Search

Additional file 3. Fig. S1. Original gel image for long PCR.

Ergodic theorem shows that ergodic averages of the posterior draws converge in probability to the posterior mean under the stationarity assumption. The literature also shows that the posterior distribution is asymptotically normal when the sample size of the original data considered goes to infinity. To the best of our knowledge, there is little discussion on the large sample behaviour of the posterior mean. In this paper, we aim to fill this gap. In particular, we extend the posterior mean idea to the conditional mean case, which is conditioning on a given summary statistics of the original data. We stablish a new asymptotic theory for the conditional mean estimator for the case when both the sample size of the original data concerned and the number of Markov chain Monte Carlo iterations go to infinity. Simulation studies show that this conditional mean estimator has very good finite sample performance. In addition, we employ the conditional mean estimator to estimate a GARCH(1,1) model for S&P 500 stock returns and find that the conditional mean estimator performs better than quasi-maximum likelihood estimation in terms of out-of-sample forecasting.

Ergodic theorem shows that ergodic averages of the posterior draws converge in probability to the posterior mean under the stationarity assumption. The literature

We propose two new nonparametric predictive models: the multi-step nonparametric predictive regression model and the multi-step additive predictive regression model, in which the predictive variables are locally stationary time series. We define estimation methods and establish the large sample properties of these methods in the short horizon and the long horizon case. We apply our methods to stock return prediction using a number of standard predictors such as dividend yield. The empirical results show that all of these models can substantially outperform the traditional linear predictive regression model in terms of both in-sample and out-of-sample performance. In addition, we _nd that these models can always beat the historical mean model in terms of in-sample fitting, and also for some cases in terms of the out-of-sample forecasting. We also compare our methods with the linear regression and historical mean methods according to an economic metric. In particular, we show how our methods can be used to deliver a trading strategy that beats the buy and hold strategy (and linear regression based alternatives) over our sample period.

In this paper, we study a class of high dimensional moment restriction panel data models with interactive effects, where factors are unobserved and factor loadings are nonparametrically unknown smooth functions of individual characteristics variables. We allow the dimension of the parameter vector and the number of moment conditions to diverge with sample size. This is a very general framework and includes many existing linear and nonlinear panel data models as special cases. In order to estimate the unknown parameters, factors and factor loadings, we propose a sieve-based generalized method of moments estimation method and we show that under a set of simple identification conditions, all those unknown quantities can be consistently estimated. Further we establish asymptotic distributions of the proposed estimators. In addition, we propose tests for over-identification, specification of factor loading functions, and establish their large sample properties. Moreover, a number of simulation studies are conducted to examine the performance of the proposed estimators and test statistics in finite samples. An empirical example on stock return prediction is studied to demonstrate the usefulness of the proposed framework and corresponding estimation methods and testing procedures.

In this paper, we introduce a regime switching panel data model with interactive fixed effects. We propose a maximum likelihood estimation method and develop an expectation and conditional maximization algorithm to estimate the unknown parameters. Simulation results show that the algorithm works well in finite samples. The biases of the maximum likelihood estimators are negligible and the root mean squared errors of the maximum likelihood estimators decrease with the increase of either cross-sectional units N or time periods T.