Abstract
This paper deals with instability in regression coefficients. We propose a Bayesian regression model with time-varying coefficients (TVC) that allows to jointly estimate the degree of instability and the time-path of the coefficients. Thanks to the computational tractability of the model and to the fact that it is fully automatic, we are able to run Monte Carlo experiments and analyze its finite-sample properties. We find that the estimation precision and the forecasting accuracy of the TVC model compare favorably to those of other methods commonly employed to deal with parameter instability. A distinguishing feature of the TVC model is its robustness to mis-specification: Its performance is also satisfactory when regression coefficients are stable or when they experience discrete structural breaks. As a demonstrative application, we used our TVC model to estimate the exposures of S&P 500 stocks to market-wide risk factors: We found that a vast majority of stocks had time-varying exposures and the TVC model helped to better forecast these exposures.
Highlights
This paper deals with instability in regression coefficients
We find that the estimation precision and the forecasting accuracy of the time-varying coefficients (TVC) model compare favorably to those of other methods commonly employed to deal with parameter instability
We have proposed a Bayesian regression model with time-varying coefficients (TVC) that has low computational requirements because it allows one to derive analytically the posterior distribution of coefficients, as well as the posterior probability that they are stable
Summary
We consider a dynamic linear model (according to West and Harrison 1997) with time-varying regression coefficients: yt = xt β t + vt (1). Where xt is a 1 × k vector of observable explanatory variables, β t is a k × 1 vector of unobservable regression coefficients, and vt is an i.i.d. disturbance with normal distribution having zero mean and variance V. The vector of coefficients β t is assumed to evolve according to the following equation:. Where wt is an i.i.d. k × 1 vector of disturbances having a multivariate normal distribution with mean of zero and covariance matrix W. wt is contemporaneously and serially independent of vt. A MATLAB function is made available on the internet at https://www.statlect.com/time_varying_regression.htm. Where y is a T × 1 vector of observations on the dependent variable and X is a T × K matrix of regressors
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