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POMA terms in arima
 

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  1. POMA terms in arima
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    <p>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:</p> <pre><code>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$resid #Time Series: #Start = 1 #End = 4 #Frequency = 1 #[1] -4.3136670 3.1436951 -1.3280435 0.6708065 predict(mod,n.ahead=5) #$pred #Time Series: #Start = 5 #End = 9 #Frequency = 1 #[1] 6.500081 7.100027 7.100027 7.100027 7.100027 # #$se #Time Series: #Start = 5 #End = 9 #Frequency = 1 #[1] 3.034798 3.917908 3.917908 3.917908 3.917908 ?arima </code></pre> <p>When looking at the specification this formula is presented: <code>X[t] = a[1]X[t-1] + … + a[p]X[t-p] + e[t] + b[1]e[t-1] + … + b[q]e[t-q]</code></p> <p>Given my choice of AR and MA terms, and considering that i have included a constant this should reduce to: <code>X[t] = e[t] + b[1]e[t-1] + constant</code></p> <p>However this does not hold up when i compare the results from R with manual calculations: <code>6.500081 != 6.429261 == -0.9999 * 0.6708065 + 7.1000</code></p> <p>Furthermore I can also not succeed in reproducing the insample errors, assuming i know the first one this should be possible: <code>-4.3136670 * -0.9999 +7.1000 != 14 - 3.1436951</code> <code>3.1436951 * -0.9999 +7.1000 != 3 + 1.3280435</code> <code>-1.3280435 * -0.9999 +7.1000 != 9 - 0.6708065</code></p> <p>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.</p>
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    1. USDennis Jaheruddin
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    1. COSince this isn't a programming question, you will probably get more/better answers on http://stats.stackexchange.com/.
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      1. POMA terms in arima
      1. USJoshua Ulrich
    2. COThanks for the advice, I have now crossposted it [http://stats.stackexchange.com/questions/20254/ma-terms-in-arima](http://stats.stackexchange.com/questions/20254/ma-terms-in-arima)
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      1. USDennis Jaheruddin
 

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