Accurate crime prediction is crucial for effective law enforcement and security, enabling proactive resource allocation and risk reduction. Criminal behavior is influenced by complex, diverse socio-economic factors, necessitating advanced models capable of extracting intricate patterns from large datasets. This research presents a methodological and applied comparison of four primary categories of time series forecasting models: Statistical Models (AutoARIMA), Machine Learning models (AutoLightGBM), Deep Learning models (N-HiTS), and Foundation Models (TimeGPT). The study’s innovation lies in (1) integrating these diverse categories in a single comparative framework tailored for security decision-makers, (2) explicitly applying cutting-edge AI, particularly Foundation Models (TimeGPT) with pre-training on vast, multi-domain time series, for crime prediction for the first time, and (3) demonstrating a comprehensive application using daily crime data from Chicago (2017–2019), with the final month serving as a challenging test set for assessing robustness against sudden fluctuations. Results indicate that Foundation (TimeGPT) and Deep Learning (N-HiTS) models outperform in accuracy, effectively capturing nonlinear relationships and complex seasonality. Statistical (ARIMA) and traditional ML (LightGBM) models offer greater interpretability and faster training but are less adept at handling unexpected surges. This comparative, automated approach offers a practical solution for security agencies seeking AI adoption without significant programming complexity. The research underscores time series modeling’s role in enhancing security operations and explores new avenues for AI-driven proactive crime prevention using big data.

Stock prices of different companies frequently display similar temporal fluctuations because of common influencing factors. Accurate prediction of stock prices is of utmost importance for investors in determining their investment strategies. Utilizing multivariate forecasting, which involves analyzing multiple time series, has been shown to be highly effective and efficient when applied to stocks that exhibit similar temporal patterns. It is possible to model the relationship between shares by using a shared temporal model approach. Nevertheless, it is important to note that not all stocks selected for prediction demonstrate a strong correlation; certain stocks may deviate from expected patterns. Therefore, the direct implementation of a comprehensive shared temporal component model is not universally applicable. This study presents a new method called the Semi-Shared Temporal Model, which focuses on the correlation structure among variables that have similar patterns, while also modeling all stocks simultaneously. This methodology is applied to the three leading stocks of 2023: Amazon (AMZN), Alphabet (GOOG), and MercadoLibre (MELI). Based on monthly data collected from January 2010 to December 2023, the study forecasts the stock prices for the months of January to December 2024. The analysis findings suggest that the temporal patterns of AMZN and GOOG shares are highly similar, which supports the idea of modeling them together with shared temporality. Three forecasting methods are utilized: univariate models, full shared temporal models, and semi-shared temporal models. The analysis determines that the semi-shared temporal model approach produces the most precise forecasting outcomes, with a Mean Absolute Percentage Error (MAPE) of 17.97%, surpassing both univariate and full shared temporal models. The forecast for 2024 indicates a favorable trajectory for all three stocks.

Deep learning techniques are making significant contributions to the rapid advancements in forecasting. A standout algorithm known for its ability to produce accurate forecasts by recognizing temporal autocorrelation within the data is the Long Short-Term Memory (LSTM) algorithm, a component of Recurrent Neural Networks (RNN). The LSTM method employs both stateless and stateful architecture approaches, providing versatility in its application. This research aims to compare stateful and stateless algorithms in LSTM models, focusing on forecasting stock prices, such as those of Apple Inc. This comparative analysis is crucial, taking into account various characteristics of time series data, including the benefits and drawbacks of temporal autocorrelation. The comparison results reveal that, despite the stateful algorithm requiring more computational time, it achieves greater accuracy than the stateless approach. The forecast indicates a potential upward trend in share prices for the period of January to December 2024, according to the projected outlook for Apple's stock value. However, it is essential to exercise prudence in interpreting these results, considering that share price fluctuations are influenced by a significant number of variables.

This research aims to present the Hybrid SSA-TBATS approach as an alternate forecasting technique that does not need specific assumptions or requirements such as stationarity, linear or nonlinear process, and normality. This analysis used Indonesian exports (in millions of USD) from January 1993 to July 2022. The findings of this research reveal that the Hybrid SSA-TBATS method outperforms SSA and TBATS in forecasting accuracy and defines the window length and number of groups. Therefore, it is highly recommended based on MAPE since it does not need any information on the characteristics of the data to be forecasted.

This paper characterizes the stockholders overreaction thorough return and price mean reverting behavior in specified ten major industry groups in Tehran Stock Exchange (TSE). For investigation of mean reversion presence, we use corporate firms from ten specified industry groups traded on the Tehran Stock Exchange and using a random walk with drift model with data over the period 2009-2013 period and recursive estimation in stability diagnostics test. The primary objective of this paper is to investigate mean reversion phenomenon in ten major industries including maximum number of real and nonstrategic investors with two different methods on quarterly return and monthly price time series. The results indicate that mean reversion occurred in the returns of these industry group. In addition, we use two major Unit Root Tests as complementary and final analysis. Out results also indicate that mean reversion takes place, significantly in eight industry groups and price time series in two industry groups follow a random walk process.

Autoregressive moving average (ARMA) process and dynamic neural networks namely the nonlinear autoregressive moving average with exogenous inputs (NARX) are compared by evaluating their ability to predict financial time series; for instance the S & P500 returns. Two classes of ARMA are considered. The first one is the standard ARMA model which is a linear static system. The second one uses Kalman filter (KF) to estimate and predict ARMA coefficients. This model is a linear dynamic system. The forecasting ability of each system is evaluated by means of mean absolute error (MAE) and mean absolute deviation (MAD) statistics. Simulation results indicate that the ARMA-KF system performs better than the standard ARMA alone. Thus, introducing dynamics into the ARMA process improves the forecasting accuracy. In addition, the ARMA-KF outperformed the NARX. This result may suggest that the linear component found in the S & P500 return series is more dominant than the nonlinear part. In sum, we conclude that introducing dynamics into the ARMA process provides an effective system for S & P500 time series prediction.