Optimal Bandwidth Selection in Heteroskedasticity-Autocorrelation Robust Testing∗

By Yixiao Sun, Peter C. B. Phillips, Sainan Jin. 2005

247 citations recorded by the source corpus.

In time series regressions with nonparametrically autocorrelated errors, it is now standard empirical practice to use kernel-based robust standard errors that involve some smoothing function over the sample autocorrelations. The underlying smoothing parameter b, which can be defined as the ratio of the bandwidth (or truncation lag) to the sample size, is a tuning parameter that plays a key role in determining the asymptotic properties of the standard errors and associated semiparametric tests. Small-b asymptotics involve standard limit theory such as standard normal or chi-squared limits, whereas fixed-b asymptotics typically lead to nonstandard limit distributions involving Brownian bridge functionals. The present paper shows that the nonstandard fixed-b limit distributions of such nonparametrically studentized tests provide more accurate approximations to the finite sample distributions than the standard small-b limit distribution. In particular, using asymptotic expansions of both the finite sample distribution and the nonstandard limit distribution, we confirm that the second-order corrected critical value based on the expansion of the nonstandard limiting distribution is also second-order correct under the standard small-b asymptotics. We further show that, for typical economic time series, the optimal bandwidth that minimizes a weighted average of type I and type II errors is larger by an order of magnitude than the bandwidth that minimizes the asymptotic mean squared error of the corresponding long-run variance estimator. A plug-in procedure for implementing this optimal bandwidth is suggested and simulations confirm that the new plug-in procedure works well in finite samples.

Subfields: Economics and Econometrics, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/00affc885c648870f9cc364d11e1d02046e4d370

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Citations in the corpus

A self‐normalized approach to confidence interval construction in time series (2010, methodology): “For heuristic and theoretical explanations of the better size property of the self-normalized approach as compared with the standard approach, we refer the reader to Bunzel et al. (2001) and Sun et al. (2008).”
Inference with dependent data using cluster covariance estimators (2011, background): “Keywords: HAC, panel, robust, spatial JEL Codes: C12, C21, C22, C23”
The Cross-Quantilogram: Measuring Quantile Dependence and Testing Directional Predictability between Time Series (2014, methodology): “viding the original sample into subsamples before applying the self-normalization procedure. 7The ﬁxed-basymptotic has been further studied by Bunzel et al. (2001), Kiefer and Vogelsang (2002, 2005), Sun et al. (2008), Kim and Sun (2011) and Sun and Kim (2012) among others. 13 is necessary to guaran”
Testing for Smooth Structural Changes in Time Series Models via Nonparametric Regression (2012, methodology): “…2), we can show that ĤĥCV also has an asymptotic N(0 1) distribution, where ĤĥCV is computed in the same way as Ĥ , with ĥCV replacing h 8Following Sun, Phillips, and Jin (2008), we may consider a data-driven bandwidth selection by minimizing a weighted average loss function, namely ĥ =…”
Spatial Heteroskedasticity and Autocorrelation Consistent Estimation of Covariance Matrix (2011, methodology): “First, we compare the performance of the spatial HAC estimator based on d̂n with other bandwidth selection procedures and the heteroskedasticity robust covariance estimator of White (1980). We evaluate them using the MSE criterion and the coverage accuracy of the associated CIs.”
Choosing instrumental variables in conditional moment restriction models (2009, background): “However, the criteria we consider do not generally provide the most accurate inference, as recently pointed out by Sun et al. (2007) in another context.”
Low-Frequency Econometrics (2015, background): “…long-run variance estimators (see Kiefer, Vogelsang, and Bunzel (2000) and Kiefer and Vogelsang (2002, 2005), Jansson (2004), Phillips (2005), Sun, Phillips, and Jin (2008), Phillips, Sun and Jin (2006, 2007) and Gonçalves and Vogelsang (2011), and Müller (2014) for a recent survey), and…”
Integrated modified OLS estimation and fixed-b inference for cointegrating regressions (2014, background): “A similar size-power trade-off with respect to kernel and bandwidth choice has been found in Kiefer and Vogelsang (2005) for stationary regressions and it is this trade-off forms the basis of the data dependent bandwidth rule developed by Sun et al. (2008).”
FIXED-b ASYMPTOTICS FOR SPATIALLY DEPENDENT ROBUST NONPARAMETRIC COVARIANCE MATRIX ESTIMATORS (2014, background): “An interesting direction for future research would be to adapt the arguments of Sun, Phillips, and Jin (2008) to the present context.”