## 1 Introduction  
Data are vital for various artificial and natural systems in the modern information era. The real-time data generated with equipment and sensors are critical to monitoring the controlled objects' operation statuses [1]. Moreover, advanced sensing and precaution are expected to be obtained for administrators. Then, the aforehand actions can be taken to adjust a system's operation and make effective decisions to avoid accidents and gain benefits. Therefore, close attention has been paid to prediction information in various applications, such as unmanned terminal control [2; 3], environment monitoring [4; 5; 6], the stock market [7], agriculture [8], etc. In a prediction, the time series data are always of nonstationary and nonlinear features with complex noises [9]. The issue of time series prediction has been a research hotspot for a dozen years. The traditional statistical methods represented by the ARIMA (Auto-Regressive Integrated Moving Average) [10], ARCH (Auto-Regressive Conditional Heteroskedasticity) [11], and intelligent machine learning methods have been studied and applied widely. However, the methods may be invalid when the historical data are on a small scale. The data size of a time series in practical applications is often not as large as we expect, although big data are always advocated in the internet world. The data in many fields are collected artificially in the traditional management style. For example, we investigated water environment monitoring in Beijing, China. The mainstream authoritative monitoring data are mainly collected by operators and assayed in the laboratory [12]. The frequency is one dataset of one day at most. There are only about 30 sets of monitoring data in a month on the official website. A similar phenomenon occurs in casual food inspections. The government administration inspects different kinds of grain and foods in markets. The highest frequency is once a day based on human resources limitations and enormous market scope. There are only hundreds of inspection datasets in a year. Another typical example is demographic statistics. Population censuses have been conducted for about ten years in China. The latest censuses were in 1990, 2000, and 2010. The demographics in the highest frequency are only measured once a year, which means the number of recent population data is only in the dozens. The slow data collection makes the data size so small that it cannot meet the requirement of intelligent computing. In many application states in the real world, the number of samples is small or minimal, and marking lots of unmarked samples will consume many human resources. Therefore, finding a way to learn with a small number of samples has become a current need. Existing prediction models mainly include shallow neural networks and deep neural networks. For existing methods, small-scale data hinder effective modeling and accurate calculations. Models fitted using statistical methods do not track new patterns because of limited information in the existing data. Building a model using machine learning methods may not be possible because the data size is too small to train the network. Deep networks often require a mass of data to train an available model. Suppose a small amount of data cannot reflect the natural characteristics of the data well. In that case, the deep network model will fail to achieve the expected accuracy, and it may lead to model overfitting. Aiming at the problem of insufficient data volume, related research has begun to introduce some data augmentation methods to enhance the data volume of samples, such as Hermite interpolation, cubic spline interpolation, generative adversarial net, etc. A Hermite spline is a piecewise cubic polynomial with a given tangent at each value point. Cubic spline interpolation takes the curve as the primary element, connects the discrete point data into a curve, and can find the function value of any point on the curve.