Chapter 3: Random walks and non-linear paths in macroeconomic time series: some evidence and implications
Franco Bevilacqua and Adriaan van Zon 1. INTRODUCTION The aim of this chapter is to identify the nature of the dynamics of macroeconomic time series. When time series are characterized by zero autocorrelation for all possible leads and lags, the issue of distinguishing between deterministic and stochastic components becomes an impossible task when linear methods are used (Hommes 1998). This impasse arises because linear methods are appropriate to detect regularities in time series like autocorrelations and dominant frequencies (Conover 1971, Oppenheim and Schafer 1989), while ﬂuctuations in real economic time series are generally characterized by zero autocorrelation and no dominant frequency. Economic ﬂuctuations seem really similar to background noise, which does not possess dominant frequencies and each noise impulse is not serially correlated. The spectral analysis of economic ﬂuctuations, seemingly as complex as noise, has led many economists to consider ﬂuctuations as identically independently distributed (i.i.d.) events. As a matter of fact the i.i.d. hypothesis is an obvious necessity for all linear models to describe, at least approximately, the irregularities in the observed data. In the past two kinds of linear economic models based on the i.i.d. hypothesis in the residuals have been presented. In the ﬁrst model, known as the deterministic trend model, variables evolve as a function in time along a linear trend. In the second model (the stochastic trend model), variables evolve as a function of their forgoing values and a shock shifts the value of the variable from the lagged value (Rappoport and Reichlin 1989). In...
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