Identify the formula used to calculate the root mean square error over a range of forecasted values, if the actual value of the time series at time t and the forecast value for time t are denoted by At and Ft respectively.
A)RMSE = $\sqrt { \frac { \sum _ { t = 1 } ^ { n } \left| A _ { t } - F _ { t } \right| } { n } }$

B)RMSE = $\sqrt { \frac { \sum _ { t = 1 } ^ { n } \sqrt { \left| A _ { t } - F _ { t } \right| } } { n } }$

C)RMSE = $\sqrt { \frac { \sum _ { t = 1 } ^ { n } \left( A _ { t } - F _ { t } \right) ^ { 2 } } { n } }$

D)RMSE = $\sqrt { \frac { \sum _ { t = 1 } ^ { n } \left| \frac { A _ { t } - F +{ t } } { 2 } \right| } { n } }$

Question

Identify the formula used to calculate the root mean square error over a range of forecasted values, if the actual value of the time series at time t and the forecast value for time t are denoted by At and Ft respectively.
A)RMSE = $\sqrt { \frac { \sum _ { t = 1 } ^ { n } \left| A _ { t } - F _ { t } \right| } { n } }$

B)RMSE = $\sqrt { \frac { \sum _ { t = 1 } ^ { n } \sqrt { \left| A _ { t } - F _ { t } \right| } } { n } }$

C)RMSE = $\sqrt { \frac { \sum _ { t = 1 } ^ { n } \left( A _ { t } - F _ { t } \right) ^ { 2 } } { n } }$

D)RMSE = $\sqrt { \frac { \sum _ { t = 1 } ^ { n } \left| \frac { A _ { t } - F +{ t } } { 2 } \right| } { n } }$

Quizplus · Accepted Answer

The formula for calculating root mean square error (RMSE) is given by option C. It involves taking the square root of the average of the squared difference between the actual and forecasted values. This formula is commonly used to measure the accuracy of a forecasting model. Option A is incorrect as it involves taking the absolute value of the difference between the actual and forecasted values; this means that negative errors will be treated the same as positive errors. Option B involves taking the square root of the absolute difference which is not the correct formula. Option D is also incorrect as it involves taking the absolute value of the average difference between the actual and forecasted values.

Identify the Formula Used to Calculate the Root Mean Square ∑t=1n∣At−Ft∣n\sqrt { \frac { \sum _ { t = 1 } ^ { n } \left| A _ { t } - F _ { t } \right| } { n } }n∑t=1n​∣At​−Ft​∣​​

Identify the Formula Used to Calculate the Root Mean Square $\sqrt { \frac { \sum _ { t = 1 } ^ { n } \left| A _ { t } - F _ { t } \right| } { n } }$