Waiting time analysis of foreign currency exchange rates: Beyond the renewal-reward theorem

We evaluate the average waiting time between observing the price of financial markets and the next price change, especially in an on-line foreign exchange trading service for individual customers via the internet. Basic technical idea of our present work is dependent on the so-called renewal-reward theorem. Assuming that stochastic processes of the market price changes could be regarded as a renewal process, we use the theorem to calculate the average waiting time of the process. In the conventional derivation of the theorem, it is apparently hard to evaluate the higher order moments of the waiting time. To overcome this type of difficulties, we attempt to derive the waiting time distribution Omega(s) directly for arbitrary time interval distribution (first passage time distribution) of the stochastic process P_{W}(tau) and observation time distribution P_{O}(t) of customers. Our analysis enables us to evaluate not only the first moment (the average waiting time) but also any order of the higher moments of the waiting time. Moreover, in our formalism, it is possible to model the observation of the price on the internet by the customers in terms of the observation time distribution P_{O}(t). We apply our analysis to the stochastic process of the on-line foreign exchange rate for individual customers from the Sony bank and compare the moments with the empirical data analysis.Comment: 8pages, 11figures, using IEEEtran.cl

R4C: A Benchmark for Evaluating RC Systems to Get the Right Answer for the Right Reason

Recent studies have revealed that reading comprehension (RC) systems learn to exploit annotation artifacts and other biases in current datasets. This prevents the community from reliably measuring the progress of RC systems. To address this issue, we introduce R4C, a new task for evaluating RC systems' internal reasoning. R4C requires giving not only answers but also derivations: explanations that justify predicted answers. We present a reliable, crowdsourced framework for scalably annotating RC datasets with derivations. We create and publicly release the R4C dataset, the first, quality-assured dataset consisting of 4.6k questions, each of which is annotated with 3 reference derivations (i.e. 13.8k derivations). Experiments show that our automatic evaluation metrics using multiple reference derivations are reliable, and that R4C assesses different skills from an existing benchmark.Comment: Accepted by ACL2020. See https://naoya-i.github.io/r4c/ for more informatio