Modelling asymmetric conditional heteroskedasticity in financial asset returns: an extension of Nelson’s EGARCH model

Recently, volatility modeling has been a very active and extensive research area in empirical finance and time series econometrics for both academics and practitioners. GARCH models have been the most widely used in this regard. However, GARCH models have been found to have serious limitations empirically among which includes, but not limited to; failure to take into account leverage effect in financial asset returns. As such so many models have been proposed in trying to solve the limitations of the leverage effect in GARCH models two of which are the EGARCH and the TARCH models. The EGARCH model is the most highly used model. It however has its limitations which include, but not limited to; stability conditions in general and existence of unconditional moments in particular depend on the conditional density, failure to capture leverage effect when the parameters are of the same signs, assuming independence of the innovations, lack of asymptotic theory for its estimators et cetera. This paper therefore is geared at extending/improving on the EGARCH model by taking into account the said empirical limitations. The main objective of this paper therefore is to develop a volatility model that solves the problems faced by the exponential GARCH model. Using the Quasi-maximum likelihood estimation technique coupled with martingale techniques, while relaxing the independence assumption of the innovations; the paper has shown that the proposed asymmetric volatility model not only provides strongly consistent estimators but also provides asymptotically efficient estimator

Modelling asymmetric conditional heteroskedasticity in financial asset returns: an extension of Nelson’s EGARCH model

Recently, volatility modeling has been a very active and extensive research area in empirical finance and time series econometrics for both academics and practitioners. GARCH models have been the most widely used in this regard. However, GARCH models have been found to have serious limitations empirically among which includes, but not limited to; failure to take into account leverage effect in financial asset returns. As such so many models have been proposed in trying to solve the limitations of the leverage effect in GARCH models two of which are the EGARCH and the TARCH models. The EGARCH model is the most highly used model. It however has its limitations which include, but not limited to; stability conditions in general and existence of unconditional moments in particular depend on the conditional density, failure to capture leverage effect when the parameters are of the same signs, assuming independence of the innovations, lack of asymptotic theory for its estimators et cetera. This paper therefore is geared at extending/improving on the EGARCH model by taking into account the said empirical limitations. The main objective of this paper therefore is to develop a volatility model that solves the problems faced by the exponential GARCH model. Using the Quasi-maximum likelihood estimation technique coupled with martingale techniques, while relaxing the independence assumption of the innovations; the paper has shown that the proposed asymmetric volatility model not only provides strongly consistent estimators but also provides asymptotically efficient estimator

Non-parametric Estimation of GARCH (2, 2) Volatility model: A new Algorithm

The main objective of this paper is to provide an estimation approach for non-parametric GARCH (2, 2) volatility model. Specifically the paper, by combining the aspects of multivariate adaptive regression splines(MARS) model estimation algorithm proposed by Chung (2012) and an algorithm proposed by Buhlman and McNeil(200), develops an algorithm for non-parametrically estimating GARCH (2,2) volatility model. Just like the MARS algorithm, the algorithm that is developed in this paper takes a logarithmic transformation as a preliminary analysis to examine a nonparametric volatility model. The algorithm however differs from the MARS algorithm by assuming that the innovations are i.d.d. The algorithm developed follows similar steps to that of Buhlman and McNeil (200) but starts by semi parametric estimation of the GARCH model and not parametric while relaxing the dependency assumption of the innovations to avoid exposing the estimation procedure to risk of inconsistency in the event of misspecification errors

A Residual-based Test For Multicointegration In Models With Structural Breaks And Threshold Adjustment To Steady State

In this paper I derive a test of Multicointegration of I (2) series that takes into account both structural breaks and threshold adjustment to steady state. I extend the I(2) –multicointegration test proposed by Berenguer-Rico and Carrion-i-Silvestre (2005), by relaxing the assumption of symmetric adjustment. In a way, I adapt the Engsted et al. (1997) approach to the concept of multicointegration and following Enders and Siklos (2001) I model the multicointegration relation while allowing for asymmetric adjustment to long run equilibrium. Further, use is made of the multivariate invariance principle, the weak convergence to stochastic integrals for dependent heterogeneous processes, and the continuous mapping theorem in order to derive an augmented Dickey-Fuller type of multicointegration test for I (2) series. I find that the limiting distributions of the estimators and test statistics associated with multicointegration depend on the cut-off point of the asymmetric response and the break point. I illustrate the test by applying it to understanding interest rate pass-through in Malawi. The derived multicointegration test confirms the presence of multicointegration among lending rates, policy rate and Treasury bill rates in Malawi in which lending rates adjust asymmetrically to steady state following a positive or negative policy rate adjustment

A semi-parametric GARCH (1, 1) estimator under serially dependent innovations

The main objective of this study is to derive semi parametric GARCH (1, 1) estimator under serially dependent innovations. The specific objectives are to show that the derived estimator is not only consistent but also asymptotically normal. Normally, the GARCH (1, 1) estimator is derived through quasi-maximum likelihood estimation technique and then consistency and asymptotic normality are proved using the weak law of large numbers and Linde-berg central limit theorem respectively. In this study, we apply the quasi-maximum likelihood estimation technique to derive the GARCH (1, 1) estimator under the assumption that the innovations are serially dependent. Allowing serial dependence of the innovations has however brought problems in terms of methodology. Firstly, we cannot split the joint probability distribution into a product of marginal distributions as is normally done. Rather, the study splits the joint distribution into a product of conditional densities to get around this problem. Secondly, we cannot use the weak laws of large numbers or/and the Linde-berg central limit theorem. We therefore employ the martingale techniques to achieve the specific objectives. Having derived the semi parametric GARCH (1, 1) estimator, we have therefore shown that the derived estimator not only converges almost surely to the true population parameter but also converges in distribution to the normal distribution with the highest possible convergence rate similar to that of parametric estimator

The Interactive Effects of Farm Input Subsidy Program and Agricultural Extension Services on Smallholder Maize Production and Technical Efficiency in Malawi

This study assessed the interactive effects of access to agricultural extension services and Farm Input Subsidy Program (FISP) on maize production,  maize production technical efficiency and maize production uncertainty in Malawi. It employed a stochastic frontier model within the spheres of two-  stage estimation technique applied on the fourth Integrated Household Survey (IHS4). The results indicated that households that have access to both  FISP and extension services experience about 0.773% higher maize yield compared to households that have access to FISP only. Further, the study  found that enhancing extension services within FISP environment improves maize production efficiency and reduces maize production uncertainty in  Malawi

Externalities of Irrigation Policy on Youth Entrepreneurship in Malawi

This paper assesses the spill-over effects of irrigation on youth entrepreneurship. Using the Fourth Integrated Household Survey (IHS4) the study  employs a hierarchical three level random effects logit model in an attempt to achieve the objective. The study confirms the presence of positive spill  over effects of irrigation programs on youth entrepreneurship. This provides more justification for increased funding to generic programs like  irrigation with additional rationale of trying to provide the much needed finance to the youth in Malawi so as to mitigate the problem of youth  unemployment