If the actual value of a time series at time t and the forecast value for time t is denoted by At and Ft respectively, then the formula for the mean absolute deviation over a range of forecasted values is ________.
A)MAD = $\frac{\sum_{t=1}^{n}\left|A_{t}-F_{t}\right|}{n}$

B)MAD = $\frac { \sum _ { t = 1 } ^ { n } \left( \left| A _ { t } - F _ { t } \right| \right) ^ { 2 } } { n }$

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

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

Question

If the actual value of a time series at time t and the forecast value for time t is denoted by At and Ft respectively, then the formula for the mean absolute deviation over a range of forecasted values is ________.
A)MAD = $\frac{\sum_{t=1}^{n}\left|A_{t}-F_{t}\right|}{n}$

B)MAD = $\frac { \sum _ { t = 1 } ^ { n } \left( \left| A _ { t } - F _ { t } \right| \right) ^ { 2 } } { n }$

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

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

Quizplus · Accepted Answer

The formula for mean absolute deviation (MAD) is the sum of the absolute differences between the actual and forecast values, divided by the number of forecasts, so option A is the correct formula. Option B is the formula for mean squared error, not MAD. Option C is not a valid formula for MAD as it uses a square root and does not compute the absolute difference. Option D divides by 2 instead of taking the absolute value of the difference.

If the Actual Value of a Time Series at Time ∑t=1n∣At−Ft∣n\frac{\sum_{t=1}^{n}\left|A_{t}-F_{t}\right|}{n}n∑t=1n​∣At​−Ft​∣​

If the Actual Value of a Time Series at Time $\frac{\sum_{t=1}^{n}\left|A_{t}-F_{t}\right|}{n}$