On Fitting the Autoregressive Investment Models to real Financial data

Abstract

The successful investment policy is an integral part of successful activity of the insurance company. The return to the shareholders of the insurance company usually thought of as comprising the underwriting result and investment income. The investment income is very important even for an insurance company, which writes mainly a short tail business. For the successful activity the insurance company needs the appropriate investment policy as well as in good investment control. For this purpose knowledge of the analysis of processes of a behavior of the various interest rates represents large interest. Recently many authors use the stochastic differential equations for description of processes of a development of a various sort of the interest rates. As it is known, solutions of such equations are the Markov processes and the observations of these processes in discrete instants will form time series circumscribed by autoregressive models of the first order. They are popular among those, who are interested in the analysis of financial data. In this connection it is useful to know about that as far as the models with real data will be precisely matched. In the present paper such problems with the special attention to the correspondence of correlation properties of real financial data to correlation properties of processes generated by autoregressive models are considered. The 12 time series of the following financial data were exposed to a research UK Share Price, Dec 1918 - Jun 1995 (919 monthly values). UK Dividend Yield Rate for Shares, Dec 1918 - Jun 1995 (919 monthly values). UK Retail Prices Index, Jun 1900 - May 1995 (1145 monthly values). UK Wages Index, Jun 1920 - Apr 1995 (904 monthly values). Internal Rate of Yield on UK 2.5% Consoles, Jun 1900 - Jun 1995 (1146 monthly values). US Treasury Securities, Jan 1991 - Dec 1995 (for 1250 business days): Short-term debt instruments (the 3-month’s Bills); Medium-term debt instruments (the 3-year’s Notes); Long-term debt instruments (the 30-year’s Bonds). Currency Exchange Rates, Jan 1991 - Dec 1995 (for 1700 business days): Swiss Franc versus US $; German Mark versus US $; British Pound versus US $; Japanese Yen versus US $. The analysis has revealed correlation properties of investigated time series of financial data and has shown, that real financial data have other correlation properties than their autoregressive models.