why auto.arima() and Arima() are different?
<p>I fitted model by function <code>auto.arima()</code>, then i tried to fit again by function <code>Arima()</code> with same model, but i got different results. </p>

<p>By <code>auto.arima()</code>:</p>

<pre><code>&gt; a&lt;-c(90,88,96,110,105,128,119,117,155,135,138,127,156,168,145,160,180,175,189,166,184)
&gt; chuoi&lt;-ts(a,frequency=1,start=c(1990))
&gt; auto.arima(chuoi)
Series: chuoi 
ARIMA(2,1,0) with drift         

Coefficients:
          ar1      ar2   drift
      -0.7075  -0.4648  4.7897
s.e.   0.1930   0.1972  1.3689

sigma^2 estimated as 163.1:  log likelihood=-79.7
AIC=167.39   AICc=170.06   BIC=171.38
</code></pre>

<p>By <code>Arima()</code> with same model, used all method "CSS-ML","ML" and "CSS":</p>

<pre><code>&gt; fit210&lt;-Arima(chuoi,c(2,1,0),method="ML")
&gt; fit210
Series: chuoi 
ARIMA(2,1,0)                    

Coefficients:
          ar1      ar2
      -0.4670  -0.1928
s.e.   0.2162   0.2201

sigma^2 estimated as 244.2:  log likelihood=-83.48
AIC=172.96   AICc=174.46   BIC=175.95
&gt; fit210&lt;-Arima(chuoi,c(2,1,0),method="CSS")
&gt; fit210
Series: chuoi 
ARIMA(2,1,0)                    

Coefficients:
          ar1      ar2
      -0.4876  -0.2111
s.e.   0.2196   0.2304

sigma^2 estimated as 268.3:  part log likelihood=-84.3
&gt; fit210&lt;-Arima(chuoi,c(2,1,0),method="CSS-ML")
&gt; fit210
Series: chuoi 
ARIMA(2,1,0)                    

Coefficients:
          ar1      ar2
      -0.4671  -0.1928
s.e.   0.2162   0.2201

sigma^2 estimated as 244.2:  log likelihood=-83.48
AIC=172.96   AICc=174.46   BIC=175.95
</code></pre>

<p>Obviously I got different coefficients ar(1), ar(2). Then, how function <code>auto.arima()</code> calculated coefficients ar(1), ar(2)? </p>