Determining the autocorrelation sequence from an AR model I have the following equation:

$$x(n)=\frac{14}{24}x(n-1)+\frac{9}{24}x(n-2)-\frac{1}{24}x(n-3)+w(n)$$
where, $w(n)$ is a stationary white noise process with variance $\sigma^2_w$

Now, I want to determine the auto correlation sequence $\gamma_{xx}(m)$, for $m = 0,1,\ldots,5$

Now, I know that the autocorrelation function for AR process which is given below:

$$\gamma_{xx}(m)= \begin{cases}\displaystyle-\sum_{k=1}^p a_k\gamma_{xx}(m-k), &amp; m &gt; 0\\
\displaystyle  -\sum_{k=1}^p a_k\gamma_{xx}(m-k) + \sigma_w^2, &amp; m = 0\\
\gamma_{xx}^*(-m), &amp; m &lt; 0\\
\end{cases}$$

Here, I already found the coefficients of ${a_k}$ which are $a_1=-\frac{14}{24}, a_2=-\frac{9}{24}, a_3=\frac{1}{24}$.

Now, I don't get, how can I calculate $\gamma_{xx}(0)$ to $\gamma_{xx}(5)$ recursively? 

Please someone tell me how can I solve  $\gamma_{xx}(0)$ and $\gamma_{xx}(1)$? Then I can do the the rest.
Looking at your definition of $\gamma_{xx}(m)$, it seems that you have 4 equations with 4 unknown (for $m=0,\ldots,3$):

\begin{align}
24\gamma_{xx}(0) &amp;= 14\gamma_{xx}(1) + 9\gamma_{xx}(2) - \gamma_{xx}(3) + 24\sigma_w^2  \\
24\gamma_{xx}(1) &amp;= 14\gamma_{xx}(0) + 9\gamma_{xx}(1) -\gamma_{xx}(2) \\ 
24\gamma_{xx}(2) &amp;= 14\gamma_{xx}(1) + 9\gamma_{xx}(0) - \gamma_{xx}(1)\\
24\gamma_{xx}(3) &amp;= 14\gamma_{xx}(2) + 9\gamma_{xx}(1) - \gamma_{xx}(0)
\end{align}

Solving the above system of equations is straight forward, and after that you can easily obtain $\gamma_{xx}(m)$ for $m=4,5$