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General nonlinear sieve learnings are classes of nonlinear sieves that canapproximate nonlinear functions of high dimensional variables much moreflexibly than various linear sieves (or series). This paper considers generalnonlinear sieve quasi-likelihood ratio (GN-QLR) based inference on expectationfunctionals of time series data, where the functionals of interest are based onsome nonparametric function that satisfy conditional moment restrictions andare learned using multilayer neural networks. While the asymptotic normality ofthe estimated functionals depends on some unknown Riesz representer of thefunctional space, we show that the optimally weighted GN-QLR statistic isasymptotically Chi-square distributed, regardless whether the expectationfunctional is regular (root-$n$ estimable) or not. This holds when the data areweakly dependent beta-mixing condition. We apply our method to the off-policyevaluation in reinforcement learning, by formulating the Bellman equation intothe conditional moment restriction framework, so that we can make inferenceabout the state-specific value functional using the proposed GN-QLR method withtime series data. In addition, estimating the averaged partial means andaveraged partial derivatives of nonparametric instrumental variables andquantile IV models are also presented as leading examples. Finally, a MonteCarlo study shows the finite sample performance of the procedure

Inference on Time Series Nonparametric Conditional Moment Restrictions Using General Sieves