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Asymptotic normality of the MASE: The Diebold-Mariano test for one-step forecasts is used to test the statistical significance of the difference between two sets of forecasts. [ 5 ] [ 6 ] [ 7 ] To perform hypothesis testing with the Diebold-Mariano test statistic, it is desirable for D M ∼ N ( 0 , 1 ) {\displaystyle DM\sim N(0,1)} , where D M ...
Further, two-step-ahead or in general p-step-ahead forecasts can be computed by first forecasting the value immediately after the training set, then using this value with the training set values to forecast two periods ahead, etc. See also. Calculating demand forecast accuracy; Consensus forecasts; Forecast error; Predictability
If a main application of the forecast is to predict when certain thresholds will be crossed, one possible way of assessing the forecast is to use the timing-error—the difference in time between when the outcome crosses the threshold and when the forecast does so.
When the model has been estimated over all available data with none held back, the MSPE of the model over the entire population of mostly unobserved data can be estimated as follows.
For example, to calculate the 95% prediction interval for a normal distribution with a mean (μ) of 5 and a standard deviation (σ) of 1, then z is approximately 2. Therefore, the lower limit of the prediction interval is approximately 5 ‒ (2⋅1) = 3, and the upper limit is approximately 5 + (2⋅1) = 7, thus giving a prediction interval of ...
While accuracy, as measured by quantitative errors, is important, it may be more crucial to accurately forecast the direction of change. Directional accuracy is similar to a binary evaluation. The metric only considers the upward or downward direction in the time series and is independent of quantitive value of increase or decrease.
Calculate another estimate of the trend using a different set of weights (known as "Henderson weights"). Remove the trend again and calculate another estimate of the seasonal factor. Seasonally adjust the series again with the new seasonal factors. Calculate the final trend and irregular components from the seasonally adjusted series.
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