Determination of the nature of growth of the main trends of time series in small quantity of observations

The problem of determining the nature of growth in the short time series (an alternative choice between linear and exponential trend). We propose a simple criterion for selection. The result can be used, including in medicine, in particular, the interpretation of dynamics in the tumor markerlinear trend; exponential trend; LS-estimate; heteroscedasticity; critical value; tumor marker

Forecasting Coherent Volatility Breakouts

The paper develops an algorithm for making long-term (up to three months ahead) predictions of volatility reversals based on long memory properties of financial time series. The approach for computing fractal dimension using sequence of the minimal covers with decreasing scale is used to decompose volatility into two dynamic components: specific and structural. We introduce two separate models for both, based on different principles and capable of catching long uptrends in volatility. To test statistical significance of its abilities we introduce several estimators of conditional and unconditional probabilities of reversals in observed and predicted dynamic components of volatility. Our results could be used for forecasting points of market transition to an unstable state

Forecasting Coherent Volatility Breakouts

The paper develops an algorithm for making long-term (up to three months ahead) predictions of volatility reversals based on long memory properties of financial time series. The approach for computing fractal dimension using sequence of the minimal covers with decreasing scale is used to decompose volatility into two dynamic components: specific and structural. We introduce two separate models for both, based on different principles and capable of catching long uptrends in volatility. To test statistical significance of its abilities we introduce several estimators of conditional and unconditional probabilities of reversals in observed and predicted dynamic components of volatility. Our results could be used for forecasting points of market transition to an unstable state