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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: Sun, 20 Dec 2009 11:41:02 -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/20/t1261334512yfuryvlvno6lnuq.htm/, Retrieved Sun, 20 Dec 2009 19:41:54 +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/20/t1261334512yfuryvlvno6lnuq.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 «

1920 2218 3032 2375 2446 2916 2434 2540 2349 2310 2189 2660 2194 2419 2742 2137 2710 2173 2363 2126 1905 2121 1983 1734 2074 2049 2406 2558 2251 2059 2397 1747 1707 2319 1631 1627 1791 2034 1997 2169 2028 2253 2218 1855 2187 1852 1570 1851 1954 1828 2251 2277 2085 2282 2266 1878 2267 2069 1746 2299 2360 2214 2825 2355 2333 3016 2155 2172 2150 2533 2058 2160 2260 2498 2695 2799 2947 2930 2318 2540 2570 2669 2450 2842 3440 2678 2981 2260 2844 2546 2456 2295 2379 2479 2057 2280 2351 2276 2548 2311 2201 2725 2408 2139 1898 2537 2069 2063 2526 2440 2191 2797 2074 2628 2287 2146 2430 2141 1827 2082 1788

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	-0.502888	-5.5089	0
2	-0.02897	-0.3174	0.375764
3	0.24951	2.7333	0.00361
4	-0.156472	-1.7141	0.04455
5	-0.049559	-0.5429	0.294106
6	0.064173	0.703	0.241717
7	-0.133477	-1.4622	0.073155
8	-0.006707	-0.0735	0.470777
9	0.169093	1.8523	0.033218
10	-0.169482	-1.8566	0.032911
11	0.024422	0.2675	0.39476
12	0.221252	2.4237	0.008428
13	-0.17821	-1.9522	0.026622
14	0.038092	0.4173	0.338611
15	0.12795	1.4016	0.081804
16	-0.172329	-1.8878	0.030736
17	0.098988	1.0844	0.14019
18	-0.117575	-1.288	0.100117
19	0.039467	0.4323	0.333136
20	-0.100612	-1.1022	0.136301
21	0.128748	1.4104	0.080509
22	-0.111894	-1.2257	0.111348
23	0.071932	0.788	0.216134
24	0.055135	0.604	0.2735
25	0.030145	0.3302	0.370904
26	-0.016482	-0.1806	0.428512
27	-0.018208	-0.1995	0.42112
28	0.035008	0.3835	0.351018
29	-0.049901	-0.5466	0.292821
30	-0.037766	-0.4137	0.339912
31	-0.07928	-0.8685	0.193437
32	0.113377	1.242	0.108332
33	-0.023564	-0.2581	0.398375
34	-0.034967	-0.383	0.351181
35	-0.010658	-0.1168	0.453627
36	0.138996	1.5226	0.065242

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.502888	-5.5089	0
2	-0.377279	-4.1329	3.3e-05
3	0.061983	0.679	0.249226
4	0.050123	0.5491	0.291991
5	-0.074675	-0.818	0.207482
6	-0.115318	-1.2632	0.104475
7	-0.234196	-2.5655	0.005767
8	-0.249507	-2.7332	0.003611
9	0.048428	0.5305	0.298371
10	0.0158	0.1731	0.431438
11	-0.076185	-0.8346	0.202812
12	0.118387	1.2969	0.098583
13	0.058183	0.6374	0.262553
14	0.01297	0.1421	0.443626
15	0.093749	1.027	0.153249
16	0.010546	0.1155	0.45411
17	0.08412	0.9215	0.179322
18	-0.147952	-1.6207	0.05385
19	-0.012628	-0.1383	0.445104
20	-0.191254	-2.0951	0.019133
21	-0.021101	-0.2312	0.408795
22	-0.052818	-0.5786	0.281973
23	0.014497	0.1588	0.437044
24	-0.032616	-0.3573	0.360753
25	0.151856	1.6635	0.049411
26	0.095069	1.0414	0.149885
27	-0.009411	-0.1031	0.459033
28	0.003012	0.033	0.486865
29	0.009978	0.1093	0.456571
30	-0.006363	-0.0697	0.472272
31	-0.170539	-1.8682	0.032089
32	0.031557	0.3457	0.36509
33	0.093906	1.0287	0.152848
34	0.044271	0.485	0.314294
35	-0.112934	-1.2371	0.109227
36	-0.031023	-0.3398	0.367287

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/20/t1261334512yfuryvlvno6lnuq/1wbvx1261334460.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/20/t1261334512yfuryvlvno6lnuq/1wbvx1261334460.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/20/t1261334512yfuryvlvno6lnuq/26jx71261334461.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/20/t1261334512yfuryvlvno6lnuq/26jx71261334461.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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