Estimation of a process I have this process to estimate:
$x_t - x_{t-1} = \lambda(\gamma-x_{t-1}+\varepsilon_{t-1})+\varepsilon_t-\varepsilon_{t-1}$
but as far I can see it is unidentified. Any suggestions how to estimate it?
 A: It is trivial to re-write the process 
$$x_t - x_{t-1} = \lambda(\gamma-x_{t-1}+\varepsilon_{t-1})+\varepsilon_t-\varepsilon_{t-1}$$
as an $ARMA(1,1)$ process with drift,
$$x_t = \lambda \gamma +(1-\lambda)x_{t-1}  + \big( \varepsilon_{t}-(1-\lambda)\varepsilon_{t-1}\big)$$ 
but the equality of the AR and the MA coefficients is crucial here.
I will write $ \phi  \equiv 1-\lambda$ so the process is
$$x_t = \lambda \gamma +\phi x_{t-1}  + \big( \varepsilon_{t}-\phi\varepsilon_{t-1}\big)$$
$$\implies (1-\phi L)x_t = (1-\phi L)\gamma + (1-\phi L) \varepsilon_{t}$$
where $L$ is the lag operator. Since the term $(1-\phi L)$ is common throughout, the above process is equivalent to 
$$x_t = \gamma +  \varepsilon_{t}$$
i.e. a white-noise with drift.
This is the case of "redundant parametrization". As Hamilton p. 60 notes "any value of $\phi$ will describe the data equally well". So indeed estimation attempts will get into trouble, but, also, the appearance of $\lambda$ is artificial, it does not represent anything related to the Data Generating Mechanism, and so there is no point in trying to estimate it.
Of course if the specific parametrization is only postulated, testing whether the process can be characterized as white noise will also tell us whether it is useful to go into $ARMA(1,1)$ estimation: if the white-noise behavior is rejected then this is also evidence against the assumed equality of the AR and MA coefficients. 
