Modeling Discrete Time Series Made of Lucas Numbers

This research focuses on discrete time series made by Lucas numbers. The time series we consider is made by n points, each of them are made of m consecutive Lucas numbers. Our main goal is to use linear algebra methods to construct polynomial models for such time series and to study the properties of our models. Finding a model is equivalent to solving a matrix equation. After appropriate row reductions, the resulting matrix has good patterns such as a relationship to the Fibonacci numbers. Homogeneous linear models were found. The general form and special models for homogeneous models were found. It is shown that no homogeneous quadratic model exists.