Tomáš Cipra

Bio: Tomáš Cipra is an academic researcher from Charles University in Prague. The author has contributed to research in topics: Kalman filter & Autoregressive model. The author has an hindex of 11, co-authored 82 publications receiving 860 citations.

Statistical Analysis of Time Series

Abstract: Chapter 31 contains formulas relevant for time series analysis: 31.1. Predictions in Time Series, 31.2. Decomposition of (Economic) Time Series, 31.3. Estimation of Correlation and Spectral Characteristics, 31.4. Linear Time Series, 31.5 Nonlinear and Financial Time Series, 31.6 Multivariate Time Series, 31.7. Kalman Filter.

Kalman filter with outliers and missing observations

Abstract: The discrete Kalman filter which enables the treatment of incomplete data and outliers is described. The incomplete, or missing observations are included in such a way as to transform the Kalman filter to the case when observations have changing dimensions. In order to treat outliers, the Kalman filter is made robust using the M-estimation principle. Some special cases are considered including a convergence result for recursive parameter estimation in AR(1) process with innovation outliers and missing observations.

Robust exponential smoothing

Abstract: The paper is devoted to robust modifications of exponential smoothing for time series with outliers or long-tailed distributions. Classical exponential smoothing applied to such time series is sensitive to the presence of outliers or long-tailed distributions and may give inadequate smoothing and forecasting results. First, simple and double exponential smoothing in the L1 norm (i.e. based on the least absolute deviations) are discussed in detail. Then, general exponential smoothing is made robust, replacing the least squares approach by M-estimation in such a way that the recursive character of the final formulas is preserved. The paper gives simple algorithmic procedures which preserve advantageous features of classical exponential smoothing and, in addition, which are less sensitive to outliers. Robust versions are compared numerically with classical ones.

Financial and Insurance Formulas

Abstract: Financial Formulas.- Simple Interest and Discount.- Compound Interest and Discount.- Continuous Interest and Discount.- Classical Analysis of Interest Rates.- Systems of Cash Flows.- Annuities.- Depreciation.- Financial Instruments.- Derivative Securities.- Utility Theory.- Rate of Return and Financial Risk.- Portfolio Analysis and CAPM Model.- Arbitrage Theory.- Financial Stochastic Analysis.- Insurance Formulas.- Insurance Classification.- Actuarial Demography.- Classical Life Insurance.- Modern Approaches to Life Insurance.- Pension Insurance.- Classical Non-Life Insurance.- Risk Theory in Insurance.- Health Insurance.- Reinsurance.- Formulas of Related Disciplines.- Mathematical Compendium.- Probability Theory.- Descriptive and Mathematical Statistics.- Econometrics.- Index Numbers.- Stochastic Processes.- Statistical Analysis of Time Series.

Forecasting, Structural Time Series Models and the Kalman Filter

Abstract: In this book, Andrew Harvey sets out to provide a unified and comprehensive theory of structural time series models. Unlike the traditional ARIMA models, structural time series models consist explicitly of unobserved components, such as trends and seasonals, which have a direct interpretation. As a result the model selection methodology associated with structural models is much closer to econometric methodology. The link with econometrics is made even closer by the natural way in which the models can be extended to include explanatory variables and to cope with multivariate time series. From the technical point of view, state space models and the Kalman filter play a key role in the statistical treatment of structural time series models. The book includes a detailed treatment of the Kalman filter. This technique was originally developed in control engineering, but is becoming increasingly important in fields such as economics and operations research. This book is concerned primarily with modelling economic and social time series, and with addressing the special problems which the treatment of such series poses. The properties of the models and the methodological techniques used to select them are illustrated with various applications. These range from the modellling of trends and cycles in US macroeconomic time series to to an evaluation of the effects of seat belt legislation in the UK.

Modelling Financial Time Series

Abstract: Features of Financial Returns Modelling Price Volatility Forecasting Standard Deviations The Accuracy of Autocorrelation Estimates Testing the Random Walk Hypothesis Forecasting Trends in Prices Evidence Against the Efficiency of Futures Markets Valuing Options Appendix: A Computer Program for Modelling Financial Time Series.