ESTIMATING THE PARAMETERS OF AUTOREGRESSISVE MODELS USING YULE-WALKER EQUATIONS
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Abstract
This research will undertake a comprehensive statistical analysis of Nigeria's
Exchange rate spanning a decade, with a focus on estimating Autoregressive (AR) models using a prominent statistical methods: the Yule-Walker method. The study aims to provide statistical insights into the underlying dynamics of Nigeria's economic performance during this period. The research will commence by delineating the statistical framework of AR models, which offer a statistical representation of a time series based on its past values. Subsequently, the Yule-Walker method will be introduced, a statistical technique leveraging autocorrelation functions to estimate AR model parameters. The statistical properties of Yule-Walker estimators will be elucidated in the context of Nigeria's Exchange rate data. In contrast, the Least Squares method will be presented as an alternative statistical approach, characterized by its objective to minimize the sum of squared prediction errors. A statistical framework for the least squares estimators will be outlined, providing insights into the statistical properties of parameter estimates and their significance in explaining variations in Nigeria's Exchange rate. The core of the research involves the statistical analysis of Nigeria's Exchange rate time series data over the forty-three year period. The Yule-Walker method will be applied to estimate AR models tailored to the Exchange rate data. The statistical comparison will be based on goodness-of-fit statistics, such as the Akaike Information Criterion (AIC), to evaluate the models' adequacy in capturing the statistical patterns within the Exchange rate dataset.
Exchange rate spanning a decade, with a focus on estimating Autoregressive (AR) models using a prominent statistical methods: the Yule-Walker method. The study aims to provide statistical insights into the underlying dynamics of Nigeria's economic performance during this period. The research will commence by delineating the statistical framework of AR models, which offer a statistical representation of a time series based on its past values. Subsequently, the Yule-Walker method will be introduced, a statistical technique leveraging autocorrelation functions to estimate AR model parameters. The statistical properties of Yule-Walker estimators will be elucidated in the context of Nigeria's Exchange rate data. In contrast, the Least Squares method will be presented as an alternative statistical approach, characterized by its objective to minimize the sum of squared prediction errors. A statistical framework for the least squares estimators will be outlined, providing insights into the statistical properties of parameter estimates and their significance in explaining variations in Nigeria's Exchange rate. The core of the research involves the statistical analysis of Nigeria's Exchange rate time series data over the forty-three year period. The Yule-Walker method will be applied to estimate AR models tailored to the Exchange rate data. The statistical comparison will be based on goodness-of-fit statistics, such as the Akaike Information Criterion (AIC), to evaluate the models' adequacy in capturing the statistical patterns within the Exchange rate dataset.
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