Abstract
In this paper we introduce new Dynamic Conditional Score (DCS) models for the Skew-Gen-t (Skewed Generalized t) and NIG (Normal-Inverse Gaussian) distributions as alternatives to the recent DCS models for the Student’s-t and EGB2 (Exponential Generalized Beta of the second kind) distributions, respectively. The DCS models we propose include stochastic local level, stochastic seasonality, and irregular components with DCS-EGARCH (Exponential Generalized Autoregressive Conditional Heteroscedasticity) volatility dynamics. DCS models are robust to extreme observations, whereas standard financial time series models are not. We use data from the Guatemalan Quetzal (GTQ) to United States Dollar (USD) exchange rate for the period of 4th January 1994–30th June 2017. This dataset exhibits significant rises and falls in the GTQ/USD that lead to extreme observations, stochastic seasonality with dynamic amplitude, and volatility dynamics. These seasonality dynamics of the GTQ/USD are related to the Guatemalan trade-related currency movements, receipt and payment of foreign loans, and remittance payments of Guatemalans working abroad. We show that the in-sample statistical performance of the DCS-Skew-Gen-t and the DCS-NIG models is superior to that of the DCS-t and the DCS-EGB2 models, respectively. Furthermore, we show that the statistical performance of all DCS models is superior to that of the standard financial time series model.
Highlights
Guatemala has ranked among the largest exporters of several agricultural products worldwide
We have studied the stochastic seasonality of the Guatemalan Quetzal (GTQ)/United States Dollar (USD) currency exchange rate, by using daily exchange rate data for the period of January 1994–June 2017
For this period, when a managed float currency exchange rate regime has been used in Guatemala, reliable GTQ/USD exchange rate data are available from the Bank of Guatemala
Summary
Guatemala has ranked among the largest exporters of several agricultural products worldwide. During the last two decades, the relative importance of sugar, coffee, banana and cardamom exports, out of Guatemala’s total exports, has decreased significantly (source: Bank of Guatemala, http://www.banguat.gob.gt; see notes of Table 4) This suggests that the impact of the export-related seasonality effects on the GTQ/USD exchange rate may have decreased over time. The new DCS models for the GTQ/USD exchange rate may be more adequate for an effective in-sample measurement of the stochastic seasonality component than the standard financial time series models (i.e. the latter are less robust to extreme observations). We compare the DCS models with a standard financial time series model that de- composes the GTQ/USD exchange rate to the three components: stochastic local level μt , stochastic seasonality st , and irregular vt.
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