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on Econometric Time Series |
| By: | David I. Harvey; Stephen J. Leybourne; Emily J. Whitehouse |
| Abstract: | In this paper, we show that when computing standard Diebold-Mariano-type tests for equal forecast accuracy and forecast encompassing, the long-run variance can frequently be negative when dealing with multi-step-ahead predictions in small, but empirically relevant, sample sizes. We subsequently consider a number of alternative approaches to dealing with this problem, including direct inference in the problem cases and use of long-run variance estimators that guarantee positivity. The finite sample size and power of the different approaches are evaluated using extensive Monte Carlo simulation exercises. Overall, for multi-step-ahead forecasts, we find that the recently proposed Coroneo and Iacone (2016) test, which is based on a weighted periodogram long-run variance estimator, offers the best finite sample size and power performance. |
| Keywords: | Forecast evaluation; Long-run variance estimation; Simulation; Diebold-Mariano test; Forecasting JEL classification: C2 |
| URL: | http://d.repec.org/n?u=RePEc:not:notgts:17/03&r=ets |
| By: | David I. Harvey; Stephen J. Leybourne; Emily J. Whitehouse |
| Abstract: | In this paper we examine the local power of unit root tests against globally stationary exponential smooth transition autoregressive [ESTAR] alternatives under two sources of uncertainty: the degree of nonlinearity in the ESTAR model, and the presence of a linear deterministric trend. First we show that the Kapetanios, Shin and Snell (2003, Journal of Econometrics, 112, 359-379) [KSS] test for nonlinear stationarity has local asymptotic power gains over standard Dickey-Fuller [DF] tests for certain degrees of nonlinearity in the ESTAR model, but that for other degrees of nonlinearity, the linear DF test has superior power. Second, we derive limiting distributions of demeaned, and demeaned and detrended KSS and DF tests under a local ESTAR alternative when a local trend is present in the DGP. We show that the power of the demeaned tests outperforms that of the detrended tests when no trend is present in the DGP, but deteriorates as the magnitude of the trend increases. We propose a union of rejections testing procedure that combines all four individual tests and show that this captures most of the power available from the individual tests across different degrees of nonlinearity and trend magnitudes. We also show that incorporating a trend detection procedure into this union testing strategy can result in higher power when a large trend is present in the DGP. |
| Keywords: | Nonlinearity, Trend uncertainty, Union of rejections JEL classification: C12, C22, C53 |
| URL: | http://d.repec.org/n?u=RePEc:not:notgts:17/02&r=ets |
| By: | Benjamin Wong |
| Abstract: | Half-lives are summary measures of persistence, and are usually characterized from impulse response functions (IRFs) of univariate time series models. Two issues which occur with half-life characterization in multivariate time series are IRFs become conditional on specific shocks and are often also not uniquely identified. I introduce an approach for characterizing the half-life in multivariate time series models which circumvents both issues. An empirical application suggests the half-life of the real exchange rate estimated from multivariate models is generally longer relative to univariate models. |
| Keywords: | Half-Life, Purchasing Power Parity, Multivariate Information |
| JEL: | C31 F41 |
| Date: | 2017–07 |
| URL: | http://d.repec.org/n?u=RePEc:een:camaaa:2017-47&r=ets |
| By: | James Morley; Benjamin Wong |
| Abstract: | We demonstrate how Bayesian shrinkage can address problems with utilizing large information sets to calculate trend and cycle via a multivariate Beveridge-Nelson (BN) decomposition. We illustrate our approach by estimating the U.S. output gap with large Bayesian vector autoregressions that include up to 138 variables. Because the BN trend and cycle are linear functions of historical forecast errors, we are also able to account for the estimated output gap in terms of different sources of information, as well as particular underlying structural shocks given identification restrictions. Our empirical analysis suggests that, in addition to output growth, the unemployment rate, CPI inflation, and, to a lesser extent, housing starts, consumption, stock prices, real M1, and the federal funds rate are important conditioning variables for estimating the U.S. output gap, with estimates largely robust to incorporating additional variables. Using standard identification restrictions, we find that the role of monetary policy shocks in driving the output gap is small, while oil price shocks explain about 10% of the variance over different horizons. |
| Keywords: | Beveridge-Nelson decomposition, output gap, Bayesian estimation, multivariate information |
| JEL: | C18 E17 E32 |
| Date: | 2017–07 |
| URL: | http://d.repec.org/n?u=RePEc:een:camaaa:2017-46&r=ets |