This paper bridges the gap between processes where shocks are permanent and those with transitory shocks by formulating a process in which the long-run impact of each innovation is time-varying and stochastic. In the stochastic permanent breaks (STOPBREAK) process, frequent transitory shocks are supplemented by occasional permanent shifts. Consistency and asymptotic normality of quasi-maximum-likelihood estimates is established, and locally best hypothesis tests of the null of a random walk are developed. The model is applied to relative prices of pairs of stocks and significant test statistics result.

A bstract-We discuss the problem of testing for constant versus time varying regression coefficients. Our alternative hypothesis allows the coefficients to follow a stationary AR(1) process with unknown autoregressive parameter. Standard testing procedures are inappropriate since this parameter is identified only under the alternative. We propose a test statistic which is a function of a sequence of Score statistics, and depends only on the regressors and the OLS residuals. The distribution of the test statistic is discussed, power and size are investigated using Monte Carlo methods, and an empirical example investigating stability in the gold and silver markets is presented.

We revisit the relation between stock market volatility and macroeconomic activity using a new class of component models that distinguish short-run from long-run movements. We formulate models with the long-term component driven by inflation and industrial production growth that are in terms of pseudo out-of-sample prediction for horizons of one quarter at par or outperform more traditional time series volatility models at longer horizons. Hence, imputing economic fundamentals into volatility models pays off in terms of long-horizon forecasting. We also find that macroeconomic fundamentals play a significant role even at short horizons.