Time series modeling and prediction

Abstract

We provide an innovative approach to time series analysis that helps automate autoregressive integrated
sliding mean-value authorization model (ARIMA) modeling and greatly facilitates the reliable
prediction-building process. Our approach is based on optimization modeling and the separation of the
time series into defined seasonal effects, autoregressive (AR) terms, moving average (MA) terms, white
noise, and any free variation outside the scope of the chosen model. Simultaneous selection of the
corresponding delayed terms and evaluation of their coefficients is achieved by minimizing normalized
errors subject to constraints including the limit of the number of combined AR and MA terms to achieve
the desired savings through mathematical programming. The White Noise estimator device serves as a
stationary benchmark signal for determining Ma coefficients and is modeled using wavelet functions that
facilitate the formation of integer linear constraints. We report the results of numerical testing of this
methodology in several real data sets and discuss the main consequences for research and practice. Our
models (i) have found that one step above other widely used interpretable methodologies, including
random forests and gradient enhancement models, achieves forward forecasting accuracy, offers
interpretable results, and is computationally consistent.