Hello sir,
I did not understand what this means properly FORECAATING THE PAST.
and how should we identify that we are forecasting the past?
can you give me some example and help me understand?
Thank you so much!
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If we forecast the future (say we predict at time t the value of variable Y in period t + 1), we must base our predictions on information we knew at time t. We could use a regression to make that forecast using the equation
Yt+1 = b0 + b1X1t + et+1
In this equation, we predict the value of Y in time t + 1 using the value of X in time t.
The error term, et+1, is unknown at time t and thus should be uncorrelated with X1t.
Unfortunately, analysts sometimes use regressions that try to forecast the value of a dependent variable at time t + 1 based on independent variable(s) that are functions of the value of the dependent variable at time t + 1. In such a model, the independent variable(s) would be correlated with the error term, so the equation would be mis-specified. As an example, an analyst may try to explain the cross-sectional returns for a group of companies during a particular year using the market-to-book ratio and the market capitalization for those companies at the end of the year. If the analyst believes that such a regression predicts whether companies with high market-to-book ratios or high market capitalizations will have high returns, the analyst is mistaken. This is because for any given period, the higher the return during the period, the higher the market capitalization and the market-to-book period will be at the end of the period.
So in this case, if all the cross-sectional data come from period t + 1, a high value of the dependent variable (returns) actually causes a high value of the independent variables (market capitalization and the market-to-book ratio), rather than the other way around. In this type of misspecification, the regression model effectively includes the dependent variable on both the right-and left-hand sides of the regression equation.