This article focuses on a problem important to automatic machine learning: the automatic processing of a nonpreprocessed time series. The convolutional neural network (CNN) is one of the most popular neural network (NN) algorithms for pattern recognition. Seasonal time series with trends are the most common data sets used in forecasting. Both the convolutional layer and the pooling layer of a CNN can be used to extract important features and patterns that reflect the seasonality, trends, and time lag correlation coefficients in the data. The ability to identify such features and patterns makes CNN a good candidate algorithm for analyzing seasonal time-series data with trends. This article reports our experimental findings using a fully connected NN (FNN), a nonpooling CNN (NPCNN), and a CNN to study both simulated and real time-series data with seasonality and trends. We found that convolutional layers tend to improve the performance, while pooling layers tend to introduce too many negative effects. Therefore, we recommend using an NPCNN when processing seasonal time-series data with trends. Moreover, we suggest using the Adam optimizer and selecting either a rectified linear unit (ReLU) function or a linear activation function. Using an NN to analyze seasonal time series with trends has become popular in the NN community. This article provides an approach for building a network that fits time-series data with seasonality and trends automatically.