008356
36	-0.311564	-2.4134	0.009438

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.87365	6.7673	0
2	-0.114344	-0.8857	0.189656
3	0.218258	1.6906	0.048049
4	0.070575	0.5467	0.293316
5	-0.104892	-0.8125	0.209862
6	0.012324	0.0955	0.462134
7	0.124517	0.9645	0.169332
8	-0.166034	-1.2861	0.101676
9	-0.088863	-0.6883	0.246948
10	-0.093956	-0.7278	0.234789
11	-0.118687	-0.9193	0.180797
12	-0.027162	-0.2104	0.417035
13	-2e-06	0	0.499995
14	0.060564	0.4691	0.320339
15	-0.003982	-0.0308	0.487747
16	-0.083574	-0.6474	0.259934
17	-0.049773	-0.3855	0.3506
18	0.085572	0.6628	0.254986
19	0.015635	0.1211	0.452005
20	0.027358	0.2119	0.416445
21	-0.092054	-0.713	0.23929
22	-0.101482	-0.7861	0.217459
23	-0.048648	-0.3768	0.353816
24	0.011036	0.0855	0.46608
25	0.043416	0.3363	0.368909
26	-0.005414	-0.0419	0.483345
27	-0.06057	-0.4692	0.320322
28	-0.051928	-0.4022	0.344472
29	-0.086124	-0.6671	0.253629
30	-0.102692	-0.7955	0.214743
31	0.008284	0.0642	0.474524
32	0.011706	0.0907	0.464028
33	-0.06187	-0.4792	0.316753
34	-0.025046	-0.194	0.423412
35	-0.004534	-0.0351	0.486049
36	-0.021491	-0.1665	0.434175

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259769167uypkprwe1wosb7d/16gkz1259769094.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259769167uypkprwe1wosb7d/16gkz1259769094.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259769167uypkprwe1wosb7d/262wm1259769094.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259769167uypkprwe1wosb7d/262wm1259769094.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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