Forecast Assessment Slides

Forecast Assessment Slides - NBER Summer Institute...

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Lecture 10 1, July 21, 2008 NBER Summer Institute Minicourse – What’s New in Econometrics: Time Series Lecture 10 July 16, 2008 Forecast Assessment
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Lecture 10 2, July 21, 2008 Outline 1. Why Forecast? 2. Forecasting basics 3. Estimating Parameters for forecasting 4. Forecast Assessment (a) Comparing Forecasts/Forecasters (b) Comparing Forecasts/Models
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Lecture 10 3, July 21, 2008 1. Why Forecast? (a) You want to know about the future (SPF, Financial Markets) (b) You want to evaluate a model Why use forecasting methods to evaluate models? (i) Less prone to data mining, in-sample overfitting (indeed, in- sample overfitting leads to out-of-sample “underfitting”) (ii) Instability (iii) In-sample methods too difficult Recently developed forecast assessment methods have focused on both of these (and it is useful to keep goals in mind as we discuss methods)
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Lecture 10 4, July 21, 2008 2. Forecasting Basics Y t + h : variable to be forecast X t : vector of variables used to make forecast (typically would include current and lags of Y t and other variables). f t + h / t : Forecast of Y t + h made a time t . e t + h : Y t + h f t + h/t L ( e ): Loss associated with the error “Risk” associated with f : E ( L ( e )).
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Lecture 10 5, July 21, 2008 (a) Minimum MSE forecasts: Loss quadratic L ( e ) = a + be 2 and Risk is Mean Squared Error (MSE). Goal is to find mind minimum MSE (MMSE) forecast. Key Result: MMSE forecast is the regression function: f t + h / t = E ( Y t + h | X t ) Some properties of MMSE forecasts: (1) E ( e t + h | X t ) = 0, so that E ( e t + h X t ) = 0 (2) If X t includes current and past values of Y t , then it implicitly includes current and lagged values of e t . Thus E ( e t + h e t ) = 0, so that e t + h follows an MA( h 1) process. (3) Y t + h = f t + h/t + e t + h , where the two rhs terms are uncorrelated. Thus, 222 Yf e σ σσ =+ , and 22 .
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Lecture 10 6, July 21, 2008 (b) More than one forecast: Let f 1 and f 2 denote two forecasts of Y . Let f 3 = β 0 + 1 f 1 + 2 f 2 denote a third forecast. Question: How should f 1 and f 2 be “combined” to form f 3 (what values of should be chosen)? Answer: MMSE forecasts are regressions, so ’s are given by the (population) values from the linear regression of Y t + h onto 1 / th t f + and 2 / t f + . (Bates and Granger (1969), Granger and Ramanathan (1984)). The extension to n 2 forecasts is obvious. References: see Timmermann (2006)
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Lecture 10 7, July 21, 2008 Problem: As a practical matter you must use estimates of the β ’s from a sample regression. Forecast combining “puzzle”: When the number of forecasts to be combined ( n ) is even moderately large, forecasts constructed using estimated s don’t perform very well. Better to use ad hoc averages like sample means, medians, trimmed means, “consensus” forecasts and so forth. (Large literature surveyed in Timmermann.) JHS will say more about this in Lecture 12.
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Lecture 10 8, July 21, 2008 (c) Other Loss Functions: Granger (1969) and Christoffersen and Diebold (1997).
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This note was uploaded on 12/26/2011 for the course ECON 245a taught by Professor Staff during the Fall '08 term at UCSB.

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Forecast Assessment Slides - NBER Summer Institute...

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