Non-stationary Stochastic Sequences as Solutions to Ill-posed Problems - Horský, Richard (Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu, 2017)
The mathematical formulation of any problem in applied sciences leads usually to an operator equation. In linear models the operator is a matrix or a difference, differential or an integral operator. If we try to solve such an operator equation we often meet different difficulties. The solution need not exist or it is not unique or it is unstable. All these bad properties of a mathematical model reflect the complexity of the real problem we are to solve. Such difficult problems are called ill-posed problems. It is not surprising that we also meet these problems in time series analysis. In this area the ill-posedness is demonstrated by the non-stationarity of a stochastic process. In economics it is well-known that the time series of logaritms of GDP or the price of overall market portfolio are almost certainly non-stationary. The typical example of the non stationary process is the random walk
20-th AMSE. Applications of Mathematics and Statistics in Economics. International Scientific Conference: Szklarska Poręba, 30 August- 3 September 2017. Conference Proceedings Full Text Papers, s. 207-216
Keywords: ill-posed problem; regularization; non-stationary sequence; differencing; lag operator; least square solution; random walk; GDP; market portfolio