Does the following function have an integral?

36 Views Asked by At

Can the following function be integrated?

$X_t = c + \phi_1X_{t-1} + \phi_2X_{t-2} + \epsilon_t$

Where:

  • $X_t$ is the variable of interest; $X_{t-1}$ is the value of $X_t$ at one time step earlier and $X_{t-2}$ is the value of $X_t$ at two time steps earlier

  • $c$, $\phi_1$ and $\phi_2$ are some real numbers.

  • $\epsilon$ is a random number from a normal distribution with a fixed mean and fixed standard deviation

Is the integral of $X_t$ defined? Is it possible to evaluate the integral of $X_t$? (I.e. the right hand side of the above equation)

Thanks