  Threshold Autoregressive (TAR) models have been widely used by statisticians
for non-linear time series forecasting during the past few decades, due to
their simplicity and mathematical properties. On the other hand, in the
forecasting community, general-purpose tree-based regression algorithms
(forests, gradient-boosting) have become popular recently due to their ease of
use and accuracy. In this paper, we explore the close connections between TAR
models and regression trees. These enable us to use the rich methodology from
the literature on TAR models to define a hierarchical TAR model as a regression
tree that trains globally across series, which we call SETAR-Tree. In contrast
to the general-purpose tree-based models that do not primarily focus on
forecasting, and calculate averages at the leaf nodes, we introduce a new
forecasting-specific tree algorithm that trains global Pooled Regression (PR)
models in the leaves allowing the models to learn cross-series information and
also uses some time-series-specific splitting and stopping procedures. The
depth of the tree is controlled by conducting a statistical linearity test
commonly employed in TAR models, as well as measuring the error reduction
percentage at each node split. Thus, the proposed tree model requires minimal
external hyperparameter tuning and provides competitive results under its
default configuration. We also use this tree algorithm to develop a forest
where the forecasts provided by a collection of diverse SETAR-Trees are
combined during the forecasting process. In our evaluation on eight publicly
available datasets, the proposed tree and forest models are able to achieve
significantly higher accuracy than a set of state-of-the-art tree-based
algorithms and forecasting benchmarks across four evaluation metrics.
