a b s t r a c tA semiparametric fixed effects model is introduced to describe the nonlinear trending phenomenon in panel data analysis and it allows for the cross-sectional dependence in both the regressors and the residuals. A pooled semiparametric profile likelihood dummy variable approach based on the firststage local linear fitting is developed to estimate both the parameter vector and the nonlinear time trend function. As both the time series length T and the cross-sectional size N tend to infinity, the resulting estimator of the parameter vector is asymptotically normal with a root-(NT ) convergence rate.Meanwhile, the asymptotic distribution for the nonparametric estimator of the trend function is also established with a root-(NTh) convergence rate. Two simulated examples are provided to illustrate the finite sample performance of the proposed method. In addition, the proposed model and estimation method are applied to a CPI data set as well as an input-output data set.

We introduce methods and theory for functional or curve time series with longrange dependence. The temporal sum of the curve process is shown to be asymptotically normally distributed, the conditions for this covering a functional version of fractionally integrated autoregressive moving averages. We also construct an estimate of the long-run covariance function, which we use, via functional principal component analysis, in estimating the orthonormal functions spanning the dominant sub-space of the curves. In a semiparametric context, we propose an estimate of the memory parameter and establish its consistency. A Monte-Carlo study of finitesample performance is included, along with two empirical applications. The first of these finds a degree of stability and persistence in intra-day stock returns. The second finds similarity in the extent of long memory in incremental age-specific fertility rates across some developed nations.

In this paper we consider estimation of common structural breaks in panel data models with interactive fixed effects which are unobservable. We introduce a penalized principal component (PPC) estimation procedure with an adaptive group fused LASSO to detect the multiple structural breaks in the models. Under some mild conditions, we show that with probability approaching one the proposed method can correctly determine the unknown number of breaks and consistently estimate the common break dates. Furthermore, we estimate the regression coefficients through the post-LASSO method and establish the asymptotic distribution theory for the resulting estimators. The developed methodology and theory are applicable to the case of dynamic panel data models. The Monte Carlo simulation results demonstrate that the proposed method works well in finite samples with low false detection probability when there is no structural break and high probability of correctly estimating the break numbers when the structural breaks exist. We finally apply our method to study the environmental Kuznets curve for 74 countries over 40 years and detect two breaks in the data.

Summary  This paper is concerned with developing a non‐parametric time‐varying coefficient model with fixed effects to characterize non‐stationarity and trending phenomenon in a non‐linear panel data model. We develop two methods to estimate the trend function and the coefficient function without taking the first difference to eliminate the fixed effects. The first one eliminates the fixed effects by taking cross‐sectional averages, and then uses a non‐parametric local linear method to estimate both the trend and coefficient functions. The asymptotic theory for this approach reveals that although the estimates of both the trend function and the coefficient function are consistent, the estimate of the coefficient function has a rate of convergence of (Th)−1/2, which is slower than (NTh)−1/2 as the rate of convergence for the estimate of the trend function. To estimate the coefficient function more efficiently, we propose a pooled local linear dummy variable approach. This is motivated by a least squares dummy variable method proposed in parametric panel data analysis. This method removes the fixed effects by deducting a smoothed version of cross‐time average from each individual. It estimates both the trend and coefficient functions with a rate of convergence of (NTh)−1/2. The asymptotic distributions of both of the estimates are established when T tends to infinity and N is fixed or both T and N tend to infinity. Both the simulation results and real data analysis are provided to illustrate the finite sample behaviour of the proposed estimation methods.

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In this paper, we consider semiparametric estimation in a partially linear singleindex panel data model with fixed effects. Without taking the difference explicitly, we propose using a semiparametric minimum average variance estimation (SMAVE) based on a dummy-variable method to remove the fixed effects and obtain consistent estimators for both the parameters and the unknown link function. As both the cross section size and the time series length tend to infinity, we not only establish an

This paper introduces a new specification for the heterogeneous autoregressive (HAR) model for the realized volatility of S&P 500 index returns. In this modelling framework, the coefficients of the HAR are allowed to be time-varying with unspecified functional forms. The local linear method with the cross-validation (CV) bandwidth selection is applied to estimate the time-varying coefficient HAR (TVC-HAR) model, and a bootstrap method is used to construct the point-wise confidence bands for the coefficient functions. Furthermore, the asymptotic distribution of the proposed local linear estimators of the TVC-HAR model is established under some mild conditions. The results of the simulation study show that the local linear estimator with CV bandwidth selection has favorable finite sample properties. The outcomes of the conditional predictive ability test indicate that the proposed nonparametric TVC-HAR model outperforms the parametric HAR and its extension to HAR with jumps and/or GARCH in terms of multi-step out-of-sample forecasting, in particular in the post-2003 crisis and 2007 GFC periods, during which financial market volatilities were unduly high.

In this paper, we propose a new diagnostic test for residual cross-section uncorrelatedness (CU) in a nonparametric panel data model. The proposed nonparametric CU test is a nonparametric counterpart of an existing parametric cross-section dependence test proposed in Pesaran (2004, Cambridge Working paper in Economics 0435). Without assuming cross-section independence, we establish asymptotic distribution for the proposed test statistic for the case where both the cross-section dimension and the time dimension go to infinity simultaneously, and then analyze the power function of the proposed test under a sequence of local alternatives that involve a nonlinear multifactor model. The simulation results and real data analysis show that the nonparametric CU test associated with an asymptotic critical value works well.