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arma

*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, 24 Dec 2009 10:52:50 -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/24/t1261677254q0awlawiu0jab1u.htm/, Retrieved Thu, 24 Dec 2009 18:54:17 +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/24/t1261677254q0awlawiu0jab1u.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 «

2058.00 2160.00 2260.00 2498.00 2695.00 2799.00 2947.00 2930.00 2318.00 2540.00 2570.00 2669.00 2450.00 2842.00 3440.00 2678.00 2981.00 2260.00 2844.00 2546.00 2456.00 2295.00 2379.00 2479.00 2057.00 2280.00 2351.00 2276.00 2548.00 2311.00 2201.00 2725.00 2408.00 2139.00 1898.00 2537.00 2069.00 2063.00 2526.00 2440.00 2191.00 2797.00 2074.00 2628.00 2287.00 2146.00 2430.00 2141.00 1827.00 2082.00 1788.00 1743.00 2245.00 1963.00 1828.00 2527.00 2114.00 2424.00

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	0.409317	3.1173	0.00142
2	0.434154	3.3064	0.000813
3	0.510198	3.8856	0.000132
4	0.229088	1.7447	0.043168
5	0.175179	1.3341	0.093689
6	0.209513	1.5956	0.058006
7	0.033888	0.2581	0.398628
8	0.159756	1.2167	0.11433
9	0.131168	0.9989	0.160986
10	0.02459	0.1873	0.426049
11	0.061758	0.4703	0.31994
12	0.111462	0.8489	0.199723
13	0.015939	0.1214	0.451903
14	0.104737	0.7977	0.214162
15	0.031993	0.2436	0.404181
16	0.029594	0.2254	0.411236
17	0.104792	0.7981	0.214043
18	-0.035898	-0.2734	0.392761
19	-0.097996	-0.7463	0.229245
20	-0.037761	-0.2876	0.387346
21	-0.026393	-0.201	0.4207
22	-0.072055	-0.5488	0.29264
23	-0.071728	-0.5463	0.29349
24	0.048985	0.3731	0.355231
25	0.028006	0.2133	0.415926
26	-0.01123	-0.0855	0.466068
27	0.007756	0.0591	0.476551
28	-0.077658	-0.5914	0.278267
29	-0.060612	-0.4616	0.323046
30	-0.091599	-0.6976	0.244108
31	-0.165025	-1.2568	0.106933
32	-0.116125	-0.8844	0.190071
33	-0.131436	-1.001	0.160495
34	-0.136769	-1.0416	0.15096
35	-0.221999	-1.6907	0.048132
36	-0.17712	-1.3489	0.091305
37	-0.188558	-1.436	0.078185
38	-0.230959	-1.7589	0.041932
39	-0.159134	-1.2119	0.115228
40	-0.208165	-1.5853	0.059164
41	-0.179742	-1.3689	0.088159
42	-0.150839	-1.1488	0.127686
43	-0.188894	-1.4386	0.077823
44	-0.199506	-1.5194	0.067049
45	-0.16457	-1.2533	0.107558
46	-0.127376	-0.9701	0.168021
47	-0.123408	-0.9398	0.175597
48	-0.037694	-0.2871	0.387541
49	-0.02485	-0.1892	0.425279
50	0.019352	0.1474	0.441671
51	0.035009	0.2666	0.395354
52	0.023432	0.1785	0.429494
53	0.039938	0.3042	0.381047
54	0.034711	0.2644	0.396223
55	-0.003489	-0.0266	0.489448
56	0.009228	0.0703	0.472107
57	-0.004956	-0.0377	0.485012
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.409317	3.1173	0.00142
2	0.320273	2.4391	0.008902
3	0.345768	2.6333	0.005411
4	-0.144692	-1.1019	0.13752
5	-0.166039	-1.2645	0.105552
6	0.011791	0.0898	0.46438
7	-0.049231	-0.3749	0.35454
8	0.203901	1.5529	0.062948
9	0.067442	0.5136	0.304734
10	-0.085196	-0.6488	0.259503
11	-0.138767	-1.0568	0.147488
12	0.072995	0.5559	0.290203
13	0.066429	0.5059	0.307419
14	0.124513	0.9483	0.173464
15	-0.095004	-0.7235	0.236131
16	-0.080023	-0.6094	0.272308
17	0.044056	0.3355	0.369221
18	-0.077461	-0.5899	0.278766
19	-0.118118	-0.8996	0.186037
20	-0.068152	-0.519	0.302856
21	0.198574	1.5123	0.067945
22	0.077031	0.5866	0.279858
23	-0.107657	-0.8199	0.207818
24	0.05217	0.3973	0.346298
25	0.036762	0.28	0.390247
26	-0.052077	-0.3966	0.346555
27	-0.055679	-0.424	0.336552
28	-0.127183	-0.9686	0.168384
29	-0.032465	-0.2472	0.402794
30	-0.028822	-0.2195	0.413516
31	-0.009767	-0.0744	0.470479
32	0.047636	0.3628	0.359041
33	-0.076901	-0.5857	0.280188
34	-0.020101	-0.1531	0.439432
35	-0.187651	-1.4291	0.079169
36	0.019835	0.1511	0.440226
37	0.019559	0.149	0.441053
38	-0.123548	-0.9409	0.175326
39	0.051223	0.3901	0.348944
40	-0.027561	-0.2099	0.417243
41	-0.064689	-0.4927	0.312059
42	-0.112023	-0.8531	0.198545
43	0.058475	0.4453	0.32887
44	0.051985	0.3959	0.346814
45	-0.031219	-0.2378	0.406453
46	0.00941	0.0717	0.471558
47	0.05458	0.4157	0.339592
48	0.089719	0.6833	0.248575
49	-0.024255	-0.1847	0.427047
50	0.011022	0.0839	0.466697
51	-0.042239	-0.3217	0.374425
52	0.10244	0.7802	0.219234
53	-0.005918	-0.0451	0.482104
54	-0.041663	-0.3173	0.37608
55	-0.023187	-0.1766	0.430224
56	-0.052536	-0.4001	0.345276
57	-0.007657	-0.0583	0.476851
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/24/t1261677254q0awlawiu0jab1u/1c5z31261677168.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/24/t1261677254q0awlawiu0jab1u/1c5z31261677168.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/24/t1261677254q0awlawiu0jab1u/2zj451261677168.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/24/t1261677254q0awlawiu0jab1u/2zj451261677168.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = -1.7 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ;

Parameters (R input):

par1 = 60 ; par2 = -1.7 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ;

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 (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='lags',ylab='ACF')

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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