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A useful strategy to examine serial correlation in panel regression models is to adopt serially correlated error terms. The random effect is also present to address the individual-specific heterogeneity. Familiar transformations can restructure the AR(1) process into a serially uncorrelated dynamic model. It may result in unfitting estimation results once the statistical inference is carried on the conditional likelihood. We discuss in the article the consequence of this action. In particular, in the case of large cross-section units and short time-sequences, we provide analytical expressions for the asymptotic bias of maximum likelihood estimates when the analyst naïvely neglects the initial conditions problem. Under several conditions, we compute the size of biases and measure the mean squared errors to illustrate this violation. We also construct a joint regression model of the initial and subsequent responses to handle the initial conditions. Then, we conduct simulation studies to determine the asymptotic behavior. [ABSTRACT FROM AUTHOR]

Stratospheric variability may affect tropospheric weather on time scales between a few weeks and a few months, thus providing great potential for sub‐seasonal to seasonal weather forecasts of extremes. Unlike standard linear regression, which is based on the conditional mean of the response variable, lagged quantile regression is used here, which enables modeling the response variable's complete conditional distribution. Using the ERA5 reanalysis, we explore the relation of prominent teleconnection indices and gridded tropospheric fields to the stratosphere during boreal winter for various quantiles and lags. Significant differences in duration, strength, and direction of the stratosphere‐troposphere connection in outer quantiles compared to the median are identified. In particular, tropospheric extremes and their relation to the polar vortex strength are discussed, and an outlook is given. Plain Language Summary: Variations in stratospheric wind and temperature may affect surface weather for a few weeks to a few months. Sub‐seasonal to seasonal weather forecasts of extreme events, highly sought after by various industrial sectors, make use of this connection. Standard linear regression (LR) models base the prediction on the conditional mean of the tropospheric response variable while assuming constant variance of corresponding residuals which is often not the case. As an alternative, we use lagged quantile regression (QR), enabling us to model the response variable's complete conditional distribution. Thereby, using ERA5 reanalysis we explore the relation of prominent teleconnections and tropospheric fields to the boreal winter stratosphere for various quantiles. We find significant differences in duration, strength, and direction of the stratosphere‐troposphere connection in outer quantiles compared to the median. Thus, the QR framework offers straightforward access to valuable, supplementary information, not derivable from LR. Key Points: Straightforward access to invaluable, supplementary information, not derivable from ordinary linear regressionAsymmetric response of teleconnection indices and mid‐tropospheric gridded fields to stratospheric variability across quantilesDistinct extreme event characteristics in for example, persistence and strength and clear lagged effect compared to the median quantile regression [ABSTRACT FROM AUTHOR]