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.