![]() It is similar to the MASE, which scales the focal forecasts's MAE by the MAE achieved (in-sample) by the naive random walk one-step forecast. If the ratio is less than one, then the nonstandard mean squared percentage error of the focal forecast is lower than the one for the naive method.Īs such, this version of Theil's U (see below for my choice of words) is a type of "scaled" or "relative" forecast accuracy measure. The numerator does this for the focal forecast, the denominator for the naive random walk one-step ahead forecast. I would call them both "nonstandard mean squared percentage errors", each period's error being expressed as a percentage of the previous observation. If you were to intuitively explain the numerator and denominator, how would you do it? Jbowman already gave some very useful pointers. The reason I am asking this question is that I want to know the underlying premise or logic behind using this formula. Why are we taking t from 1 to n-1? Shouldn't it be t from 1 to n? This is because if we are taking the forecast of (t+1) then every number in the formula should be of (t+1). Hence, if we follow this formula of MAPE in the numerator, then Y(t) should be Y(t+1) i.e. How do numerator and denominator represent the MAPE formulas for a general forecast and naive approach forecast? This is because MAPE of any forecast is represented by this formula: MAPE = Mean of (sum of (Forecast - Actual)/Actual). I am not able to understand 2 things here. I am able to understand the above interpretation but when I dig deep into the formula, I am not able to understand the below lines from the book.įor simplicity, I am also attaching equation (2.18). APE of the forecast is even bigger than naive method forecasts. Hence, a general pattern can be seen that as U increases forecast is wrong and at 1 forecast is same as naive and hence by extrapolating this we can say that if U>1 then the forecast is worse than naive method forecast, i.e. When it reaches 1, it means Forecast is equivalent to Naive Method. As we keep increasing U, the forecasts will keep becoming more and more imperfect. That means if U>0 then forecasts are not perfect. I am facing difficulty in understanding the interpretation of Theil's U statistic.Īccording to my understanding, when U = 0 the forecasts are perfect. I was reading "Forecasting Methods and Applications" book and came across Theil's U statistic formula. ![]()
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