The dissetation includes three main parts, with the first part studies investigate empirically whether or not and to what extent the GM technology has improved realized yields. We study this question for non-irrigated U.S. maize and soybean yields over 1964-2010, having controlled for local effects, weather, fertilization and the pre-existing (non-GM) crop improvement trend. For maize we find that GM varieties have increased realized yields, with a stronger gain in the Central Corn Belt. For soybeans, GM varieties appear to have slightly reduced yields. For both crops we nd a strong trend in yield growth, which may have accelerated in recent years. The second part of the dissertation studies the impact of pricing errors on implied volatilities.Financial researchers and practitioners frequently propose their models and design the pricing formulae based on the observed implied volatility pattern in reality. We find that, in addition to the pattern caused by the mismatch of Black-Scholes formula and true pricing formulae, the observed implied volatility pattern is also influenced by the pricing errors. We propose to study the combined effects of pricing errors and pricing formula on the implied volatility. We find that implied volatility is adversely impacted by pricing errors and stylish patterns of the inverse Black-Scholes price function. Hence, the implied volatility is not a reliable estimator to the underlying volatility even it is carried out for short maturity at the money options. We propose an alternative volatility estimator by inverting a nonparametrically estimated price based on a kernel smoothing estimator of the underlying price function. The proposal can consistently recover the underlying volatility for general price formulae and is free of the afore-mentioned problems with the conventional implied volatility. The third part of the dissertation focused on a situation that the seasonal pattern is a long cycle and the study period covers only a few of the long cycles, such as a daily series with an annual pattern and includes only 5-30 years. This situation is in contrast with the asymptotic study, corresponding to the situation that the sample includes many long cycles, and has been ignored in the literature. Although the estimator based on seasonal-dummy-regression is consistent, unbiased and asymptotically normal-distributed, we find this estimator does not perform well in our focused situation. We propose smoothing the estimated long-cycle patterns by seasonal-dummy regression and evaluate the benefit of smoothing. We study our proposed smoothing-seasonal-dummy-regression estimator for seasonal time series with a long cycle and no short cycle, a short cycle and many short cycles, both theoretically, and via simulation studies, and then apply our methodology to an empirical study of the return rates of electricity prices.