Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider an adversarial formulation of the problem of predicting a time series with square loss. The aim is to predict an arbitrary sequence of vectors almost as ll as the best smooth comparator sequence in retrospect. Our approach allows natural measures of smoothness such as the squared norm of increments. More generally,  consider a linear time series model and penalize the comparator sequence through the energy of the implied driving noise terms.  derive the minimax strategy for all problems of this type and show that it can be implemented efficiently. The optimal predictions are linear in the previous observations.  obtain an explicit expression for the regret in terms of the parameters defining the problem. For typical, simple definitions of smoothness, the computation of the optimal predictions involves only sparse matrices. In the case of norm-constrained data, where the smoothness is defined in terms of the squared norm of the comparator's increments,  show that the regret grows as T/√ λT, where T is the length of the game and λT is an increasing limit on comparator smoothness.
['Wouter M. Koolen', 'Alan Malek', 'Peter L. Bartlett', 'Yasin Abbasi-Yadkori']
I am writing a research paper on a idea Minimax time series prediction
[{"from": "human", "value": "I am writing a research paper on a idea Minimax time series prediction"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider an adversarial formulation of the problem of predicting a time series with square loss. The aim is to predict an arbitrary sequence of vectors almost as ll as the best smooth comparator sequence in retrospect. Our approach allows natural measures of smoothness such as the squared norm of increments. More generally,  consider a linear time series model and penalize the comparator sequence through the energy of the implied driving noise terms.  derive the minimax strategy for all problems of this type and show that it can be implemented efficiently. The optimal predictions are linear in the previous observations.  obtain an explicit expression for the regret in terms of the parameters defining the problem. For typical, simple definitions of smoothness, the computation of the optimal predictions involves only sparse matrices. In the case of norm-constrained data, where the smoothness is defined in terms of the squared norm of the comparator's increments,  show that the regret grows as T/\u221a \u03bbT, where T is the length of the game and \u03bbT is an increasing limit on comparator smoothness."}]