Page 1. LIST OF CONTRIBUTORS Torben G. Andersen Department of Finance, Kellogg School of Manageme... more Page 1. LIST OF CONTRIBUTORS Torben G. Andersen Department of Finance, Kellogg School of Management, Northwestern University, IL, USA ... Ngai Hang Chan Department of Statistics, The Chinese University of Hong Kong, New Territories, Hong Kong ...
To find approximations for bias, variance and mean-squared error of least-squares estimators for ... more To find approximations for bias, variance and mean-squared error of least-squares estimators for all coefficients in a linear dynamic regression model with a unit root, we derive asymptotic expansions and examine their accuracy by simulation. It is found that in this particular context useful expansions exist only when the autoregressive model contains at least one non-redundant exogenous explanatory variable. Surprisingly, the large-sample and smalldisturbance asymptotic techniques give closely related results, which is not the case in stable dynamic regression models. We specialize our general expressions for moment approximations to the case of the random walk with drift model and find that they are unsatisfactory when the drift is small. Therefore, we develop what we call small-drift asymptotics which proves to be very accurate, especially when the sample size is very small. and , and extended by to the case of included exogenous variables under normality assumptions, while Peters (1987) analysed the same ARX(1) model with non-normal disturbances. These papers did not provide explicit expressions for moments that allow further analysis, but they did yield useful numerical results for different disturbance structures and specific exogenous data series. Such numerical results, however, can also be obtained to a high degree of accuracy by straightforward simulation.
Page 1. LIST OF CONTRIBUTORS Torben G. Andersen Department of Finance, Kellogg School of Manageme... more Page 1. LIST OF CONTRIBUTORS Torben G. Andersen Department of Finance, Kellogg School of Management, Northwestern University, IL, USA ... Ngai Hang Chan Department of Statistics, The Chinese University of Hong Kong, New Territories, Hong Kong ...
To find approximations for bias, variance and mean-squared error of least-squares estimators for ... more To find approximations for bias, variance and mean-squared error of least-squares estimators for all coefficients in a linear dynamic regression model with a unit root, we derive asymptotic expansions and examine their accuracy by simulation. It is found that in this particular context useful expansions exist only when the autoregressive model contains at least one non-redundant exogenous explanatory variable. Surprisingly, the large-sample and smalldisturbance asymptotic techniques give closely related results, which is not the case in stable dynamic regression models. We specialize our general expressions for moment approximations to the case of the random walk with drift model and find that they are unsatisfactory when the drift is small. Therefore, we develop what we call small-drift asymptotics which proves to be very accurate, especially when the sample size is very small. and , and extended by to the case of included exogenous variables under normality assumptions, while Peters (1987) analysed the same ARX(1) model with non-normal disturbances. These papers did not provide explicit expressions for moments that allow further analysis, but they did yield useful numerical results for different disturbance structures and specific exogenous data series. Such numerical results, however, can also be obtained to a high degree of accuracy by straightforward simulation.
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