Abstract

Rather than time series forecasting, we apply a machine learning method to analyze time series data, with a purpose to derive meaningful statistics based on the characteristics of the data. Firstly, we introduce an Artificial Neural Network (i.e., ANN) approach to estimate the autoregressive process AR(1) when the autocorrelation parameter is near one. Traditional OLS estimators suffer from biases in small samples, necessitating various correction methods proposed in the literature. To reduce the bias of the autoregressive parameter estimator, the ANN is designed to incorporate the prescribed characteristics of the data as inputs instead of easily taking the whole series, efficiently speeding up the training process. As a result, the ANN, trained on simulated data, outperforms other competing methods due to its nonlinear structure. Unlike competitors requiring simulations for bias corrections based on specific sample sizes, the ANN directly incorporates sample size as input, eliminating the need for repeated simulations. Stability tests involve exploring different ANN architectures and activation functions, as well as robustness to varying distributions of the process innovations. Empirical observations show that the ANN owns a high degree of generalization with limited signs of overfitting. Based on the same architecture , this technology is extended to deriving statistics without any model specification. Given a high-frequency time series, the ANN accepts the prescribed characteristics of the data and then generates an estimator of the higher cumulants, competing against the realized higher moments estimator from Neuberger & Payne (2020).