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Forecasting and Forecast Errors

# Forecasting and Forecast Errors - Forecasting and Forecast...

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Forecasting and Forecast Errors First, we use the words forecasting and predicting interchangeably. The word forecasting is often reserved for predicting values of the dependent variable beyond the current time period or beyond the range of the sample of data. But here, we assume these two words mean the same thing: estimating a value for the dependent variable given a specific value for the independent variable . There are two things that we can forecast: (1) the expected value of the dependent variable - 0 [ ] E Y X ; or (2) an actual value of the dependent variable - 0 Y X . We have just one estimator that we can use: 0 0 1 0 ˆ Y b b X = + . In forecasting, there will be errors that occur, and the magnitude of those errors will logically be affected by the population value we are forecasting or predicting and the level of the independent variable for which we are forecasting. If we are to forecast, we will be interested in the sampling properties (distributions) for these two forecast errors. Let’s review/clarify three related concepts: (1) the sampling distribution for the estimator ˆ Y ; (2) the sampling properties (a sampling distribution) of the errors in forecasting 0 [ ] E Y X ; and (3) the sampling properties (a sampling distribution) of the errors in forecasting 0 Y X . Just as the distribution of the disturbance ( u ) also is the distribution of the dependent variable ( Y ) 1 , so too is the sampling distribution of our first type of forecast error equivalent to the sampling distribution of our estimator ( ˆ Y ). The second forecast error has a different set of sampling properties.

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Forecasting and Forecast Errors - Forecasting and Forecast...

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