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Given an ARMA(1,1) process $x_t = a + bx_{t-1} + \varepsilon_t + \theta\varepsilon_{t-1}$, how can we

  1. find the conditional variance, i.e. $Var_{t-1}(x_t)$,
  2. find the unconditional variance, i.e. $Var(x_t)$,
  3. find the autocovariance and autocorrelation for the lags 1 and 2?

I would appreciate a detailed answer.

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