Forecasts can either be short term, medium term or long term. In this work we considered short term forecast because of the problem of limited data or time series data that is often encounter in time series analysis. ...Forecasts can either be short term, medium term or long term. In this work we considered short term forecast because of the problem of limited data or time series data that is often encounter in time series analysis. This simulation study considered the performances of the classical VAR and Sims-Zha Bayesian VAR for short term series at different levels of collinearity and correlated error terms. The results from 10,000 iteration revealed that the BVAR models are excellent for time series length of T=8 for all levels of collinearity while the classical VAR is effective for time series length of T=16 for all collinearity levels except when ρ = -0.9 and ρ = -0.95. We therefore recommended that for effective short term forecasting, the time series length, forecasting horizon and the collinearity level should be considered.展开更多
The method of condition number is commonly used to diagnose a normal matrix N whether it is ill conditioned state or not. For its shortcoming, a method to measure multi collinearity of a matrix was put forward. The me...The method of condition number is commonly used to diagnose a normal matrix N whether it is ill conditioned state or not. For its shortcoming, a method to measure multi collinearity of a matrix was put forward. The method is that implement Gram Schmidt orthogonalizing process to column vectors of a design matrix A (α l ), then calculate the norms of every vector before and after orthogonalization process and their corresponding ratio, and use the minimum ratio among the group of ratios to measure the multi collinearity of A. According to the corresponding relationship between the multi collinearity and the ill conditioned state of a matrix, the method also studies and offers reference indexes weighing the ill conditioned state of a matrix based on the relative norm. The remarkable characteristics of the method are that the measure of multi collinearity has idiographic geometry meaning and clear lower and upper limit, the size of the measure reflects the multi collinearity of column vectors objectively. It is convenient to study the reason that results in the matrix being multi collinearity and to put forward solving plan according to the method which is summarized as the method of minimum norm and abbreviated as F method.展开更多
文摘Forecasts can either be short term, medium term or long term. In this work we considered short term forecast because of the problem of limited data or time series data that is often encounter in time series analysis. This simulation study considered the performances of the classical VAR and Sims-Zha Bayesian VAR for short term series at different levels of collinearity and correlated error terms. The results from 10,000 iteration revealed that the BVAR models are excellent for time series length of T=8 for all levels of collinearity while the classical VAR is effective for time series length of T=16 for all collinearity levels except when ρ = -0.9 and ρ = -0.95. We therefore recommended that for effective short term forecasting, the time series length, forecasting horizon and the collinearity level should be considered.
文摘The method of condition number is commonly used to diagnose a normal matrix N whether it is ill conditioned state or not. For its shortcoming, a method to measure multi collinearity of a matrix was put forward. The method is that implement Gram Schmidt orthogonalizing process to column vectors of a design matrix A (α l ), then calculate the norms of every vector before and after orthogonalization process and their corresponding ratio, and use the minimum ratio among the group of ratios to measure the multi collinearity of A. According to the corresponding relationship between the multi collinearity and the ill conditioned state of a matrix, the method also studies and offers reference indexes weighing the ill conditioned state of a matrix based on the relative norm. The remarkable characteristics of the method are that the measure of multi collinearity has idiographic geometry meaning and clear lower and upper limit, the size of the measure reflects the multi collinearity of column vectors objectively. It is convenient to study the reason that results in the matrix being multi collinearity and to put forward solving plan according to the method which is summarized as the method of minimum norm and abbreviated as F method.
