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使用相关预测成本函数估计时间序列模型AI 解读

In many forecasting problems, the forecast cost function is used only in evaluating the forecasts; a second cost function is used in estimating the parameters in the model. In this paper, I explore some of the ways in which the forecast cost function can be used in estimating the parameters and, more generally, in producing the forecasts. I define the optimal forecast and note that it may depend on the entire conditional distribution of the data, which is typically unknown.…

使用相关成本函数估计时间序列模型AI 解读

In many forecasting problems, the forecast cost function is used only in evaluating the forecasts; a second cost function is used in estimating the parameters in the model. In this paper, I explore some of the ways in which the forecast cost function can be used in estimating the parameters and, more generally, in producing the forecasts. I define the optimal forecast and note that it may depend on the entire conditional distribution of the data, which is typically unknown.…

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利用最小绝对误差估计非线性动态模型AI 解读

We consider least absolute error estimation in a dynamic nonlinear model with neither independent nor identically distributed errors. The estimator is shown to be consistent and asymptotically normal, with asymptotic covariance matrix depending on the errors through the heights of their density functions at their medians (zero). A consistent estimator of the asymptotic covariance matrix of the estimator is given, and the Wald, Lagrange multiplier, and likelihood ratio tests…

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普通最小二乘与最小绝对误差估计的比较AI 解读

In a linear-regression model with heteroscedastic errors, we consider two tests: a Hausman test comparing the ordinary least squares (OLS) and least absolute error (LAE) estimators and a test based on the signs of the errors from OLS. It turns out that these are related by the well-known equivalence between Hausman and the generalized method of moments tests. Particular cases, including homoscedasticity and asymmetry in the errors, are discussed.

ARCH 模型的渐近理论：估计与检验AI 解读

In the context of a linear dynamic model with moving average errors, we consider a heteroscedastic model which represents an extension of the ARCH model introduced by Engle [4]. We discuss the properties of maximum likelihood and least squares estimates of the parameters of both the regression and ARCH equations, and also the properties of various tests of the model that are available. We do not assume that the errors are normally distributed.

ARCH 与双线性时间序列模型：比较与结合AI 解读

Two extensions to the ARMA model, bilinearity and ARCH errors are compared, and their combination is considered. Starting with the ARMA model, tests for each extension are discussed, along with various least squares and maximum likelihood estimates of the parameters and tests of the estimated models based on these. The effects each may have on the identification, estimation, and testing of the other are given, and it is seen that to distinguish between the two properly, it…

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