4.1 Naive forecast

For a naive forecast of the anchovy landings in 1988, we just use the 1987 landings.

\[\hat{x}_{1988} = x_{1987}\] Which is the same as saying that we put 100% of the ‘weight’ on the most recent value and no weight on any value prior to that.

\[\hat{x}_{1988} = 1 \times x_{1987} + 0 \times x_{1986} + 0 \times x_{1985} + \dots\]

Past values in the time series have information about the current state, but only the most recent past value.

That’s a bit extreme. Often the values prior to the last value also have some information about future states. But the ‘information content’ should decrease the farther in the past that we go.