On the Stratonovich – Kalman - Bucy filtering algorithm application for accurate characterization of financial time series with use of state-space model by central banks

The central banks introduce and implement the monetary and financial stabilities policies, going from the accurate estimations of national macro-financial indicators such as the Gross Domestic Product (GDP). Analyzing the dependence of the GDP on the time, the central banks accurately estimate the missing observations in the financial time series with the application of different interpolation models, based on the various filtering algorithms. The Stratonovich – Kalman – Bucy filtering algorithm in the state space interpolation model is used with the purpose to interpolate the real GDP by the US Federal Reserve and other central banks. We overviewed the Stratonovich – Kalman – Bucy filtering algorithm theory and its numerous applications. We describe the technique of the accurate characterization of the economic and financial time series with application of state space methods with the Stratonovich – Kalman - Bucy filtering algorithm, focusing on the estimation of Gross Domestic Product by the Swiss National Bank. Applying the integrative thinking principles, we developed the software program and performed the computer modeling, using the Stratonovich – Kalman – Bucy filtering algorithm for the accurate characterization of the Australian GDP, German GDP and the USA GDP in the frames of the state-space model in Matlab. We also used the Hodrick-Prescott filter to estimate the corresponding output gaps in Australia, Germany and the USA. We found that the Australia, Germany on one side and the USA on other side have the different business cycles. We believe that the central banks can use our special software program with the aim to greatly improve the national macroeconomic indicators forecast by making the accurate characterization of the financial time-series with the application of the state-space models, based on the Stratonovich – Kalman – Bucy filtering algorithm.