Coronavirus disease (COVID-19) is a severe ongoing novel pandemic that has emerged in Wuhan, China, in December 2019. As of October 13, the outbreak has spread rapidly across the world, affecting over 38 million people, and causing over 1 million deaths. In this article, I analysed several time series forecasting methods to predict the spread of COVID-19 second wave in Italy, over the period after October 13, 2020. I used an autoregressive model (ARIMA), an exponential smoothing state space model (ETS), a neural network autoregression model (NNAR), and the following hybrid combinations of them: ARIMA-ETS, ARIMA-NNAR, ETS-NNAR, and ARIMA-ETS-NNAR. About the data, I forecasted the number of patients hospitalized with mild symptoms, and in intensive care units (ICU). The data refer to the period February 21, 2020-October 13, 2020 and are extracted from the website of the Italian Ministry of Health (www.salute.gov.it). The results show that i) the hybrid models, except for ARIMA-ETS, are better at capturing the linear and non-linear epidemic patterns, by outperforming the respective single models; and ii) the number of COVID-19-related hospitalized with mild symptoms and in ICU will rapidly increase in the next weeks, by reaching the peak in about 50-60 days, i.e. in mid-December 2020, at least. To tackle the upcoming COVID-19 second wave, on one hand, it is necessary to hire healthcare workers and implement sufficient hospital facilities, protective equipment, and ordinary and intensive care beds; and on the other hand, it may be useful to enhance social distancing by improving public transport and adopting the double-shifts schooling system, for example.