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model portfolio stock return series level diversification probability asset distribution break downside order table forecast market result 1.000 downside risk number memory value method index measure fi-break model solution vries / journal parameter journal hyung estimate fi-break investor estimation sample component criterion theorem forecasting factor finance jansen corner solution benefit safety analysis observation variance paper x 2 n speed selection period tail index function scale assumption downside risk measure order expansion expansion security proof arfi model tail indices theory 1.001 ar model corner time series condition figure example var level effect indices problem portfolio diversification downside risk measures forecast errors