A Random Coefficients Autoregressive Model with Exogenously-Driven Stochastic Unit Roots

No 609, Working Papers from Department of Economics, University of Missouri

Abstract: We develop a random coefficients autoregressive (RCA) model with time-varying coefficients generated by a bounded nonlinear function of an exogenous time series that may be a mixingale or integrated. Moreover, we allow for exogenously-driven heteroskedasticity in the error term. By restricting the range of the function essentially to the unit interval, we show that the two series of autoregressive coefficients and variances of such a model are covariance stationary, even though these series may be nonergodic. Time series driven by such a data generating process are stationary, but may have (stochastic) unit or near-unit roots over periods of time. Under appropriate assumptions, we show that maximum likelihood estimation yields asymptotically normal or mixed normal parameter estimates. A data generating process of this form may engender commonly observed time series characteristics that defy the simple I(0)-I(1) dichotomy, but is more structural in nature than statistical I(d) models. Moreover, this approach provides a nonspurious way to model relationships between a nonstationary and a stationary time series. The utility of the proposed econometric model is demonstrated with an empirical application, in which inflation drives the autoregressive coefficient of interest rate volatility.

Keywords: random coefficients autoregressive models; stochastic unit roots; nonlinear transformations; mixingales; near-epoch dependent processes; integrated processes; interest rate volatility (search for similar items in EconPapers)
JEL-codes: C13 C22 C32 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm and nep-ets
Date: Written 2006-01-15
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