Financial time series including high frequency structures like jumps, spikes and stochastic volatility are usually modeled in an ad-hoc manner by stochastic differential equations together with Levy processes. Estimating the parameters and determining the jump size distributions do not have a precise and universally accepted method. Under these circumstances, complexities and confusions usually arise. This book, approaches to this issue from a very different angle through introducing an autocorrelation one process together with finite number of Fourier series terms. Introduction of Fourier series to estimate the dynamics of the process is not done in an ad-hoc manner or as done before in dealing with seasonality. Here the moving average is transformed to a “moving and fluctuating” average by the help of Fourier series. Instead of adding jump structures to the model which makes the parameter estimation quite cumbersome, our model in discrete time can easily be transformed to a well-known mean reverting continuous time process. Moreover, our alternative model turned out to be a quite powerful and accurate forecasting technique.

This book offers a comprehensive journey through the evolving world of cryptocurrencies and their intersection with modern econometric forecasting. From the origins of Bitcoin and the rise of decentralized finance to the emergence of smart contracts and digital communities, readers gain a deep understanding of blockchain’s economic and societal impact. Bridging theory and practice, the book explores ARIMA models, machine learning, and neural networks as powerful tools for forecasting in a data-driven economy. It also addresses critical issues such as model interpretability, ethics, and regulatory challenges. Ideal for economists, data scientists, and crypto enthusiasts alike, this work emphasizes the importance of interdisciplinary thinking in navigating the future of finance, technology, and economic modeling in an increasingly digital world.