We consider the problem of estimating the conditional quantile of a time series <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\{ Y_t\}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mo stretchy="false">{</mo> <msub> <mi>Y</mi> <mi>t</mi> </msub> <mo stretchy="false">}</mo> </mrow> </math> </EquationSource> </InlineEquation> at time <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$t$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>t</mi> </math> </EquationSource> </InlineEquation> given covariates <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$\varvec{X}_{t}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mrow> <mi mathvariant="bold-italic">X</mi> </mrow> <mi>t</mi> </msub> </math> </EquationSource> </InlineEquation>, where <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$\varvec{X}_{t}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mrow> <mi mathvariant="bold-italic">X</mi> </mrow> <mi>t</mi> </msub> </math> </EquationSource> </InlineEquation> can be either exogenous variables or lagged variables of <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$${ Y_t}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi>Y</mi>...</msub></math></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

The main uniform convergence results of Hansen (2008) are generalized in two directions: Data is allowed to (i) be heterogenously dependent and (ii) depend on a (possibly unbounded) parameter. These results are useful in semiparametric estimation problems involving time-inhomogenous models...

We consider the problem of estimating the conditional quantile of a time series at time t given observations of the same and perhaps other time series available at time t - 1. We discuss sieve estimates which are a nonparametric versions of the Koenker-Bassett regression quantiles and do not...