COVID-19 Forecasting and Investigating the Impact of the Lockdown in India

The world was caught unaware by the COVID-19 pandemic in December 2019, when the Wuhan city of China had its first case of COVID-19. It quickly spread to other parts of the world, affecting almost 188 countries and territories and causing deaths in large numbers. With over 16.056 million cases and 6,44,661 deaths as of 25 July 2020 (JHU 2020). The first positive COVID-19 case in India was reported on 30 January 2020. As per the Government of India (GOI), the total number of cases stand at 13,85,522 and the total number of deaths stand at 32,063 in India as of 26 July 2020 (GoI 2020). The disease was declared to be a pandemic by the World Health Organization (WHO) as it became more widespread and affected the humankind. The first nationwide lockdown in India was announced from 25 March 2020 and continued for long; the movement of
people and economic activities in the country was severely disturbed. The primary purpose of this paper is to make short-term forecasts for the COVID-19 situation in India and to examine how the lockdown policy had affected the pandemic’s cases and deaths in India.

In forecasting literature, many techniques and tools are proposed to make short-term forecasting of various time series. Each method has its own relative advantages and disadvantages over the others in producing an accurate estimate. It has been observed in the literature that hybrid models tend to perform better as compared to single time-series models (Aladag et al 2009). We look at various forecasts generated by single ARIMA (autoregressive integrated moving average), hybrid ARIMA–FFT (fast Fourier transform) analysis (with error remodelling), hybrid ARIMA–wavelet (with error remodelling) and wavelet–ARIMA (without error remodelling). The autoregressive (AR) model of order p (AR[p]) has the advantage of predicting future values in a time-series data, based on the past values, and the number of AR terms is denoted by p. It is applicable to data sets where there is a correlation between the given data in the time series and the past or future values. The moving average (MA) model of order q (MA[q]) is famously applied to univariate data sets where the values of a variable are dependent on its current or past values in a linear fashion. Here, q is used to denote the number of lagged errors in forecasting. Together, the AR and MA models are used as autoregressive moving average (ARMA) model where AR method regresses a variable on its own lagged values and MA method takes care of the error term. However, ARMA is applicable to stationary data only. ARIMA (p, d, q) is an integrated approach where “I” is a pre-processing method which uses a differencing term, d (d is the number of times the raw values are differenced), used to stationarise a non-stationary time series (Hyndman and Athanasopoulos 2018; SAS Institute 2015). ARIMA has been efficient in capturing the linear trends in a time-series model, while FFT analysis converts time
domains into frequency domains, thus making it useful for prediction purposes. In the case of a Fourier transform, signals are decomposed into sines and cosines which are the functions localised in the Fourier space. The wavelet transformation, on the other hand, makes use of functions that are localised in the real space in addition to those localised in the Fourier space (Bhirud and Prabhu 2014).