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and prediction of financial bubbles Case1: US house bubble (20232023) Case2: Crude Oil Bubble (20232023) Recurrence interval of price returns ? Return ? Return interval of price returns ( ) l n( ( ) ) l n( ( 1 ) )R t Y t Y t? ? ?1 / 222()()( ) ( )RtrtR t R t??????1q?? 1q???PDF of recurrence interval of price returns ? Scaling or not ? ? Formula of the function f ? Shanghai Stock Exchange Composite Index (SSEC) Shenzhen Stock Exchange Composite Index (SSEC) It’s application to risk estimation Probability Wq(Δt|t) m in()( | ) ( 1 ) / ,()ttqtqqtPdW t t t t t xPd?????????? ? ? ? ? ? ? ??? t Δt r q Conditional loss probability p* * ()qq number of r et ur ns t hat r qp p r dr t ot al number of r et ur ns ??????? 1= For empirical data, the tail of the return distribution follows a powerlaw behavior , then . ( 1 )()p r k r ???? k ?????1 q , q 2 Mean conditional return interval after 0?0 00| 1???? ???? ? ????? ? ? ????? ? ? ? ?? ? ? ?? ? ? ??? Analytical result Empirical data Conditional loss probability p* Thank you! 謝謝觀看 /歡迎下載 BY FAITH I MEAN A VISION OF GOOD ONE CHERISHES AND THE ENTHUSIASM THAT PUSHES ONE TO SEEK ITS FULFILLMENT REGARDLESS OF OBSTACLES. BY FAITH I BY FAITH