Is the annual growth rate in balance of trade time series for Ireland nonlinear

TL;DR

This paper introduces the TSMARS method for modeling nonlinear structures in time series and applies it to Irish trade balance data, revealing nonlinear dynamics and long-range effects.

Contribution

The paper presents TSMARS as a new approach for identifying nonlinear patterns in time series data, demonstrated on Irish trade balance data.

Findings

Trade balance change is nonlinear and has weak long-range effects.

Pre-1993 data shows a significant linear component, suggesting over-smoothing in earlier models.

Post-1993 data indicates increased nonlinearity and complexity.

Abstract

We describe the Time Series Multivariate Adaptive Regressions Splines (TSMARS) method. This method is useful for identifying nonlinear structure in a time series. We use TSMARS to model the annual change in the balance of trade for Ireland from 1970 to 2007. We compare the TSMARS estimate with long memory ARFIMA estimates and long-term parsimonious linear models. We show that the change in the balance of trade is nonlinear and possesses weakly long range effects. Moreover, we compare the period prior to the introduction of the Intrastat system in 1993 with the period from 1993 onward. Here we show that in the earlier period the series had a substantial linear signal embedded in it suggesting that estimation efforts in the earlier period may have resulted in an over-smoothed series.