STATIONARY PROCESSES THAT LOOK LIKE RANDOM WALKS— THE BOUNDED RANDOM WALK PROCESS IN DISCRETE AND CONTINUOUS TIME

Several economic and financial time series are bounded by an upper and lower finite limit (e.g., interest rates). It is not possible to say that these time series are random walks because random walks are limitless with probability one (as time goes to infinity). Yet, some of these time series behav...

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Bibliographic Details
Published in:	Econometric theory 2002-02, Vol.18 (1), p.99-118
Main Author:	Nicolau, João
Format:	Article
Language:	eng
Subjects:	Differential equations Econometrics Economic models Ergodic theory Exchange rates Foreign exchange rates Hypotheses Interest rates Mathematical independent variables Musical intervals Random walk Stationary processes Time series Volatility
Online Access:	Get full text
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Summary:	Several economic and financial time series are bounded by an upper and lower finite limit (e.g., interest rates). It is not possible to say that these time series are random walks because random walks are limitless with probability one (as time goes to infinity). Yet, some of these time series behave just like random walks. In this paper we propose a new approach that takes into account these ideas. We propose a discrete-time and a continuous-time process (diffusion process) that generate bounded random walks. These paths are almost indistinguishable from random walks, although they are stochastically bounded by an upper and lower finite limit. We derive for both cases the ergodic conditions, and for the diffusion process we present a closed expression for the stationary distribution. This approach suggests that many time series with random walk behavior can in fact be stationarity processes.
ISSN:	0266-4666 1469-4360