title: Definition of ARIMA output in r
body: <p>I have been asked to try and find the parameters from an ARIMA model (µ,Φ,θ) I originally thought that it was just the order of the ARIMA model e.g (1,0,1)(1,1,0) but my manger says this isn't what he wants. </p>
  
  <p>I looked at the summary of the ARIMA model once it had been run and I found values for phi, theta and delta, but there is more than one value and I am very unsure on which is the one I need. </p>
  
  <p>Here is how I found the values:</p>
  
  <pre><code>M&lt;-matrix(c("08Q1", "08Q2", "08Q3", "08Q4", "09Q1", "09Q2", "09Q3", "09Q4", "10Q1", "10Q2", "10Q3", "10Q4", "11Q1", "11Q2", "11Q3", "11Q4", "12Q1",  "12Q2", "12Q3", "12Q4", "13Q1", "13Q2", "13Q3", "13Q4", "14Q1", "14Q2", 79160.56,  91759.73, 91186.48, 106353.82,  70346.47,  80279.15,  82611.60, 131392.72, 93798.99, 105944.78, 103913.13, 154530.69, 110157.40, 117416.09, 127423.42, 156752.00,120097.81, 121307.75, 115021.12, 150657.83, 113711.53, 115353.14, 112701.98, 154319.18,116803.54, 118352.54),ncol=2,byrow=FALSE)
  deltaT&lt;-1/4
  horiz&lt;-4
  startY&lt;-c(8,1)
  aslog&lt;-"y"
  Nu&lt;-M[,length(M[1,])]
  Nu&lt;-as.numeric(Nu)
  Nu&lt;-ts(Nu,deltat=deltaT,start=startY)
  Mdates&lt;-as.character(M[,1])
  if(aslog=="y")
    {N&lt;-log(Nu)} else
      {N&lt;-Nu}
  library(forecast)  
  library(tseries)
  max.sdiff &lt;- 3
  arima.force.seasonality &lt;- "n"
  suppressWarnings(kpssW &lt;- kpss.test(N, null="Level"))
  suppressWarnings(ppW &lt;- tryCatch({ppW &lt;- pp.test(N, alternative = "stationary")},  error = function(ppW) {ppW &lt;- list(error = "TRUE", p.value = 0.99)}))
  suppressWarnings(adfW &lt;- adf.test(N, alternative = "stationary", k = trunc((length(N)-1)^(1/3))))
  if(kpssW$p.value &lt; 0.05 | ppW$p.value &gt; 0.05 | adfW$p.value &gt; 0.05) {ndiffsW = 1} else {ndiffsW = 0}
  aaw &lt;- auto.arima(N, max.D= max.sdiff, d=ndiffsW, seasonal=TRUE, 
                    allowdrift=FALSE, stepwise=FALSE, trace=FALSE, seasonal.test="ch")
  orderWA &lt;- c(aaw$arma[1], aaw$arma[6] , aaw$arma[2])
  orderWS &lt;- c(aaw$arma[3], aaw$arma[7] , aaw$arma[4])
  if(sum(aaw$arma[1:2])==0) {orderWA[1] &lt;- 1} else {NULL}
  if(arima.force.seasonality == "y") {if(sum(aaw$arma[3:4])==0) {orderWS[1] &lt;- 1} else {NULL}} else {NULL}
  ArimaW1 &lt;- Arima(N, order= orderWA, seasonal=list(order=orderWS), method="ML")
  ArimaW1$model
  </code></pre>
  
  <p>This shows 5 different values for phi, 4 for theta and 1 for Delta. How do I know which is the correct parameter value? Or do I use all of them to show the parameters and also force the parameters on a truncated version of my data to test the accuracy of the fit?</p>