Temporal Aggregation and Ordinary Least Squares Estimation of Cointegrating Regressions

The paper derives the asymptotic distribution of the ordinary least squares estimator of cointegrating vectors with temporally aggregated time series. It is shown, that temporal aggregation reduces the bias and variance of the estimator for average sampling (temporal aggregation of flow series) and does not affect the limiting distribution for systematic sampling (temporal aggregation of stock series). A Monte Carlo experiment shows the consistency of the finite sample results with the asymptotic theory.

Estimating the intercept in an orthogonally blocked experiment when the block effects are random.

Abstract: For an orthogonally blocked experiment, Khuri (1992) has shown that the ordinary least squares estimator and the generalized least squares estimator of the factor effects in a response surface model with random block effects coincide. However, the equivalence does not hold for the estimation of the intercept when the block sizes are heterogeneous. When the block sizes are homogeneous, ordinary and generalized least squares provide an identical estimate for the intercept.Effects;

Simultaneous Prediction of Actual and Average Values of Study Variable Using Stein-rule Estimators

The simultaneous prediction of average and actual values of study variable in a linear regression model is considered in this paper. Generally, either of the ordinary least squares estimator or Stein-rule estimators are employed for the construction of predictors for the simultaneous prediction. A linear combination of ordinary least squares and Stein-rule predictors are utilized in this paper to construct an improved predictors. Their efficiency properties are derived using the small disturbance asymptotic theory and dominance conditions for the superiority of predictors over each other are analyzed

Limit Laws in Transaction-Level Asset Price Models

We consider pure-jump transaction-level models for asset prices in continuous time, driven by point processes. In a bivariate model that admits cointegration, we allow for time deformations to account for such e®ects as intraday seasonal patterns in volatility, and non-trading periods that may be di®erent for the two assets. Most assumptions are stated directly on the point process, though we provide su±cient conditions on the corresponding inter-trade durations for these assumptions to hold. We obtain the asymptotic distribution of the log-price process. We also obtain the asymptotic distribution of the ordinary least-squares estimator of the cointegrat- ing parameter based on data sampled from an equally-spaced discretization of calendar time, in the case of weak fractional cointegration. Finally, we obtain the limiting distribution of the ordinary least-squares estimator of the autoregressive parameter in a simpli¯ed transaction-level univariate model with a unit root.NYU, Stern, Center for Digital Economy Researc

Nonlinear Cointegration, Misspecification and Bimodality

We show that the asymptotic distribution of the ordinary least squares estimator in a cointegration regression may be bimodal. A simple case arises when the intercept is erroneously omitted from the estimated model or in nonlinear-in-variables models with endogenous regressors. In the latter case, a solution is to use an instrumental variable estimator. The core results in this paper also generalises to more complicated nonlinear models involving integrated time series.Cointegration, nonlinearity, bimodality, misspecification, instrumental variables, asymptotic theory.

Improving weighted least squares inference

These days, it is common practice to base inference about the coefficients in a hetoskedastic linear model on the ordinary least squares estimator in conjunction with using heteroskedasticity consistent standard errors. Even when the true form of heteroskedasticity is unknown, heteroskedasticity consistent standard errors can also used to base valid inference on a weighted least squares estimator and using such an estimator can provide large gains in efficiency over the ordinary least squares estimator. However, intervals based on asymptotic approximations with plug-in standard errors often have coverage that is below the nominal level, especially for small sample sizes. Similarly, tests can have null rejection probabilities that are above the nominal level. It is shown that under unknown hereroskedasticy, a bootstrap approximation to the sampling distribution of the weighted least squares estimator is valid, which allows for inference with improved finite-sample properties. For testing linear constraints, permutations tests are proposed which are exact when the error distribution is symmetric and is asymptotically valid otherwise. Another concern that has discouraged the use of weighting is that the weighted least squares estimator may be less efficient than the ordinary least squares estimator when the model used to estimate the unknown form of the heteroskedasticity is misspecified. To address this problem, a new estimator is proposed that is asymptotically at least as efficient as both the ordinary and the weighted least squares estimator. Simulation studies demonstrate the attractive finite-sample properties of this new estimator as well as the improvements in performance realized by bootstrap confidence intervals