Score-driven models of stochastic seasonality in location and scale: an application case study of the Indian rupee to USD exchange rate

We estimate the stochastic seasonality of the Indian rupee (INR) to United States dollar (USD) exchange rate by using new dynamic conditional score (DCS) specifications. We use the DCS-Skew-Gen-$$t$$t (DCS-skewed generalized t distribution) and DCS-NIG (DCS-normal-inverse Gaussian distribution) models, which are alternatives to the DCS-$$t$$t (DCS-Student’s $$t$$t -distribution) and DCS-EGB2 (DCS-exponential generalized beta distribution of the second kind) models from the literature. DCS models are robust to outliers, and such models effectively disentangle the local level, seasonality and irregular components. For the latter, we apply DCS-EGARCH (DCS-exponential generalized autoregressive conditional heteroscedasticity) scale dynamics, and we use new DCS models with seasonal volatility. We use INR/USD data for the period of 1 January 1982 to 7 July 2017. We find that the DCS-Skew-Gen-$$t$$t and DCS-NIG models are superior to the DCS-$$t$$t and DCS-EGB2 models, respectively. The amplitude of the INR/USD seasonality is relatively high during the last decade of the sample. We explain this by using the currency movements that are related to increased seasonal exports and imports of India. We show the robustness of our results for different exchange rate regimes: (i) pegged exchange rate regime period (until February 1993); (ii) liberalized exchange rate management system period (since March 1993).