Ilias Kevork

A comparison of alternative unit root tests

In this paper we evaluate the performance of three methods for testing the existence of a unit root in a time series, when the models under consideration in the null hypothesis do not display autocorrelation in the error term. In such cases, simple versions of the Dickey–Fuller test should be used as the most appropriate ones instead of the known augmented Dickey–Fuller or Phillips–Perron tests. Through Monte Carlo simulations we show that, apart from a few cases, testing the existence of a unit root we obtain actual type I error and power very close to their nominal levels. Additionally, when the random walk null hypothesis is true, by gradually increasing the sample size, we observe that p-values for the drift in the unrestricted model fluctuate at low levels with small variance and the Durbin–Watson (DW) statistic is approaching 2 in both the unrestricted and restricted models. If, however, the null hypothesis of a random walk is false, taking a larger sample, the DW statistic in the restricted model starts to deviate from 2 while in the unrestricted model it continues to approach 2. It is also shown that the probability not to reject that the errors are uncorrelated, when they are indeed not correlated, is higher when the DW test is applied at 1% nominal level of significance. Email: kevork@uth.gr

Forecasting the stationary AR(1) with an almost unit root

Although unit root tests have made a great contribution in time series econometrics, their major disadvantage is the low powers they attain on certain occasions, as for the case of the stationary AR(1), when φis close to one. In this study, considering the random walk as the true model, we derive the probability of the prediction interval to include any future value yT + s of AR(1). Using certain estimates from Monte Carlo simulations, we proceed to numerical computations, resulting in the main finding that the values for the specific probability depend upon the location the most recent available observation in the sample possesses in its marginal distribution.

Evaluating alternative Frequentist inferential approaches for optimal order quantities in the newsvendor model under Exponential demand

Three estimation policies for the optimal order quantity of the classical newsvendor model under exponential demand are evaluated in the current paper. According to the principle of the first estimation policy, the corresponding estimator is obtained replacing in the theoretical formula which gives the optimal order quantity the parameter of exponential distribution with its maximum likelihood estimator. The estimator of the second estimation policy is derived in such a way as to ensure that the requested critical fractile is attained. For the third estimation policy, the corresponding estimator is obtained maximizing the a-priori expected profit with respect to a constant which has been included into the form of the estimator. Three statistical measures have been chosen to perform the evaluation. The actual critical fractile attained by each estimator, the mean square error, and the range of deviation of estimates from the optimal order quantity, when the probability to take such a range is the same for the three estimation policies. The behavior of the three statistical measures is explored under different combinations of sample sizes and critical fractiles. With small sample sizes, no estimation policy predominates over the others. The estimator which attains the closest actual critical fractile to the requested one, this estimator has the largest mean square and the largest range of deviation of estimates from the optimal order quantity. On the contrary, with samples over 40 observations, the choice is restricted among the estimators of the first and third estimation policy. To facilitate this choice, at different sample sizes, we offer the required values of the critical fractile which determine which estimation policy eventually should be applied.

Estimating Malmquist productivity indexes using probabilistic directional distances: An application to the European banking sector

Our paper by adopting the latest advances on the probabilistic characterization of directional distance functions as has been introduced by Daraio and Simar (2014), develops a Malmquist productivity index and presents its main decompositions. Specifically, the proposed productivity index is based on the probabilistic version of directional distance functions which are expressed as transformations of radial distances. We illustrate how these indexes can be computed and how different components can be derived. Specifically, we demonstrate how a probabilistic version of the following categories of change can be obtained: technical, efficiency, pure efficiency, scale efficiency, scale change factor and scale bias of technical change. Finally, we apply the probabilistic productivity indexes alongside with their decompositions to inputs/outputs data from a sample of 644 banks from 28 European countries between the years 2007, 2010 and 2014. The results suggest that the EU banks’ productivity levels remained relative unchanged from the initiation of U.S. prime crisis and during the EU sovereign debt crisis. Finally, during the U.S. prime crisis and the Global Financial Crisis, banks’ maintained their productivity levels by utilizing better their inputs and by exploiting scale economies. However, during the sovereign debt crisis banks maintained their productivity levels by investing on financial engineering competences.

Critical values for testing a unit root in finite samples from the MA(1)

This study, using a certain simulation strategy, for the exact maximum likelihood estimator of θ from the MA(1), estimates appropriate percentiles, together with their standard errors, offering a new set of critical values for testing in finite samples H0: θ = −1, against H1: θ>−1. In this way, appropriate regions for rejecting the null or being in uncertainty are defined, regardless of the values of MA(1) parameters. The new set of critical values produce both actual level of significance close to the nominal one and, when θ is not very close to −1, comparable power with the up to now suggested asymptotic values. These asymptotic values, unfortunately, lead to actual level of significance considerably greater than the nominal one, especially in large samples.

Testing for a unit root under the alternative hypothesis of ARIMA (0, 2, 1)

Showing a dual relationship between ARIMA (0, 2, 1) with parameter θ = −1 and the random walk, a new alternative hypothesis in the form of ARIMA (0, 2, 1) is established in this article for evaluating unit root tests. The power of four methods of testing for a unit root is investigated under the new alternative, using Monte Carlo simulations. The first method testing θ = −1 in second differences and using a new set of critical values suggested by the two authors in finite samples, is the most appropriate from the integration order point of view. The other three methods refer to tests based on t and φ statistics introduced by Dickey and Fuller, as well as, the nonparametric Phillips–Perron test. Additionally, for cases where for the first method a low power is met, we studied the validity of prediction interval for a future value of ARIMA (0, 2, 1) with θ close but greater of −1, using the prediction equation and the error variance of the random walk. Keeping the forecasting horizon short, the coverage of the interval ranged at expected levels, but its average half-length ranged up to four times more than its true value.

European financial crisis and bank productivity: evidence from Eastern European Countries

ABSTRACT The paper examines the productivity levels of the largest banks operating in the Eastern European countries over the period of the ongoing European financial crisis. Specifically, the analysis covers the periods of U.S. subprime crisis, the global financial crisis and the sovereign debt crisis. By adopting a fully nonparametric framework, it provides a probabilistic version of a directional input-oriented Malmquist productivity index alongside with its main decomposition. The results from the analysis suggest that banks have faced a deterioration of their productivity levels between the examined periods. It is evident that during the initiation of European sovereign debt crisis, the banks have weakened their ability to utilize efficiently their inputs of production and their ability to realize scale economies.

A sequential procedure for testing the existence of a random walk model in finite samples

Given the random walk model, we show, for the traditional unrestricted regression used in testing stationarity, that no matter what the initial value of the random walk is or its drift or its error standard deviation, the sampling distributions of certain statistics remain unchanged. Using Monte Carlo simulations, we estimate, for different finite samples, the sampling distributions of these statistics. After smoothing the percentiles of the empirical sampling distributions, we come up with a new set of critical values for testing the existence of a random walk, if each statistic is being used on an individual base. Combining the new sets of critical values, we finally suggest a general methodology for testing for a random walk model.