Time Series Model Identification in the Frame of Random Walk Model
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In principle, any stochastic process can be expressed in the frame of the random walk model (RWM) because it equals to the sum of its regular increments (or errors), with its initial value equal to 0. Using this intrinsic versatility of the RWM, we herein demonstrate that the RWM can serve as a useful frame for identifying the underlying time series models. This is done by reparametrization of the RWM based on the “linear dependency of error”. Our approach is applied to various time series models (e.g., stationary processes, trend stationary process (TSP), mixture model, asymmetric difference, fractional Brownian motion and symmetric α-stable self-similar stationary increment process). As an empirical application of our approach, we discuss the well-known RWM vs. TSP controversy over macroeconomic time series.
Abstract
In principle, any stochastic process can be expressed in the frame of the random walk model (RWM) because it equals to the sum of its regular increments (or errors), with its initial value equal to 0. Using this intrinsic versatility of the RWM, we herein demonstrate that the RWM can serve as a useful frame for identifying the underlying time series models. This is done by reparametrization of the RWM based on the “linear dependency of error”. Our approach is applied to various time series models (e.g., stationary processes, trend stationary process (TSP), mixture model, asymmetric difference, fractional Brownian motion and symmetric α-stable self-similar stationary increment process). As an empirical application of our approach, we discuss the well-known RWM vs. TSP controversy over macroeconomic time series.
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