Mean Square Error (MSE) with time series

Mean Square Error (MSE) is the squared difference between the actual and predicted values forecasted.

Scenario: Given the yearly Tinder statistics from Delta Apple Pi at Crammer Nation University, calculate the MSE.

Year201920202021202220232024
Tinder Matches12041329129714321406-
Estimated (y-tilde)--1276.6671352.6671378.333-
Predicted (y-hat)---1276.6671352.6671378.333

n is the number of periods with a predicted and actual value.
yt is the actual value for a given period "t".
y-hatt is the predicted value for a given period "t".

We're only looking for years that have predicted and actual values!

2022
Actual = 1432
Predicted = 1276.667

2023
Actual = 1406
Predicted = 1352.667

n = 2 (for 2022 & 2023)

MSE = (1 / n) x [(yt - y-hatt)2 + ...]
MSE = (1 / 2) x [(1432 - 1276.667)2 + (1406 - 1352.667)2]
MSE = (0.50) x [(155.333)2 + (53.333)2]
MSE = (0.50) x [24128.34 + 2844.41]
MSE = (0.50) x [26972.75]
MSE = 13486.38

Answer: On average, the squared difference between actual vs. predicted Tinder matches is 13486.38.

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