A spurious regression occurs when a pair of independent series, but with strong temporal properties, are found apparently to be related according to standard inference in an OLS regression. Although this is well known to occur with pairs of independent unit root processes, this paper finds evidence that similar results are found with positively autocorrelated autoregressive series or long moving averages. This occurs regardless of the sample size and for various distributions of the error terms.
on all empirical results, reported and unreported, can be obtained from the corresponding author. econometric tools. Indeed, various recent studies show that neglecting occasional breaks may lead to a spurious finding of long-memory properties. In this paper we focus on this issue within the context of out-of-sample forecasting. First, we show that indeed data with breaks can be viewed as long-memory data. Next, we compare time series models with structural breaks, models with long-memory and linear autoregressive models for 23 monthly US inflation rates in terms of out-of-sample forecasting for various horizons. A key finding is that the linear models do not perform as well as the other two, and that the model with breaks and the model with long memory perform about equally well. We also examine their joint performance by combining the forecasts. A by-product of our empirical analysis is that we can relate the value of the long-memory parameter with the number of detected breaks, in which case we find a strong positive relationship.
A spurious regression occurs when a pair of independent series, but with strong temporal properties, are found apparently to be related according to standard inference in an OLS regression. Although this is well known to occur with pairs of independent unit root processes, this paper finds evidence that similar results are found with positively autocorrelated autoregressive series on long moving averages. This occurs regardless of the sample size and for various distributions of the error terms.
Consider the portfolio problem of choosing the mix between stocks and bonds under a downside risk constraint. Typically stock returns exhibit fatter tails than bonds corresponding to their greater downside risk. Downside risk criteria like the safety …rst criterion therefore often select corner solutions in the sense of a bonds only portfolio. This is due to a focus on the asymptotically dominating …rst order Pareto term of the portfolio return distribution. We show that if second order terms are taken into account, a balanced solution emerges. The theory is applied to empirical examples from the literature.
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