Sainan Jin

Spectral Density Estimation and Robust Hypothesis Testing Using Steep Origin Kernels Without Truncation

In this paper, we construct a new class of kernel by exponentiating conventional kernels and use them in the long run variance estimation with and without smoothing. Depending on whether the exponent is allowed to grow with the sample size, we establish different asymptotic approximations to the sampling distribution of the proposed estimator. When the exponent is passed to infinity with the sample size, the new estimator is consistent and shown to be asymptotically normal. When the exponent is fixed, the new estimator is inconsistent and has a nonstandard limiting distribution. It is shown via Monte Carlo experiments that, when the chosen exponent is small in practical applications, the nonstandard limit theory provides better approximations to the finite sampling distributions of the spectral density estimator and the associated test statistic in regression settings.

The KPSS Test with Seasonal Dummies

It is shown that the KPSS test for stationarity may be applied without change to regressions with seasonal dummies. In particular, the limit distribution of the KPSS statistic is the same under both the null and alternative hypotheses whether or not seasonal dummies are used.

A Nonparametric Poolability Test for Panel Data Models with Cross Section Dependence

In this article we propose a nonparametric test for poolability in large dimensional semiparametric panel data models with cross-section dependence based on the sieve estimation technique. To construct the test statistic, we only need to estimate the model under the alternative. We establish the asymptotic normal distributions of our test statistic under the null hypothesis of poolability and a sequence of local alternatives, and prove the consistency of our test. We also suggest a bootstrap method as an alternative way to obtain the critical values. A small set of Monte Carlo simulations indicate the test performs reasonably well in finite samples.

Robustify Financial Time Series Forecasting with Bagging

In this paper we propose a revised version of (bagging) bootstrap aggregating as a forecast combination method for the out-of-sample forecasts in time series models. The revised version explicitly takes into account the dependence in time series data and can be used to justify the validity of bagging in the reduction of mean squared forecast error when compared with the unbagged forecasts. Monte Carlo simulations show that the new method works quite well and outperforms the traditional one-step-ahead linear forecast as well as the nonparametric forecast in general, especially when the in-sample estimation period is small. We also find that the bagging forecasts based on misspecified linear models may work as effectively as those based on nonparametric models, suggesting the robustification property of bagging method in terms of out-of-sample forecasts. We then reexamine forecasting powers of predictive variables suggested in the literature to forecast the excess returns or equity premium. We find that, consistent with Goyal and Welch (2008), the historical average excess stock return forecasts may beat other predictor variables in the literature when we apply traditional one-step linear forecast and the nonparametric forecasting methods. However, when using the bagging method or its revised version, which help to improve the mean squared forecast error for “unstable” predictors, the predictive variables have a better forecasting power than the historical mean.

Power Maximization and Size Control in Heteroskedasticity and Autocorrelation Robust Tests with Exponentiated Kernels

Using the power kernels of Phillips, Sun and Jin (2006, 2007), we examine the large sample asymptotic properties of the t-test for different choices of power parameter (rho). We show that the nonstandard fixed-rho limit distributions of the t-statistic provide more accurate approximations to the finite sample distributions than the conventional large-rho limit distribution. We prove that the second-order corrected critical value based on an asymptotic expansion of the nonstandard limit distribution is also second-order correct under the large-rho asymptotics. As a further contribution, we propose a new practical procedure for selecting the test-optimal power parameter that addresses the central concern of hypothesis testing: the selected power parameter is test-optimal in the sense that it minimizes the type II error while controlling for the type I error. A plug-in procedure for implementing the test-optimal power parameter is suggested. Simulations indicate that the new test is as accurate in size as the nonstandard test of Kiefer and Vogelsang (2002a, 2002b; KV), and yet it does not incur the power loss that often hurts the performance of the latter test. The new test therefore combines the advantages of the KV test and the standard (MSE optimal) HAC test while avoiding their main disadvantages (power loss and size distortion, respectively). The results complement recent work by Sun, Phillips and Jin (2008) on conventional and bT HAC testing.

Testing the Martingale Hypothesis

We propose new tests of the martingale hypothesis based on generalized versions of the Kolmogorov–Smirnov and Cramér–von Mises tests. The tests are distribution-free and allow for a weak drift in the null model. The methods do not require either smoothing parameters or bootstrap resampling for their implementation and so are well suited to practical work. The article develops limit theory for the tests under the null and shows that the tests are consistent against a wide class of nonlinear, nonmartingale processes. Simulations show that the tests have good finite sample properties in comparison with other tests particularly under conditional heteroscedasticity and mildly explosive alternatives. An empirical application to major exchange rate data finds strong evidence in favor of the martingale hypothesis, confirming much earlier research.

Robust Forecast Comparison

Forecast accuracy is typically measured in terms of a given loss function. However, as a consequence of the use of misspecified models in multiple model comparisons, relative forecast rankings are loss function dependent. This paper addresses this issue by using a novel criterion for forecast evaluation which is based on the entire distribution of forecast errors. We introduce the concepts of general-loss (GL) forecast superiority and convex-loss (CL) forecast superiority, and we establish a mapping between GL (CL) superiority and first (second) order stochastic dominance. This allows us to develop a forecast evaluation procedure based on an out-of-sample generalization of the tests introduced by Linton, Maasoumi and Whang (2005). The asymptotic null distributions of our test statistics are nonstandard, and resampling procedures are used to obtain the critical values. Additionally, the tests are consistent and have nontrivial local power under a sequence of local alternatives. In addition to the stationary case, we outline theory extending our tests to the case of heterogeneity induced by distributional change over time. Monte Carlo simulations suggest that the tests perform reasonably well in finite samples; and an application to exchange rate data indicates that our tests can help identify superior forecasting models, regardless of loss function.

Sieve estimation of time-varying panel data models with latent structures

We propose a heterogeneous time-varying panel data model with a latent group structure that allows the coefficients to vary over both individuals and time. We assume that the coefficients change smoothly over time and form different unobserved groups. When treated as smooth functions of time, the individual functional coefficients are heterogeneous across groups but homogeneous within a group. We propose a penalized-sieve-estimation-based classifier-Lasso (C-Lasso) procedure to identify the individuals’ membership and to estimate the group-specific functional coefficients in a single step. The classification exhibits the desirable property of uniform consistency. The C-Lasso estimators and their post-Lasso versions achieve the oracle property so that the group-specific functional coefficients can be estimated as well as if the individuals’ membership were known. Several extensions are discussed. Simulations demonstrate excellent finite sample performance of the approach in both classification and estimation. We apply our method to study the heterogeneous trending behavior of GDP per capita across 91 countries for the period 1960–2012 and find four latent groups.

Forecasting the car penetration rate (CPR) in China: a nonparametric approach

With strong economic growth, the auto industry has made great breakthroughs in recent years and has become a backbone industry in China, while cars play an increasingly important role, and are now the principal part of the auto industry. Both Chinas government and academic circles take strong interest in the prediction of CPR (i.e. car penetration rate or cars per thousand people), which will be the main guidance for the future industry policy. We summarize the existing problems in recent research and propose to use nonparametric methods to estimate the CPR and its elasticity with respect to GDP per capita (GDPPC). The results indicate that the nonparametric methods provide a much better fit than the conventional OLS method, and more importantly, it captures the nonlinearity of the elasticity of CPR with respect to GDPPC. Finally, we predict future CPR in China.

Adaptive Nonparametric Regression with Conditional Heteroskedasticity

In this paper, we study adaptive nonparametric regression estimation in the presence of conditional heteroskedastic error terms. We demonstrate that both the conditional mean and conditional variance functions in a nonparametric regression model can be estimated adaptively based on the local profile likelihood principle. Both the one-step Newton-Raphson estimator and the local profile likelihood estimator are investigated. We show that the proposed estimators are asymptotically equivalent to the infeasible local likelihood estimators (e.g., Aerts and Claeskens, 1997), which require knowledge of the error distribution. Simulation evidence suggests that when the distribution of the error term is different from Gaussian, the adaptive estimators of both conditional mean and variance can often achieve significant efficiency over the conventional local polynomial estimators. JEL classifications: C13, C14