An Inconvenient Truth about Forecast Combinations
It is well-known that the weighted averages of two competing forecasts may reduce mean squared prediction errors (MSPE) and may also introduce certain inefficiencies. In this paper, we take an in-depth view of one particular type of inefficiency stemming from simple combination schemes: Mincer and Z...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-09-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/11/18/3806 |
| _version_ | 1797579035196260352 |
|---|---|
| author | Pablo Pincheira-Brown Andrea Bentancor Nicolás Hardy |
| author_facet | Pablo Pincheira-Brown Andrea Bentancor Nicolás Hardy |
| author_sort | Pablo Pincheira-Brown |
| collection | DOAJ |
| description | It is well-known that the weighted averages of two competing forecasts may reduce mean squared prediction errors (MSPE) and may also introduce certain inefficiencies. In this paper, we take an in-depth view of one particular type of inefficiency stemming from simple combination schemes: Mincer and Zarnowitz inefficiency or auto-inefficiency for short. Under mild assumptions, we show that linear convex forecast combinations are almost always auto-inefficient, and, therefore, greater reductions in MSPE are almost always possible. In particular, we show that the process of taking averages of forecasts may induce inefficiencies in the combination, even when individual forecasts are efficient. Furthermore, we show that the so-called “optimal weighted average” traditionally presented in the literature may indeed be inefficient as well. Finally, we illustrate our findings with simulations and an empirical application in the context of the combination of headline inflation forecasts for eight European economies. Overall, our results indicate that in situations in which a number of different forecasts are available, the combination of all of them should not be the last step taken in the search of forecast accuracy. Attempts to take advantage of potential inefficiencies stemming from the combination process should also be considered. |
| first_indexed | 2024-03-10T22:30:08Z |
| format | Article |
| id | doaj.art-8da6e418374d43a2ac3f2e54436b1e32 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T22:30:08Z |
| publishDate | 2023-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-8da6e418374d43a2ac3f2e54436b1e322023-11-19T11:47:52ZengMDPI AGMathematics2227-73902023-09-011118380610.3390/math11183806An Inconvenient Truth about Forecast CombinationsPablo Pincheira-Brown0Andrea Bentancor1Nicolás Hardy2School of Business, Universidad Adolfo Ibáñez, Diagonal Las Torres 2640, Peñalolén, Santiago 7940000, ChileFacultad de Economía y Negocios, Universidad de Talca, Talca 8460000, ChileFacultad de Administración y Economía, Universidad Diego Portales, Huechuraba 8170641, ChileIt is well-known that the weighted averages of two competing forecasts may reduce mean squared prediction errors (MSPE) and may also introduce certain inefficiencies. In this paper, we take an in-depth view of one particular type of inefficiency stemming from simple combination schemes: Mincer and Zarnowitz inefficiency or auto-inefficiency for short. Under mild assumptions, we show that linear convex forecast combinations are almost always auto-inefficient, and, therefore, greater reductions in MSPE are almost always possible. In particular, we show that the process of taking averages of forecasts may induce inefficiencies in the combination, even when individual forecasts are efficient. Furthermore, we show that the so-called “optimal weighted average” traditionally presented in the literature may indeed be inefficient as well. Finally, we illustrate our findings with simulations and an empirical application in the context of the combination of headline inflation forecasts for eight European economies. Overall, our results indicate that in situations in which a number of different forecasts are available, the combination of all of them should not be the last step taken in the search of forecast accuracy. Attempts to take advantage of potential inefficiencies stemming from the combination process should also be considered.https://www.mdpi.com/2227-7390/11/18/3806forecast combinationstime seriesmathematicspredictabilityinflationefficiency |
| spellingShingle | Pablo Pincheira-Brown Andrea Bentancor Nicolás Hardy An Inconvenient Truth about Forecast Combinations Mathematics forecast combinations time series mathematics predictability inflation efficiency |
| title | An Inconvenient Truth about Forecast Combinations |
| title_full | An Inconvenient Truth about Forecast Combinations |
| title_fullStr | An Inconvenient Truth about Forecast Combinations |
| title_full_unstemmed | An Inconvenient Truth about Forecast Combinations |
| title_short | An Inconvenient Truth about Forecast Combinations |
| title_sort | inconvenient truth about forecast combinations |
| topic | forecast combinations time series mathematics predictability inflation efficiency |
| url | https://www.mdpi.com/2227-7390/11/18/3806 |
| work_keys_str_mv | AT pablopincheirabrown aninconvenienttruthaboutforecastcombinations AT andreabentancor aninconvenienttruthaboutforecastcombinations AT nicolashardy aninconvenienttruthaboutforecastcombinations AT pablopincheirabrown inconvenienttruthaboutforecastcombinations AT andreabentancor inconvenienttruthaboutforecastcombinations AT nicolashardy inconvenienttruthaboutforecastcombinations |