Modelling of Cointegration with Student's T-errors

Abstract

Two or more non-stationary time series are said to be co-integrated if a certain linear combination of them becomes stationary. Identification of co-integrating relationships among the relevant time series helps the researchers to develop efficient forecasting methods. The classical approach of analyzing such series is to express the co-integrating time series in the form of error correction models with Gaussian errors. However, the modeling and analysis of cointegration in the presence of non-normal errors needs to be developed as most of the real time series in the field of finance and economics deviates from the assumption of normality. This paper focuses on modeling of a bivariate cointegration with a student's-t distributed error. The co-integrating vector obtained from the error correction equation is estimated using the method of maximum likelihood. A unit root test of first order non stationary process with student's t-errors is also defined. The resulting estimators are used to construct test procedures for testing the unit root and cointegration associated with two time series. The likelihood equations are all solved using numerical approaches because the estimating equations do not have an explicit solution. A simulation study is carried out to illustrate the finite sample properties of the model. The simulation experiments show that the estimates perform reasonably well. The applicability of the model is illustrated by analyzing the data on time series of Bombay stock exchange indices and crude oil prices and found that the proposed model is a good fit for the data sets.