Time series forecasting has a rich research history, with a variety of use cases across diverse domains. Many machine learning and deep learning forecasting algorithms approach the problem as regression by windowing. Given a univariate time series \(Y=(y_1,...,y_T)\) , a training set of input-output pairs \((x_i, y_i)\) is constructed where the input window \(x_i=(y_{i-p+1},...,y_i)\) contains the most recent p observations, and the target variable \(z_i\) is a future value \(y_{i+h}\) , with h as the forecasting horizon. We call this approach time series forecasting regression (TSFR). Recently, an alternative type of problem, time series extrinsic regression (TSER), has been described. In TSER, each training instance is a complete time series \(\boldsymbol{X}_i \subset \Re \) , assumed independent of the others, paired with an external response variable \(z_i \subset \Re \) . Unlike TSFR, the response is not a future point of the same series but an exogenous variable to be predicted from the overall dynamics of the series. An archive of 63 TSER datasets was released in 2024. Our aim is to bridge the gap between TSER and TSFR by providing a common framework for both. We reformat a selection of diverse series used in forecasting research as TSER problems through windowing and create train/test splits. We then compare state-of-the-art TSER algorithms on these data and benchmark them against standard statistical and deep learning approaches. We find that the pattern of results seen on the TSFR archive does not mirror that on the TSER data. We propose a simple reformulation that allows the best TSER algorithm to achieve performance equivalent to statistical forecasters.

错误:搜索内容不能为空,请输入英文关键词
错误:关键词超出字数限制,请精简
高级检索

Time Series Extrinsic Regression Algorithms for Forecasting Long Time Series with a Short Horizon

  • Alexander Banwell,
  • Anthony Bagnall

摘要

Time series forecasting has a rich research history, with a variety of use cases across diverse domains. Many machine learning and deep learning forecasting algorithms approach the problem as regression by windowing. Given a univariate time series \(Y=(y_1,...,y_T)\) , a training set of input-output pairs \((x_i, y_i)\) is constructed where the input window \(x_i=(y_{i-p+1},...,y_i)\) contains the most recent p observations, and the target variable \(z_i\) is a future value \(y_{i+h}\) , with h as the forecasting horizon. We call this approach time series forecasting regression (TSFR). Recently, an alternative type of problem, time series extrinsic regression (TSER), has been described. In TSER, each training instance is a complete time series \(\boldsymbol{X}_i \subset \Re \) , assumed independent of the others, paired with an external response variable \(z_i \subset \Re \) . Unlike TSFR, the response is not a future point of the same series but an exogenous variable to be predicted from the overall dynamics of the series. An archive of 63 TSER datasets was released in 2024. Our aim is to bridge the gap between TSER and TSFR by providing a common framework for both. We reformat a selection of diverse series used in forecasting research as TSER problems through windowing and create train/test splits. We then compare state-of-the-art TSER algorithms on these data and benchmark them against standard statistical and deep learning approaches. We find that the pattern of results seen on the TSFR archive does not mirror that on the TSER data. We propose a simple reformulation that allows the best TSER algorithm to achieve performance equivalent to statistical forecasters.