The out-of-sample performance of an exact median-unbiased estimator for the near-unity AR(1) model

Abstract

We analyse the forecasting performance of several strategies when estimating the near-unity AR(1) model. We focus on the Andrews’ (1993) exact median-unbiased estimator (BC), the OLS estimator and the driftless random walk (RW). We also explore two pairwise combinations between these strategies. We do this to investigate whether BC helps in reducing forecast errors. Via simulations, we find that BC forecasts typically outperform OLS forecasts. When BC is compared to the RW we obtain mixed results, favouring the latter while the persistence of the true process increases. Interestingly, we find that the combination of BC-RW performs well in a near-unity scheme.

Keywords:

• Near-unity autoregression
• median-unbiased estimation
• unbiasedness
• unit root model
• forecasting
• forecast combinations

JEL Classification:

• C22
• C52
• C53
• C63

Notes

¹ Some examples – for the AR() also – are the methods of Orcutt and Winokur (1969), Stine and Shaman (1989), Andrews and Chen (1994), Hansen (1999), So and Shin (1999), Roy and Fuller (2001), Kim (2003) and Withers and Nadarajah (2011), among others.

² We use equal weights following the ‘combination puzzle’ (Bates and Granger 1969; Stock and Watson 2004). This states that complex estimations of the weights in a composite forecast do not guarantee a superior out-of-sample performance.

³ We denote the expected value, variance, covariance, and autocovariance with , , , and , respectively.