# [R] MA terms in arima

testrider testrider at gmail.com
Wed Dec 21 19:27:15 CET 2011

```With the arima function I found some nice results, however now i have trouble
interpreting them for use outside R.
I am currently struggeling with the MA terms, here is a short example:

ser=c(1, 14, 3, 9)        #Example series
mod=arima(ser,c(0,0,1))   #From {stats} library
mod
#Series: ser
#ARIMA(0,0,1) with non-zero mean
#
#Coefficients:
#          ma1  intercept
#      -0.9999     7.1000
#s.e.   0.5982     0.8762
#
#sigma^2 estimated as 7.676:  log likelihood = -10.56
#AIC = 27.11   AICc = Inf   BIC = 25.27

mod\$resid

#Time Series:
#Start = 1
#End = 4
#Frequency = 1
# -4.3136670  3.1436951 -1.3280435  0.6708065

#\$pred
#Time Series:
#Start = 5
#End = 9
#Frequency = 1
# 6.500081 7.100027 7.100027 7.100027 7.100027
#
#\$se
#Time Series:
#Start = 5
#End = 9
#Frequency = 1
# 3.034798 3.917908 3.917908 3.917908 3.917908
?arima

When looking at the specification this formula is presented:
X[t] = aX[t-1] + … + a[p]X[t-p] + e[t] + be[t-1] + … + b[q]e[t-q]

Given my choice of AR and MA terms, and considering that i have included a
constant this should reduce to:
X[t] =  e[t] + be[t-1] + constant

However this does not hold up when i compare the results from R with manual
calculations:
6.500081 != 6.429261 == -0.9999 * 0.6708065 + 7.1000

Furthermore I can also not succeed in reproducing the insample errors,
assuming i know the first one this should be possible:
-4.3136670 * -0.9999 +7.1000 !=  14 - 3.1436951
3.1436951 * -0.9999 +7.1000 !=   3 + 1.3280435
-1.3280435 * -0.9999 +7.1000 !=  9 - 0.6708065

I hope someone can shed some light on this matter so i will actually be able
to use the nice results that I have obtained.

Dennis

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