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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: Thu, 26 Nov 2009 12:32:46 -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/26/t1259264144bxtzkn0bigt7k1l.htm/, Retrieved Thu, 26 Nov 2009 20:35:46 +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/26/t1259264144bxtzkn0bigt7k1l.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 «

115.6 111.9 107 107.1 100.6 99.2 108.4 103 99.8 115 90.8 95.9 114.4 108.2 112.6 109.1 105 105 118.5 103.7 112.5 116.6 96.6 101.9 116.5 119.3 115.4 108.5 111.5 108.8 121.8 109.6 112.2 119.6 104.1 105.3 115 124.1 116.8 107.5 115.6 116.2 116.3 119 111.9 118.6 106.9 103.2 118.6 118.7 102.8 100.6 94.9 94.5 102.9 95.3 92.5 102.7 91.5 89.5

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	0.413466	3.2027	0.00109
2	0.191229	1.4813	0.071886
3	0.388727	3.0111	0.001903
4	0.218847	1.6952	0.047613
5	0.270758	2.0973	0.020095
6	0.336471	2.6063	0.005764
7	0.120295	0.9318	0.177587
8	0.025292	0.1959	0.422671
9	-0.003002	-0.0233	0.490763
10	-0.258498	-2.0023	0.024888
11	-0.051313	-0.3975	0.346215
12	0.272721	2.1125	0.019408
13	-0.090726	-0.7028	0.242463
14	-0.275943	-2.1374	0.018323
15	-0.152396	-1.1805	0.121238
16	-0.13265	-1.0275	0.154154
17	-0.083757	-0.6488	0.259479
18	-0.054923	-0.4254	0.336023
19	-0.097242	-0.7532	0.227127
20	-0.172402	-1.3354	0.093392
21	-0.169821	-1.3154	0.096686
22	-0.258641	-2.0034	0.024827
23	-0.130254	-1.0089	0.158527
24	0.099399	0.7699	0.222179
25	-0.097459	-0.7549	0.226627
26	-0.309277	-2.3956	0.009864
27	-0.175666	-1.3607	0.089348
28	-0.114396	-0.8861	0.189548
29	-0.133356	-1.033	0.152882
30	-0.066656	-0.5163	0.303767
31	-0.080742	-0.6254	0.267033
32	-0.181906	-1.409	0.081992
33	-0.139	-1.0767	0.142964
34	-0.134753	-1.0438	0.150385
35	-0.128383	-0.9944	0.162
36	0.079642	0.6169	0.269816

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.413466	3.2027	0.00109
2	0.024456	0.1894	0.425196
3	0.363867	2.8185	0.003263
4	-0.085617	-0.6632	0.254876
5	0.264288	2.0472	0.022514
6	0.041522	0.3216	0.374427
7	-0.070031	-0.5425	0.294756
8	-0.15798	-1.2237	0.112923
9	-0.156796	-1.2145	0.114651
10	-0.413665	-3.2042	0.001085
11	0.193201	1.4965	0.06988
12	0.400319	3.1009	0.001469
13	-0.055703	-0.4315	0.333837
14	-0.250793	-1.9426	0.028379
15	-0.142541	-1.1041	0.136975
16	0.175924	1.3627	0.089035
17	-0.04308	-0.3337	0.369887
18	-0.188061	-1.4567	0.075205
19	-0.008204	-0.0635	0.474771
20	-0.081252	-0.6294	0.265746
21	0.116979	0.9061	0.18425
22	0.041742	0.3233	0.373784
23	-0.038338	-0.297	0.383758
24	-0.143587	-1.1122	0.13524
25	-0.04166	-0.3227	0.374022
26	-0.065181	-0.5049	0.307743
27	0.045039	0.3489	0.364203
28	-0.185621	-1.4378	0.077841
29	-0.069428	-0.5378	0.296356
30	0.020574	0.1594	0.436957
31	0.153954	1.1925	0.118876
32	-0.0859	-0.6654	0.254179
33	-0.058872	-0.456	0.325012
34	0.034315	0.2658	0.39565
35	-0.132675	-1.0277	0.154108
36	-0.074464	-0.5768	0.283117

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259264144bxtzkn0bigt7k1l/1dawu1259263964.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259264144bxtzkn0bigt7k1l/1dawu1259263964.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259264144bxtzkn0bigt7k1l/2fmru1259263964.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259264144bxtzkn0bigt7k1l/2fmru1259263964.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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