Modelling the Volatility of the USD/KES Exchange Rate Using the Nadaraya-watson Kernel Regression Estimator

Exchange rate volatility poses significant challenges for economic planning, risk management, and policy formulation in emerging economies such as Kenya. This study models the volatility of the United States Dollar/ Kenyan Shillings (USD/KES) exchange rate using the nonparametric Nadaraya-Watson kernel regression estimator. Daily buying rates from the Central Bank of Kenya spanning January 2, 2003, to December 29, 2023 (4,764 observations) were used. The Nadaraya-Watson estimator smooths the data using kernel functions and bandwidth parameters, enabling it to adapt to localized features in the volatility pattern that conventional parametric models may overlook. The conditional mean and conditional variance functions were estimated using a Gaussian kernel with cross-validated fixed bandwidths. The optimal bandwidth for the conditional mean was 0.02750928 and for the conditional variance was 0.1349632, with a bandwidth ratio of 4.905869, indicating that the volatility function requires smoother estimation. The conditional variance function exhibited a distinct U-shape, showing higher volatility following extreme positive or negative lagged returns. The model achieved a Root Mean Squared Error (RMSE) of 1.919 for variance, capturing major volatility episodes including the 2008-2009 financial crisis, the 2011 currency crisis, and the 2016 reserves depletion shock. The study concludes that the Nadaraya-Watson kernel regression estimator successfully captures nonlinear volatility dynamics without imposing rigid parametric assumptions, making it suitable for emerging market currencies like the Kenyan shilling.