Dec

23

Here's a pretty kettle of fish. Suppose you have two forecasts that are disparate. One is bullish and the other is bearish. For example it's up 100 over 4 days. That's bearish. But it's up 4 days in a row, that's bullish. How to combine? There's a bayesian approach, a regression approach, and an inverse variance weighted approach, and a practical approach that Zarnowitz found. Just add up the number of bullish and bearish and that's your forecast. But what's your best way of solving same? The answer might provide a meal for a lifetime. I asked Stigler this question 15 years ago, and he thought it was a very good question, and I've not seen a good answer yet.

Alex Castaldo writes:

I would start with Diebold and Pauly: The use of prior information in forecast combination.

Gary Rogan writes: 

There has got to be some way of incorporating the rare nature of one of the set of circumstances. Clearly 100 points is more unique than 4 days. Does this carry any special weight? Also there is a very large number of other possible "circumstances", like time of day, month, year, what the future portends if prior history was similar during this time of day, month, year. where are we in the economic cycle? With respect to various moving averages? What's the money supply and it's history? What has the price of oil and any number of other thing doing and where is it? And what matters more: all these other things or the one unique thing?

anonymous writes: 

You're mixing apples and oranges. The premise for regression and related approaches is that there is a fixed law that can be discerned, or at least modeled, in such a way that it does not vary in any dimension. Whatever the model/rule was 50 years ago is still what it is today—unless of course, additional information either disproves the model or allows for its refinement. Either way, it's time invariant. Bayesian analyses are different by definition. Unless the prior is the same, the result will be different. Since priors will change with the passage of time, the analysis is time-dependent. You might try to specify the Bayesian model as fixed at any one point in time and try some form of combination, but since the moment you do that, the prior will shift and the exercise becomes worthless.


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