A comparison of some out-of-sample tests of predictability in iterated multi-step-ahead forecasts

We consider tests of equal population forecasting ability when mean squared prediction error is the metric for forecasting ability, the two competing models are nested, and the iterated method is used to obtain multistep forecasts. We use Monte Carlo simulations to explore the size and power of the MSPE-adjusted test of Clark and West (2006, 2007) (CW) and the Diebold–Mariano–West (DMW) test. The empirical size of the CW test is almost always tolerable: across a set of 252 simulation results that span 5 DGPs, 9 horizons, and various sample sizes, the median size of nominal 10% tests is 8.8%. The comparable figure for the DMW test, which is generally undersized, is 2.2%. An exception for DMW occurs for long horizon forecasts and processes that quickly revert to the mean, in which case CW and DMW perform comparably. We argue that this is to be expected, because at long horizons the two competing models are both forecasting the process to have reverted to its mean. An exception for CW occurs with a nonlinear DGP, in which CW is usually oversized. CW has greater power and greater size adjusted power than does DMW in virtually all DGPs, horizons and sample sizes. For both CW and DMW, power tends to fall with the horizon, reflecting the fact that forecasts from the two competing models both converge towards the mean as the horizon grows. Consistent with these results, in an empirical exercise comparing models for inflation, CW yields many more rejections of equal forecasting ability than does DMW, with most of the rejections occurring at short horizons.