Pronósticos de series de tiempo macroeconómicas no lineales con TSARX: un estudio comparativo en tres economías

The nonlinearity and seasonality of the business cycle account for the majority of short-run movements in quarterly or monthly macroeconomic time series. The multiplicative seasonal threshold autoregressive model with exogenous inputs (TSARX) combines threshold dynamics, multiplicative seasonality, and external regressor, the model is a special case of a general nonmultiplicative TAR model, but there is limited evidence on how it performs in forecasting relative to simpler models and machine-learning algorithms. We evaluate the performance out-of-sample of TSARX models using seasonally unadjusted macroeconomic time series for three economies (Colombia, the United States of America, and the United Kingdom) and three key variables (gross domestic product (GDP), unemployment rate, and inflation). For each country-variable pair, we compare the TSARX models with four competitor models: a TAR model, a linear seasonal autoregressive model (SAR), Holt-Winters exponential smoothing (ES), and long short-term memory (LSTM) neural networks. Multi-step forecasts at horizons from one to four periods ahead are produced under a rolling-window design, and accuracy is assessed using Mean Squared Error (MSE) and Diebold-Mariano tests (DM) for equal predictive ability. Across 36 series-country-horizon combinations, the TSARX achieves the lowest MSE in three cases and is often statistically indistinguishable from the best benchmark; in many situations simpler models remain di‑cult to beat. These findings show that additional nonlinear and seasonal structure does not guaranty superior forecasts and that the benefits of the TSARX models are context- and horizon-dependent.