Use of recurrence plot and recurrence quantification analysis in Taiwan unemployment rate time series

Abstract

The aim of the article is to answer the question if the Taiwan unemployment rate dynamics is generated by a non-linear deterministic dynamic process. This paper applies a recurrence plot and recurrence quantification approach based on the analysis of non-stationary hidden transition patterns of the unemployment rate of Taiwan. The case study uses the time series data of the Taiwan’s unemployment rate during the period from 1978/01 to 2010/06. The results show that recurrence techniques are able to identify various phases in the evolution of unemployment transition in Taiwan.

Introduction

Understanding, modeling, and forecasting the evolution of an employment system in the labor market is a hard task. The movement of the monthly Taiwan unemployment rate (UR) over the course of the business cycle is nonlinear. Such nonlinear dynamic behavior is said to be asymmetric in the sense that the UR increases rapidly in recessions and falls slowly in the subsequent expansions. Cyclical asymmetry of this dynamic behavior is inconsistent with the conventional linear time-series tools used in the analysis of UR data [1]. There has recently been considerable interest in chaotic dynamics in a variety of disciplines, especially in economic time series [2]. Using the postwar US quarterly UR series, Rothman [3] was the first to correctly identify asymmetric evidence within a Markov chain context. Brock and Sayers [4] applied the Grassberger–Procaccia’s dimension calculation algorithm [5] to support the claim that the US UR is generated by a set of states in the labor market’s state space with very special properties, which is said to be a chaotic attractor. Amos and Jeffrey [6] successfully built a nonlinear, nonparametric model to forecast the US UR and suggested that the unemployment data are highly nonlinear and chaotic. Strong evidence of nonlinear behavior was also found by Rita and Timo [7], as well as by Teräsvirta and Anderson [8] when they tested thirteen OECD UR series for linearity against several nonlinear alternatives.

To suggest that UR data is chaotic, would assume that such employment systems in the labor market are ultimately very unstable. The complex interaction of macroeconomic systems makes the UR oscillation extremely irregular. We assume that the system of Taiwan labor markets can be thought of as a complex dynamical process, may be chaotic, that are continuously subjected to and updated by many nonlinear feed-forward and feedback inputs. The aim of the paper is to answer the question if the Taiwan employment market dynamics is generated by a non-linear deterministic dynamic process. To solve this complex problem requires using complicated computational operations to analyze the historical UR data input. To overcome this barrier a statistical physics/non-linear dynamics method called visual recurrence analysis (VRA) is applied in this study. This method allows us to visualize the phase space reconstructed from the UR time series in the so-called recurrent plot (RP). The RP was conceived originally to detect nonlinearities and eventually chaotic dynamics in experimental signals in physics, but it has been used recently to identify changes of dynamic patterns in time series in many other fields, for instance in financial data time series [9], [10] and ecosystem time series [11]. Further, it quantifies various geometric structures occurring in the RPs in the so-called recurrent quantification analysis (RQA). The RQA provides us more exact measures on the nature of the underlying process generating the time series.

The remainder of this paper is organized as follows. Section 2 introduces RP and RQA. Results with RP and RQA analysis for Taiwan’s URs are presented in Section 3. Finally, Section 4 summarizes the conclusions.