تجسم عملکرد الگوریتم پیش بینی با استفاده از سری زمانی به عنوان مثال فضاها   Visualising forecasting algorithm performance using time series instance spaces

1. Introduction The M3 data (Makridakis & Hibon, 2000) are used widely for testing the performances of new forecasting algorithms. These 3003 series have become the de facto standard test base in forecasting research. When a new univariate forecasting method is proposed, it is unlikely to receive any further attention or be adopted unless it performs better on the M3 data than other published algorithms. gorithms. We see several problems with this approach. The M3 dataset was a convenience sample that was collected from several disciplines, namely demography, finance, business and economics. All of the data were positive, with series lengths ranging from 14 to 126, and were observed annually, quarterly or monthly (apart from 174 ‘‘other’’ series, whose frequencies of observation were not provided). Methods that work well on this data set may overfit data with similar data structures. Thus, testing algorithms on this data set will tend to favour forecasting methods that work well with data from these domains, and of these lengths and frequencies. Furthermore, there is no guarantee that the series will be in any way ‘‘representative’’ of the types of data that are found within those domains, as is noted in the subsequent discussion of the M3 data (Ord, 2001). Finally, given that 15 years have elapsed since the M3 results were published, it is highly likely that the patterns seen within typical time series will have changed over time, even within the collection constraints of the competition. There has been no attempt in the published M3 results to study why some methods perform better on certain series than other methods. Is it just chance, or do some time series have particular features that make them particularly amenable to being forecast by one method rather than another? In discussing the M3 results, Lawrence (2001) wrote,