Lecture9_2005 - Green Stats Forecasting and Prediction To...

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Green // Stats Forecasting and Prediction To this point in the course, we have focused primarily on parameter estimation rather than prediction. In this lecture, I want to discuss prediction and forecasting. Forecasting is usually understood to be a subset of prediction. Prediction may involve both in-sample and out-of-sample guesses; the latter are termed forecasts when they are based on analysis of data from an earlier point in time. Thus, a lot of what is termed prediction is probably better described as retro-diction – predicting the past. In-Sample vs. Out-of-Sample Prediction We have already met one form of prediction: regression estimates of the “fitted values” of Y. Simply take the coefficients from an equation and plug them into the regression model. Sometimes this type of analysis is called “in-sample” prediction, because it is using the data from a given sample to estimate parameters that are in turn used to predict the values of Y within that sample. That is quite different from “out-of-sample” prediction, where the parameter estimates from one sample are used to predict the values of Y in a different sample. Out-of-sample prediction is generally more difficult to do than in-sample prediction. Does One Need a Model? The character of any predictive exercise, it should be stressed, depends on whether the model used to predict Y meets the core regression assumptions, namely, (1) no measurement error in X and (2) no correlation between X and U. If one believes that one’s parameter estimates may be interpreted causally (as would be the case if the data were generated through randomized experimentation), then prediction is really a matter of applying a general causal law to a given set of data. On the other hand, a prediction exercise may be based on regression models that have no causal interpretation. For example, journalists may conduct pre-election polls in order to forecast which legislative elections are likely to be closely contested; the polls may be highly accurate predictors of the actual vote, even if the polls are conducted in secret and have no effect on the outcome. (To see that secret poll results do not cause outcomes, consider the pollster who, due to sampling error, puts one candidate ahead of another; this mistaken poll does not alter the outcome of the election.) The point here is that sometimes predictions are based on a causal understanding of the world; other times, they rest on non-causal empirical regularities. The utility of each approach will depend on the idiosyncrasies of the application. How much predictive accuracy do non-causal independent variables contribute? How risky is it to rely on them, given that the empirical regularity is contingent on factors other than a direct causal relationship?
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To refresh memories: the two statistical criteria for evaluating the predictive accuracy of a regression model are s , the estimated standard deviation of the disturbances, and R 2 , the squared correlation between the observed and fitted values of Y. Example 1: Prediction based on Causal Modeling
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This note was uploaded on 04/07/2008 for the course STAT 102 taught by Professor Jonathanreuning-schererdonaldgreen during the Fall '05 term at Yale.

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Lecture9_2005 - Green Stats Forecasting and Prediction To...

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