Smoothing of numerical series by the triangle method on the example of hungarian gdp data 1992-2022 based on approximation by series of exponents
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三角法平滑与指数级数逼近：匈牙利1992—2022年GDP案例
- 研究问题
- 对于含观测误差和异常值的长期 GDP 序列，如何通过平滑及函数逼近描述其变化，并估计观测表中没有列出的中间值？
- 方法与思路
- 作者用三角法平均和平滑数据，再以复变量的三十项指数级数逼近匈牙利1992—2022年的 GDP 序列。
- 材料陈述的贡献
- 摘要称，指数级数可用于难以由幂函数描述的长期 GDP 数据，三角法平滑有助于处理异常值并提高所述逼近精度。
- 阅读关注点
- 应核对 GDP 数据口径、三角法及复指数级数的实现、精度评估标准，以及平滑是否掩盖经济变化或造成过度拟合。
- 阅读边界
- 这是 arXiv 预印本，不能据此认定已同行评审或期刊接收；摘要未给出误差数值或比较设计，不能确认预测能力或优于其他方法。
原文摘要
In practice , quite often there is a need to describe the values set by means of a table in the form of some functional dependence . The observed values , due to certain circumstances , have an error . For approximation, it is advisable to use a functional dependence that would allow smoothing out the errors of the observation results. Approximation allows you to determine intermediate values of functions that are not listed among the data in the observation table. The use of exponential series for data approximation allows you to get a result no worse than from approximation by polynomials In the economic scientific literature, approximation in the form of power functions, for example, the Cobb-Douglas function, has become widespread. The advantage of this type of approximation can be called a simple type of approximating function , and the disadvantage is that in nature not all processes can be described by power functions with a given accuracy. An example is the GDP indicator for several decades . For this case , it is difficult to find a power function approximating a numerical series . But in this case, as shown in this article, you can use exponential series to approximate the data. In this paper, the time series of Hungary's GDP in the period from 1992 to 2022 was approximated by a series of thirty exponents of a complex variable. The use of data smoothing by the method of triangles allows you to average the data and increase the accuracy of approximation . This is of practical importance if the observed random variable contains outliers that need to be smoothed out.