This paper suggests the use of simple minimum distance methods to estimate restricted cointegrating vectors. The method directly employs minimum distance methods on unrestricted cointegrating matrices estimated in the usual way to estimate restricted parameters which are linearly or nonlinearly related to the unrestricted cointegrating vector coefficients. The limiting distribution of the estimates as well as the usual test for the restrictions are derived. A Monte Carlo experiment is undertaken to examine the effectiveness of these methods for cointegrating vectors.

# Your search: "author:"Elliott, Graham""

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## Scholarly Works (17 results)

We derive the family of tests for a unit root with maximal power against a point alternative when an arbitrary number of stationary covariates are modeled with the potentially integrated series. We show that very large power gains are available when such covariates available. We then derive tests which are simple to construct (involving the running of vector autoregressions) and achieve at a point the power envelopes derived under very general conditions. These tests are excellent properties in small samples. We also show that these are obvious and internally consistent tests to run when identifying structural VAR's using long run restrictions.

Existing results on the properties and performance of forecast combinations have been derived in the context of mean squared error loss. Under this loss function empirical studies have generally found that estimates of optimal forecast combination weights lead to higher losses than equally-weighted combined forecasts which in turn outperform the best individual predictions. We show that this and other results can be overturned when asymmetries are introduced in the loss function and the forecast error distribution is skewed. We characterize the optimal combination weights for the most commonly used alternatives to mean squared error loss and demonstrate how the degree of asymmetry in the loss function and skews in the underlying forecast error distribution can significantly change the optimal combination weights. We also propose estimation methods and investigate their small sample properties in simulations and in an inflation forecasting exercise.

We derive the family of tests for a unit root with maximal power against a point alternative when an arbitrary number of stationary covariates are modeled with the potentially integrated series. We show that very large power gains are available when such covariates are available. We then derive tests which are simple to construct (involving the running of vector autoregressions) and achieve at a point the power envelopes derived under very general conditions. These tests have excellent properties in small samples. We also show that these are obvious and internally consistent tests to run when identifying structural VAR's using long run restrictions.

The paper analyzes the impact of the initial observation on the problem of testing for unit roots. To this end, we derive a family of optimal tests that maximize a weighted average power criterion with respect to the initial observation. We then investigate the relationship of this optimal family to unit root tests in an asymptotic framework. We find that many popular unit root tests are closely related to specific members of the optimal family, but the corresponding members employ very different weightings for the initial observation. The popular Dickey-Fuller tests, for instance, are closely related to optimal tests which put a large weight on extreme derivations of the initial observation from the deterministic component, whereas other popular tests put more weight on moderate deviations. At the same time, the power of the various unit root tests varies dramatically with the initial observation. This paper therefore helps to explain the results of the comparative power studies of unit root tests, and allows a much deeper understanding of the merits of particular tests in specific circumstances.

Instability of parametric models is a common problem in many fields of economics. In econometrics, these changes in the underlying data generating process are referred to as structural breaks. Although there is an extensive literature on estimation and statistical tests of structural breaks, existing methods fail to adequately capture a break. This dissertation consists of three papers on developing econometric methods for structural breaks and forecasting.

The first chapter develops a new method in estimating the location of a structural break in a linear model and provide theoretical results and empirical applications of the estimator. In finite sample the conventional least-squares estimates a break occurred at either ends of the sample with high probability, regardless of the true break point. I suggest an estimator of the break point that resolves this pile up issue and thus, provide a more accurate estimate of the break. The second chapter constructs a statistical test to test existence of a structural break when the direction of the parameter shift is known. In practice it is likely that a researcher is interested in testing for a structural break in a particular direction because the direction is known, such as policy change or historical data. We incorporate this information in constructing three tests that have higher power when direction is correctly specified. The last chapter proposes a multi-period forecasting method that is robust to model misspecification. When we are interested in obtaining long horizon ahead forecasts, the direct forecast method is more favorable than the iterated forecast because it is more robust to misspecification. However, direct forecast estimates tend to have jagged shapes across horizons. I use a mechanism analogous to ridge regression on the direct forecast model to maintain robustness while smoothing out erratic estimates.

This paper examines the efficiency of the forward yen/dollar market using micro survey data. Conventional tests of unbiasedness do not correspond directly to the zero-profit condition. Instead, we use the survey data to calculate potential profits of individual forecasters based on a natural trading rule. We find that although the survey data are not the best predictor of future spot rates in terms of typical mean square forecast error criteria, the survey data can be used to obtain on average positive profits. However, these profits are small and highly variable. Similar results are found when we examine profits generated by a trading rule using regression forecasts. The profits are found to be correlated with risk type variables but not other available information