The Data Statistical Analysis And Its Application Base On Functional Data Analysis

Functional data analysis is to find a smooth curve to fit the data, which is discrete, it has a unique advantage in the process of high-dimensional data. Functional data analysis enriches the statistical analysis method, because it realizes the transformation between the discrete data and continuous data; and it rarely dependents on the model building and assumptions; when meeting the infinite dimensional, using the functional data analysis transform it to finite dimensional, the data information is more reliable, more abundant,, more close to reality. In recent years, functional data analysis is applied to many fields, such as in medicine, biology, population statistics, environment and other fields of application, and the research result is also very valuable.Functional characteristic is the main characteristic of the functional data. When we want to analyze the data, choosing appropriate basis function to fit the data, and then getting a smooth curve, by analyzing the smooth curve can predict the observation point data value. In addition, from the perspective of function analysis this kind of data, will dig out more potential data information, such as get data speed by solving the first derivative, the second derivative get acceleration data changes, three derivative get jerk diagram, and so on.This paper studies the functional data in the application of economic data. The B-spline basis functions and Legendre functions are introduced to transform the discrete data into the continuous functional type data. And the hidden data inherent regularity and related information can be revealed via functional principal component analysis. So that the extraction of information is more abundant, reliable, and less dependent on the model and its assumptions when the corresponding data conversion occurred between the infinite-dimension and finite-dimension. Empirical analysis shows that the results with expanded PCA based on B-spline functions and Legendre functions can coincide with the actual economic performance. Experimental results show that using the proposed method, it can accurately reflect the long-term trend of economic indicators. In particular, based on Functional data principal component analysis with Legendre functions, it can reflect both short-term economic impact of external factors, and more accurately long-term economic future trends.