Time Series Analysis: yesterday, today, tomorrow

TL;DR

This paper tackles forecasting of a volatile, nonlinear time series derived from historical airplane crashes by comparing traditional statistical models, deep learning, and kernel methods. It employs stationarity diagnostics (visual decomposition and Augmented Dickey-Fuller tests), differencing and transformations, and models including ARMA/ARIMA/SARIMA, various RNN architectures (Simple RNN, LSTM, Bidirectional LSTM, GRU), and kernel methods (kernel ridge regression, support vector regression). Key findings show ARIMA-based approaches perform best for longer horizons with manual parameterization; deep learning captures longer-term trends but yields modest improvements over linear models, while kernel methods effectively model nonlinearities and sometimes outperform others with proper transformation. The work highlights practical considerations for time-series forecasting under nonstationarity and volatility, and points to future directions such as IgNet-inspired recurrent architectures to address gradient-vanishing and further improve predictive performance.

Abstract

Forecasts of various processes have always been a sophisticated problem for statistics and data science. Over the past decades the solution procedures were updated by deep learning and kernel methods. According to many specialists, these approaches are much more precise, stable, and suitable compared to the classical statistical linear time series methods. Here we investigate how true this point of view is.

Figures (13)

• Figure 1: Time series aggregated over various time intervals
• Figure 2: Decomposition of the original time series in Fig. \ref{['fig:ts_12']}
• Figure 3: $\arcsin$-transformed data
• Figure 4: Decomposition of the differenced series of Fig. \ref{['fig:ts_12']}
• Figure 5: Autocorrelation functions in action.