WITH THE AIM OF MITIGATING THE DAMAGE CAUSED BY THE CORONAVIRUS DISEASE 2019 (COVID-19) PANDEMIC, IT IS IMPORTANT TO USE MODELS THAT ALLOW FORECASTING POSSIBLE NEW INFECTIONS ACCURATELY IN ORDER TO FACE THE PANDEMIC IN SPECIFIC SOCIOCULTURAL CONTEXTS IN THE BEST POSSIBLE WAY. OUR FIRST CONTRIBUTION IS EMPIRICAL. WE USE AN EXTENSIVE COVID-19 DATASET FROM NINE LATIN AMERICAN COUNTRIES FOR THE PERIOD OF 1 APRIL 2020 TO 31 DECEMBER 2021. OUR SECOND AND THIRD CONTRIBUTIONS ARE METHODOLOGICAL. WE EXTEND RELEVANT (I) STATE-SPACE MODELS WITH SCORE-DRIVEN DYNAMICS AND (II) NONLINEAR STATE-SPACE MODELS WITH UNOBSERVED COMPONENTS, RESPECTIVELY. WE USE WEEKLY SEASONAL EFFECTS, IN ADDITION TO THE LOCAL-LEVEL AND TREND FILTERS OF THE LITERATURE, FOR (I) AND (II), AND THE NEGATIVE BINOMIAL DISTRIBUTION FOR (II). WE FIND THAT THE STATISTICAL AND FORECASTING PERFORMANCES OF THE NOVEL SCORE-DRIVEN SPECIFICATIONS ARE SUPERIOR TO THOSE OF THE NONLINEAR STATE-SPACE MODELS WITH UNOBSERVED COMPONENTS MODEL, PROVIDING A POTENTIAL VALID ALTERNATIVE TO FORECASTING THE NUMBER OF POSSIBLE NEW COVID-19 INFECTIONS.

AN EXTENSION OF THE GENERALIZED AUTOREGRESSIVE SCORE (GAS) MODEL IS PRESENTED FOR TIME SERIES WITH EXCESS NULL OBSERVATIONS TO INCLUDE EXPLANATORY VARIABLES. AN EXTENSION OF THE GAS MODEL PROPOSED BY HARVEY AND ITO IS SUGGESTED, AND IT IS APPLIED TO PRECIPITATION DATA FROM A CITY IN CHILE. IT IS CONCLUDED THAT THE MODEL PROVIDES ADEQUATE PREDICTION, AND FURTHERMORE, AN ANALYSIS OF THE RELATIONSHIP BETWEEN THE PRECIPITATION VARIABLE AND THE EXPLANATORY VARIABLES IS SHOWN. THIS RELATIONSHIP IS COMPARED WITH THE METEOROLOGY LITERATURE, DEMONSTRATING CONCURRENCE.