In this paper the identification problem is considered for initial conditionsin a non-minimal state-space model that includes interpretable state variablesgenerated by non-stationary stochastic processes. In order to solve theidentification problem, structural restrictions are imposed on initial conditionsin a state-space model with redundant state variables. The correspondingrestricted maximum likelihood estimator of initial conditions is derived.The restricted estimator of initial conditions can be used in order tocompute uniquely identified realizations of interpretable latent variables. Theidentification problem is illustrated analytically using a simple structuraleconomic model.

This paper presents some new results on exogeneity in models with latent variables. The concept of exogeneity is extended to the class of models with latent variables, in which a subset of parameters and latent variables is of interest. Exogeneity is discussed from the Bayesian point of view. We propose sufficient weak and strong exogeneity conditions in the vector error correction model (VECM) with stochastic volatility (SV) disturbances. Finally, an empirical illustration based on the VECM-SV model for the daily growth rates of two main official Polish exchange rates: USD/PLN and EUR/PLN, as well as EUR/USD from the international Forex market is presented. The exogeneity of the EUR/USD rate is examined. The strong exogeneity hypothesis of the EUR/USD rate is not rejected by the data.

News might trigger jump arrivals in financial time series. The “bad” news and “good” news seem to have distinct impact. In the research, a double exponential jump distribution is applied to model downward and upward jumps. Bayesian double exponential jump-diffusion model is proposed. Theorems stated in the paper enable estimation of the model’s parameters, detection of jumps and analysis of jump frequency. The methodology, founded upon the idea of latent variables, is illustrated with simulated data.

The historical datasets at operating mine sites are usually large. Directly applying large datasets to build prediction models may lead to inaccurate results. To overcome the real-world challenges, this study aimed to handle these large datasets using Gaussian mixture modelling (GMM) for developing a novel and accurate prediction model of truck productivity. A large dataset of truck haulage collected at operating mine sites was clustered by GMM into three latent classes before the prediction model was built. The labels of these latent classes generated a latent variable. Two multiple linear regression (MLR) models were then constructed, including the ordinary-MLR (O-MLR) and the hybrid GMM-MLR models. The GMM-MLR model incorporated the observed input variables and a latent variable in the form of interaction terms. The O-MLR model was the baseline model and did not involve the latent variable. The GMM-MLR model performed considerably better than the O-MLR model in predicting truck productivity. The interaction terms quantitatively measured the differences in how the observed input variables affected truck productivity in three classes (high, medium, and low truck productivity). The haul distance was the most crucial input variable in the GMM-MLR model. This study provides new insights into handling massive amounts of data in truck haulage datasets and a more accurate prediction model for truck productivity.

The primary goal of the study is to diagnose satisfaction and loyalty drivers in Polish retail banking sector. The problem is approached with Customer Satisfaction Index (CSI) models, which were developed for national satisfaction studies in the United States and European countries. These are multiequation path models with latent variables. The data come from a survey on Poles’ usage and attitude towards retail banks, conducted quarterly on a representative sample. The model used in the study is a compromise between author’s synthesis of national CSI models and the data constraints.

There are two approaches to the estimation of the CSI models: Partial Least Squares – used in national satisfaction studies and Covariance Based Methods (SEM, Lisrel). A discussion is held on which of those two methods is better and in what circumstances. In this study both methods are used. Comparison of their performance is the secondary goal of the study.