Exponential Smoothing

With exponential smoothing, to determine the estimated value for a given period, we'll weigh the current value (y_t) against the previous period's estimated value (y-tilde_t-1).

y-tilde_t is the estimated value for a current period "t".
y_t is the actual value for a current period "t".
α is the alpha level.
y-tilde_t-1 is the estimated value for the previous period "t - 1"

Since we don't have a previously estimated value, we're just going to plug in the current value for the estimated value for our first period (2019).

y-tilde₂₀₂₀ = 0.75(1329) + (1 - 0.75)(1204)
y-tilde₂₀₂₀ = 996.75 + (0.25)(1204)
y-tilde₂₀₂₀ = 996.75 + 301
y-tilde₂₀₂₀ = 1297.75

α determines the impact of the current value (y_t) vs. the previous period's estimate (y-hat_t-1) when estimating a period's value.

In the visual below...

• α = 0.75 is more reactive to the current values
• α = 0.25 is less reactive to the current values

The higher / lower α is, the more / less reactive the forecast is to the current value (y_t)!

When α is higher, our current value (y_t) makes up a larger percentage (α% to be exact) of our forecast!

This causes our forecast to be more reactive to the current value of each period.

With the α = 0.75 above, our current value made up 75% of the estimated value...

...versus when α = 0.25, our current value only made up 25% of the estimated value.