Mean Reversion
A time series displays mean reversion to a value of 0.0971, with each future observation predicted as 0.62 times the prior observation, plus a constant. The constant is closest to:
Incorrect.
This may reflect a decimal error in the algebra. Start with the equation for the mean level: $$ \overline{x} = \frac{b_0}{1 - b_1} $$ and solve explicitly for the intercept coefficient.
Correct!
The mean level is predicted by
$$\displaystyle \overline{x} = \frac{b_0}{1 - b_1} $$.
In this case:
$$\displaystyle \overline{x} = 0.0971 = \frac{b_0}{1 - 0.62} $$.
From here, the intercept can be solved for explicitly as:
$$\displaystyle b_0 = 0.0971(1 - 0.62) = 0.0369 $$.
Incorrect.
This is the product of the mean level and the b1 coefficient, but this is not the correct explicit expression for the intercept term.
0.006.
0.037.
0.060.
