ECON/FIN 250: Forecasting in Finance and Economics: Section 4.1 Forecasting Fundamentals
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1 ECON/FIN 250: Forecasting in Finance and Economics: Section 4.1 Forecasting Fundamentals Patrick Herb Brandeis University Spring 2016 Patrick Herb (Brandeis University) Forecasting Fundamentals ECON/FIN 250: Spring / 18
2 Course Overview 1 Loss Functions 2 Forecast Statement 3 Forecast Horizons 4 Information Set 5 Parsimony and Bias Patrick Herb (Brandeis University) Forecasting Fundamentals ECON/FIN 250: Spring / 18
3 Loss Functions 1 Loss Functions 2 Forecast Statement 3 Forecast Horizons 4 Information Set 5 Parsimony and Bias Patrick Herb (Brandeis University) Forecasting Fundamentals ECON/FIN 250: Spring / 18
4 Decision Environment Forecasts Decisions Decisions Gains or Losses Patrick Herb (Brandeis University) Forecasting Fundamentals ECON/FIN 250: Spring / 18
5 Symmetric Losses Agent wants to minimize losses: Demand High Demand Low Increase Inventory 0 10,000 Reduce Inventory 10,000 0 Patrick Herb (Brandeis University) Forecasting Fundamentals ECON/FIN 250: Spring / 18
6 Asymmetric Losses Agent wants to minimize losses: Demand High Demand Low Increase Inventory 0 10,000 Reduce Inventory 20,000 0 Patrick Herb (Brandeis University) Forecasting Fundamentals ECON/FIN 250: Spring / 18
7 Asymmetric Losses Forecaster wants to minimize losses: High Sales Low Sales Forecast High Sales Forecast Low Sales 1,000 0 Patrick Herb (Brandeis University) Forecasting Fundamentals ECON/FIN 250: Spring / 18
8 Forecast Losses: Loss Function (L) Squared Error: L(e) = et 2 = (y t ŷ t ) 2 Absolute Error: L(e) = e t = y t ŷ t Asymmetric Losses Sign Matching L(e) = { 1, if sign( y) sign( ŷ) 0, otherwise. (1) Trading rule profits E[α t (I t )r t+1 + (1 α t (I t ))r f ] (2) Patrick Herb (Brandeis University) Forecasting Fundamentals ECON/FIN 250: Spring / 18
9 Forecast Statement 1 Loss Functions 2 Forecast Statement 3 Forecast Horizons 4 Information Set 5 Parsimony and Bias Patrick Herb (Brandeis University) Forecasting Fundamentals ECON/FIN 250: Spring / 18
10 Forecast Object Point Forecast: ŷ t Interval Forecast: [ŷ L, ŷ H ] Density Forecast Discrete Forecast / Probability Forecast Euro collapse, market crash, super bowl Stata is actually good at this (logistic regression) We will not have time for this Timing Forecast (when will a bubble burst) Alternative Histories (Counter Factual) Patrick Herb (Brandeis University) Forecasting Fundamentals ECON/FIN 250: Spring / 18
11 Forecast Horizons 1 Loss Functions 2 Forecast Statement 3 Forecast Horizons 4 Information Set 5 Parsimony and Bias Patrick Herb (Brandeis University) Forecasting Fundamentals ECON/FIN 250: Spring / 18
12 Forecast Horizon How far into the future? Data observations from 1 to T Forecasts T+1, T+2,..., T+h Methods for h-step ahead forecasts Direct to T+h Dynamic to T+h Patrick Herb (Brandeis University) Forecasting Fundamentals ECON/FIN 250: Spring / 18
13 Information Set 1 Loss Functions 2 Forecast Statement 3 Forecast Horizons 4 Information Set 5 Parsimony and Bias Patrick Herb (Brandeis University) Forecasting Fundamentals ECON/FIN 250: Spring / 18
14 Information Set Current and lagged target series: y t, y t 1, y t 2,... Other series: x t, x t 1, x t 2,... Need to be very careful Trading rules (exactly what is known) Macro forecasting (revised numbers) Real time forecasts Patrick Herb (Brandeis University) Forecasting Fundamentals ECON/FIN 250: Spring / 18
15 Parsimony and Bias 1 Loss Functions 2 Forecast Statement 3 Forecast Horizons 4 Information Set 5 Parsimony and Bias Patrick Herb (Brandeis University) Forecasting Fundamentals ECON/FIN 250: Spring / 18
16 Parsimony In sample bias and/or overfitting Complex models fit current data well, but lousy forecasts Fitting every little wiggle in sample (even random wiggles) Push toward simple models Fewer parameters Much more on this Patrick Herb (Brandeis University) Forecasting Fundamentals ECON/FIN 250: Spring / 18
17 In Sample Bias Data ( ), monthly In sample forecasting Fit model y t = ρy t 1 + ɛ using all the data ( ) Generate 1 month ahead forecasts for This is somewhat unfair (why?) True out of sample experiment Estimate using only data in ( ) Forecast Patrick Herb (Brandeis University) Forecasting Fundamentals ECON/FIN 250: Spring / 18
18 Useful Quotes Essentially, all models are wrong, but some are useful. -George E. P. Box, Empirical Model-Building and Response Surfaces, Just as the ability to devise simple but evocative models is the signature of the great scientist, so overelaboration and overparameterization is often the mark of mediocrity. -George E. P. Box, Science and Statistics, Patrick Herb (Brandeis University) Forecasting Fundamentals ECON/FIN 250: Spring / 18
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