Real-time forecasts and risk assessment of novel coronavirus (COVID-19) cases: A data-driven analysis

Tanujit Chakraborty; Indrajit Ghosh

It is interesting to see that the error series (residuals) generated by ARIMA are oscillating and nonstationary for all the datasets. These seasonal oscillations can be captured through the wavelet transform, which can decompose a time series into a linear combination of different frequencies. These residual series as in Figure 1 ) satisfy the admissibility condition (zero mean) that forces wavelet functions to wiggle (oscillate between positive and negative), a typical property of wavelets. Thus, we remodel the residuals obtained using the ARIMA model with that of the WBF model. The value of Wavelet levels is obtained by using the formula, as mentioned in Algorithm 1. WBF model was implemented using 'WaveletArima' [26] package in R software with 'periodic' boundary and all the other parameters were kept as default. As the WBF model is fitted on the residual time series, predictions are generated for the next ten time steps (5 April 2020 to 14 April 2020). Further, both the ARIMA forecasts and WBF residual forecasts are added together to get the final out-of-sample forecasts for the next ten days (5 April 2020 to 14 April 2020). The hybrid model fittings (training data) for five countries, namely Canada, France, India, South Korea and the UK are displayed in Figures 2(a) , 3(a), 4(a), 5(a) and 6(a) respectively. The real-time (short-term) forecasts using ARIMA, WBF, and hybrid ARIMA-WBF model for Canada, France, India, South Korea, and the UK are displayed in Figures 2(b) , 3(b), 4(b), 5(b) and 6(b) respectively.