In this paper we examine the application of the Least Absolute Deviations (LAD) method for ridge-type parameter estimation of Seemingly Unrelated Regression Equations (SURE) models. The methodology is aimed to deal with the SURE models with non-Gaussian error terms and highly collinear predictors in each equation. Some biasing parameters used in the literature are taken and the efficiency of both Least Squares (LS) ridge estimation and the LAD ridge estimation of the SURE models, through the Mean Squared Error (MSE) of parameter estimators, is evaluated.

In this paper, we suggest a unit root test for a system of equations using a spectral variance decomposition method based on the Maximal Overlap Discrete Wavelet Transform. We obtain the limiting distribution of the test statistic and study its small sample properties using Monte Carlo simulations. We find that, for multiple time series of small lengths, the wavelet-based method is robust to size distortions in the presence of cross-sectional dependence. The wavelet-based test is also more powerful than the Cross-sectionally Augmented Im et al. unit root test (Pesaran, M. H. 2007. "A Simple Panel Unit Root Test in the Presence of Cross-section Dependence." Journal of Applied Econometrics 22 (2): 265-312.) for time series with between 20 and 100 observations, using systems of 5 and 10 equations. We demonstrate the usefulness of the test through an application on evaluating the Purchasing Power Parity theory for the Group of 7 countries and find support for the theory, whereas the test by Pesaran (Pesaran, M. H. 2007. "A Simple Panel Unit Root Test in the Presence of Cross-section Dependence." Journal of Applied Econometrics 22 (2): 265-312.) finds no such support. 

Based on a panel wavelet efficiency analysis, we conclude that there is a systematic pattern of positive asymmetric price transmission inefficiencies in the interest rates of the largest Swedish mortgage lenders. Thus, there seems to be a higher propensity for mortgage lenders to swiftly increase their customers’ mortgage interest rates subsequent to an increase in its borrowing costs, than to decrease their customers’ mortgage rates subsequent to a corresponding decrease in the cost of borrowing. A unique contribution is our proposed wavelet method which enables a robust detection of positive asymmetric price transmission effects at various time-frequency scales, while simultaneously controlling for non-stationary trends, autocorrelation, and structural breaks. Since traditional time-series analysis methods essentially implies that several wavelet time scales are aggregated into one single time series, the blunt traditional error correction analysis totally failed to discover APT effects for this data set. In summary, using the wavelet method we show that even though the customers in the end finally will benefit from decreases in the mortgage lenders’ financing costs, the lenders wait disproportionally long before the customers’ mortgage rates are decreased.

This paper introduces shrinkage estimators (Ridge DOLS) for the dynamic ordinary least squares (DOLS) cointegration estimator, which extends the model for use in the presence of multicollinearity between the explanatory variables in the cointegration vector. Both analytically and by using simulation techniques, we conclude that our new Ridge DOLS approach exhibits lower mean square errors (MSE) than the traditional DOLS method. Therefore, based on the MSE performance criteria, our Monte Carlo simulations demonstrate that our new method outperforms the DOLS under empirically relevant magnitudes of multicollinearity. Moreover, we show the advantages of this new method by more accurately estimating the environmental Kuznets curve (EKC), where the income and squared income are related to carbon dioxide emissions. Furthermore, we also illustrate the practical use of the method when augmenting the EKC curve with energy consumption. In summary, regardless of whether we use analytical, simulation-based, or empirical approaches, we can consistently conclude that it is possible to estimate these types of relationships in a considerably more accurate manner using our newly suggested method.

This article considers several estimators for estimating the ridge parameter k for multinomial logit model based on the work of Khalaf and Shukur (2005), Alkhamisi et al. (2006), and Muniz et al. (2012). The mean square error (MSE) is considered as the performance criterion. A simulation study has been conducted to compare the performance of the estimators. Based on the simulation study we found that increasing the correlation between the independent variables and the number of regressors has negative effect on the MSE. However, when the sample size increases the MSE decreases even when the correlation between the independent variables is large. Based on the minimum MSE criterion some useful estimators for estimating the ridge parameter k are recommended for the practitioners

Generalized least squares estimation of a system of seemingly unrelated regressions is usually a two-stage method: (1) estimation of cross-equation covariance matrix from ordinary least squares residuals for transforming data, and (2) application of least squares on transformed data. In presence of multicollinearity problem, conventionally ridge regression is applied at stage 2. We investigate the usage of ridge residuals at stage 1, and show analytically that the covariance matrix based on the least squares residuals does not always result in more efficient estimator. A simulation study and an application to a system of firms' gross investment support our finding.

In this article, two new powerful tests for cointegration are proposed. The general idea is based on an intuitively appealing extension of the traditional, rather restrictive cointegration concept. In this article, we allow for a nonlinear, but most importantly a different, asymmetric convergence process to account for negative and positive changes in our cointegration approach. Using Monte Carlo simulations we verify, that the estimated size of the first test depends on the unknown value of a signal-to-noise ratio q. However, our second test—which is based on the original ideas of Kanioura and Turner—is more successful and robust in the sense that it works in all of the different evaluated situations. Furthermore it is shown to be more powerful than the traditional residual based Enders and Siklos method. The new optimal test is also applied in an empirical example in order to test for potential nonlinear asymmetric price transmission effects on the Swedish power market. We find that there is a higher propensity for power retailers to rapidly and systematically increase their retail electricity prices subsequent to increases in Nordpool's wholesale prices, than there is for them to reduce their prices subsequent to a drop in wholesale spot prices.

This article introduces two different non-parametric wavelet-based panel unit-root tests in the presence of unknown structural breaks and cross-sectional dependencies in the data. These tests are compared with a previously suggested non-parametric wavelet test, the parameteric Im-Pesaran and Shin (IPS) test and a Wald type of test. The results from the Monte Carlo simulations clearly show that the new wavelet-ratio tests are superior to the traditional tests both in terms of size and power in panel unit-root tests because of its robustness to cross-section dependency and structural breaks. Based on an empirical Central American panel application, we can, in contrast to previous research (where bias due to structural breaks is simply disregarded), find strong, clear-cut support for purchasing power parity (PPP) in this developing region.

The Forecasting of sales in a company is one of the crucial challenges that must be faced. Nowadays, there is a large spectrum of methods that enable making reliable forecasts. However, sometimes the nature of time series excludes many well-known and widely used forecasting methods (e.g. econometric models). Therefore, the authors decided to forecast on the basis of a seasonally adjusted median of selected probability distributions. The obtained forecasts were verified by means of distributions of the Theil U² coefficient and unbiasedness coefficient.

This paper suggests some Liu type shrinkage estimators for the dynamic ordinary least squares (DOLS) estimator that may be used to combat the multicollinearity problem. DOLS is an estimator suggested to solve the finite sample bias of OLS caused by endogeneity issue when estimating regression models based on cointegrated variables. In this paper using simulation techniques it is shown that multicollinearity and non-normality of the error term is a problem in finite samples for the DOLS model. The merit of proposed Liu type estimator are shown by means of a Monte Carlo simulation study and using an empirical application.