Let Y = (y Yn) be a set of n vector observations of dimension q such...

 

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Let Y = (y₁ Yn) be a set of n vector observations of dimension q such that y₁ = R. For modeling these observations we propose to use the parametric model (yli qi) given by **** Y₁ = P₁yi-1 + P2Y₁-2 + ... + $pyi-p+ €₁ where are independent identically distributed normal random variables with mean vector zero and qx q variance-covariance matrix E modeling the approximation errors and the $₁, j= 1,..., p are qx q coefficient or parameter matrices. (a) How many vector observations need to be lost to work with this model? And what is the effective number of observation ? (b) Provide a linear matrix form for the model where the parameters are represented in a (pq) xq matrix form = [₁,₂], derive the least square estimator of and the maximum likelihood estimate of E (c) What could you describe as an inconvenience of this model and find the number of pa- rameters involved in the model (d) Derive the expression of the log-likelihood for this model (e) Use the obtained log-likelihood expression to obtain the expressions of AIC and BIC (f) What consequences this model has on selection criteria ? Let Y = (y₁ Yn) be a set of n vector observations of dimension q such that y₁ = R. For modeling these observations we propose to use the parametric model (yli qi) given by **** Y₁ = P₁yi-1 + P2Y₁-2 + ... + $pyi-p+ €₁ where are independent identically distributed normal random variables with mean vector zero and qx q variance-covariance matrix E modeling the approximation errors and the $₁, j= 1,..., p are qx q coefficient or parameter matrices. (a) How many vector observations need to be lost to work with this model? And what is the effective number of observation ? (b) Provide a linear matrix form for the model where the parameters are represented in a (pq) xq matrix form = [₁,₂], derive the least square estimator of and the maximum likelihood estimate of E (c) What could you describe as an inconvenience of this model and find the number of pa- rameters involved in the model (d) Derive the expression of the log-likelihood for this model (e) Use the obtained log-likelihood expression to obtain the expressions of AIC and BIC (f) What consequences this model has on selection criteria ?

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a The number of vector observations needed to work with this model is n p The effective number of ob... View the full answer