During the COVID-19 pandemic, cryptocurrency prices showed abnormal volatility that attracted the participation of many investors. Studying the behaviour of volatility for the prices of cryptocurrency is an interesting problem to be investigated. This research implements the state space model framework for volatility incorporating the Kalman filter. This method directly forecasts the conditional volatility of five cryptocurrency prices (Bitcoin (BTC), Ethereum (ETH), Ripple (XRP), Litecoin (LTC) and Bitcoin Cash (BCH)) for 10,000 consecutive hours, i.e., approximately 417 days during the COVID-19 pandemic from 26 February 2020, 00:00 h until 18 April 2021, 00:00 h. The performance of this model is compared to the GARCH (1,1) model and the neural network autoregressive (NNAR) based on root mean square error (RMSE), mean absolute error (MAE) and the volatility plot. The autocorrelation function plot, histogram and the residuals plot are used to examine the model adequacy. Among the three models, the state space model gives the best fit. The state space model gives the narrowest confidence interval of volatility and value-at-risk forecasts among the three models.

The Lee–Carter model is a well-known model in modeling mortality. We aim to compare three probability models (Poisson, negative binomial and binomial) based on the Generalized Linear Model (GLM) framework of the Lee–Carter model. These models are applied to mortality data for 10 selected countries (Japan, United States, United Kingdom, Australia, Sweden, Spain, Belgium, Canada, Netherlands and Bulgaria) and the fit of these models is assessed using the deviance statistics and standardized residuals against fitted value plot. Among these three models, the negative binomial Lee–Carter model gave the best fit based on the deviance statistics and estimates of the log of deaths.

The heteroscedastic and volatile characteristics of stock price data have attracted the interest of researchers from various disciplines, particularly in the realm of price forecasting. The stock market’s non-stationary and volatile nature, driven by complex interrelationships among financial assets, economic developments, and market participants, poses significant challenges for accurate forecasting. This research aims to develop a robust forecasting model to improve the accuracy and reliability of stock price predictions using machine learning. A two-stage forecasting model is introduced. First, a random forest subset-based (RFS) feature selection with repeated k -fold cross-validation selects the best subset of features from eight predictors: highest price, lowest price, closing price, volume, change, price change ratio, and amplitude. These features are then used as input in a bidirectional gated recurrent unit with an attention mechanism (BiGRU-AM) model to forecast daily opening prices of ten stock indices. The proposed model exhibits superior forecasting performance across ten stock indices when compared to twelve benchmarks, evaluated using root mean squared error (RMSE), mean absolute error (MAE), and the coefficient of determination, R2 . The improved prediction accuracy enables financial professionals to make more reliable investment decisions, reducing risks and increasing profits.