Volatility forecast comparison using imperfect volatility proxies

The use of a conditionally unbiased, but imperfect, volatility proxy can lead to undesirable outcomes in standard methods for comparing conditional variance forecasts. We motivate our study with analytical results on the distortions caused by some widely used loss functions, when used with standard volatility proxies such as squared returns, the intra-daily range or realised volatility. We then derive necessary and sufficient conditions on the functional form of the loss function for the ranking of competing volatility forecasts to be robust to the presence of noise in the volatility proxy, and derive some useful special cases of this class of “robust” loss functions. The methods are illustrated with an application to the volatility of returns on IBM over the period 1993 to 2003.     

Chi-squared tests for evaluation and comparison of asset pricing models

This paper presents a general statistical framework for estimation, testing and comparison of asset pricing models using the unconstrained distance measure of Hansen and Jagannathan (1997). The limiting results cover both linear and nonlinear models that could be correctly specified or misspecified. We propose modified versions of the existing model selection tests and new pivotal specification and model comparison tests with improved finite-sample properties. In addition, we provide formal tests of multiple model comparison. The excellent size and power properties of the proposed tests are demonstrated using simulated data from linear and nonlinear asset pricing models.     

A note on invariance of multiple tests

The property of invariance—well-known for a single test problem—is extended to multiple test problems. It is shown that the invariance of the components of a multiple test is necessary and sufficient for the multiple test to be invariant. Furthermore, the invariance of stepwise procedures is investigated. An example is given addressing some related aspects.     

A nonparametric multiple comparison test for differences in scale parameters

A nonparametric multiple comparison test for differences in scale parameters is suggested The asymptotic distribution of the test statistic is derived. A modification of the test when the location parameters are unknown and unequal is suggested. This modified test is not asymptotically distribution free for all underlying location-scale families; however, we give sufficient conditions on the families under which the test is asymptotically distribution free.     

A comparison of two nonparametric k -sample slippage tests

The tests which are discussed here are Mosteller's k -sample slippage test for an extreme population [8] and the k -sample slippage analogue of the Wilcoxon two-sample test proposed by D oornbos and P rins [3]. A comparison is made between both tests in respect of their consistency against normal, exponential and uniform shifts and against Lehmann-alternatives. For some small sample sizes the powers of the two tests have been calculated.     

Local comparison of linear rank tests,in the Bahadur sense

Summary As continuation ofKremer [1979a] a theory of asymptotic comparison based on local Bahadur efficiency is derived for general linear rank tests of the one-sample symmetry problem and thek-sample problem (k2). The results are similar to former considerations based on Pitman efficiency but hold under weaker conditions on the scores-generating functions or local alternatives.     

Efficiency comparison of the Wilcoxon tests in paired and independent survey samples

The efficiency concepts of Bahadur and Pitman are used to compare the Wilcoxon tests in paired and independent survey samples. A comparison through the length of corresponding confidence intervals is also done. Simple conditions characterizing the dominance of a procedure are derived. Statistical tests for checking these conditions are suggested and discussed.     

Least-squares forecast averaging

This paper proposes forecast combination based on the method of Mallows Model Averaging (MMA). The method selects forecast weights by minimizing a Mallows criterion. This criterion is an asymptotically unbiased estimate of both the in-sample mean-squared error (MSE) and the out-of-sample one-step-ahead mean-squared forecast error (MSFE). Furthermore, the MMA weights are asymptotically mean-square optimal in the absence of time-series dependence. We show how to compute MMA weights in forecasting settings, and investigate the performance of the method in simple but illustrative simulation environments. We find that the MMA forecasts have low MSFE and have much lower maximum regret than other feasible forecasting methods, including equal weighting, BIC selection, weighted BIC, AIC selection, weighted AIC, Bates–Granger combination, predictive least squares, and Granger–Ramanathan combination.