Local regression type methods applied to the study of geophysics and high frequency financial data

In this work we applied locally weighted scatterplot smoothing techniques (Lowess/Loess) to Geophysical and high frequency financial data. We first analyze and apply this technique to the California earthquake geological data. A spatial analysis was performed to show that the estimation of the earthquake magnitude at a fixed location is very accurate up to the relative error of 0.01%. We also applied the same method to a high frequency data set arising in the financial sector and obtained similar satisfactory results. The application of this approach to the two different data sets demonstrates that the overall method is accurate and efficient, and the Lowess approach is much more desirable than the Loess method. The previous works studied the time series analysis; in this paper our local regression models perform a spatial analysis for the geophysics data providing different information. For the high frequency data, our models estimate the curve of best fit where data are dependent on time.