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1 CHAPTER 4 TOOLS OF THE FORECASTER González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. Table 4.1 OLS Regression.

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Presentation on theme: "1 CHAPTER 4 TOOLS OF THE FORECASTER González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. Table 4.1 OLS Regression."— Presentation transcript:

1 1 CHAPTER 4 TOOLS OF THE FORECASTER González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. Table 4.1 OLS Regression Results: House Prices and Mortgages Rates Some Information Sets Are More Valuable than Others Model (i)Model (ii) 4.1 The Information Set

2 2 Figure 4.1 Forecasting Environments: Recursive Scheme González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc Forecasting Environments t +1 t +j Estimation sample (t+1 observations) 0 t+1 t+2T Prediction sample Estimation sample (t observations) 0 t+1 t T Estimation sample (t+j observations) 0 t+j t+j+1 T Prediction sample One-step ahead prediction at time t Prediction sample

3 3 González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. Figure 4.2 Forecasting Environments: Rolling Scheme t+j Estimation sample (t observations) t +10 t+2T Prediction sample Estimation sample (t observations) One-step ahead prediction at time t 0 t+1 t T Prediction sample Estimation sample (t observations) 0 t+j t+j+1 T Prediction sample 1 j

4 4 González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. Figure 4.3 Forecasting Environments: Fixed Scheme Estimation sample (t observations) t+10 t+2 T Prediction sample Estimation sample (t observations) One-step ahead prediction at time t 0 t+1 t T Prediction sample Estimation sample t observations) t+j0 t+j+1 T t t t+1 ………… Update information set Update Prediction sample

5 González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 5 Figure 4.4 Symmetric Loss Functions 4.3 The Loss Function Quadratic loss function Absolute value loss function L(e) e 0 e Examples

6 6 Figure 4.5 Asymmetric Loss Functions González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. L(e) 0 e Lin-lin function Linex function L(e) e 0 e 0

7 González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 7 Figure 4.6 The Forecasting Problem Optimal Forecast: An Introduction time Conditional density t t+h ………. ….. Information set time

8 González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 8 Figure 4.7 Optimal Forecast Under Quadratic Loss time t t+h ………. ….. Information set


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