Financial Time Series Forecasting: A Review of Models and Applications

1. Time Series Basics

Financial time series are ordered observations of variables such as deposit amounts or loan profit rates. They exhibit trends, seasonality, serial correlation, and random noise, all of which must be examined before modeling.

2. Forecasting Workflow and Feature Engineering

The typical workflow includes data collection, cleaning, feature engineering (handling missing values, extracting trend/seasonality features), visual analysis, splitting into training/validation/test sets, model training, hyper‑parameter tuning (grid search, Bayesian optimization), and performance evaluation using appropriate metrics.

Common feature‑engineering techniques are:

Rolling statistics (mean, median, std, min, max) to smooth noise.

Lag features (e.g., lag‑1, lag‑7) to capture autocorrelation.

First‑order and seasonal differencing to remove trend/seasonality.

Date‑time attributes (hour of day, day of week, month).

Transformations (log, sqrt) to stabilize variance.

Fourier transforms to extract periodic components and create sine/cosine cyclical features.

External variables such as holidays or macro‑economic indicators.

3. Statistical Models

ARMA combines autoregressive (AR) terms, which model the linear dependence on past observations, with moving‑average (MA) terms, which model the linear relationship with past white‑noise errors. Model order (p, q) is selected by minimizing information criteria such as AIC or BIC. ARMA is suitable for stationary series and is commonly applied to macro‑economic indicators, stock prices, interest rates, and exchange rates.

SARIMAX extends ARIMA by adding seasonal components and exogenous regressors. It includes AR, differencing (to achieve stationarity), MA, seasonal terms, and external factors. Typical applications are macro‑economic forecasting, interest‑rate and inflation prediction, and short‑term asset‑return modeling where seasonality and external drivers are important.

4. Deep‑Learning Models

TimesNet reshapes a univariate series into a 2‑D tensor to capture intra‑ and inter‑period patterns using 2‑D convolutions. It leverages fast Fourier transform to move from time to frequency domain and aggregates multi‑scale features via TimesBlocks. It is applied to stock‑price prediction, multi‑asset portfolio optimization, and trading‑signal generation.

TimeMixer builds on multilayer perceptrons by decoupling time and feature dimensions. It projects past observations into multiple scales, uses fully‑connected layers (avoiding attention), and processes the whole sequence in parallel, achieving fast training and inference. Applications include asset‑return forecasting, implied volatility prediction, and credit‑risk assessment.

PatchTST adapts the transformer architecture for time series by segmenting the series into patches, feeding them to a transformer that models long‑range dependencies while preserving local patterns. Advantages are simultaneous handling of local and global features, suitability for multivariate series, and reduced computational cost for long sequences. It is used for high‑frequency trading data analysis, quantitative strategy development, and market‑risk monitoring.

5. Applications in Finance

Time‑series models support asset‑price forecasting, market‑trend analysis, portfolio optimization, high‑frequency trading, macro‑economic prediction, customer‑behavior analysis, and anomaly detection. Model choice depends on required interpretability, data characteristics, and computational constraints; a comparison table (omitted here) summarizes the trade‑offs.

6. Conclusion

The article provides a systematic overview of financial time‑series forecasting, from basic statistical methods (ARMA, SARIMAX) that offer high interpretability to advanced deep‑learning models (TimesNet, TimeMixer, PatchTST) that deliver higher accuracy on complex patterns. As algorithms continue to evolve, larger models are expected to further advance financial time‑series prediction.