Predicting Daily Confirmed COVID-19 Cases in India: Time Series Analysis (ARIMA)

Arima Model

A Time Series is said to be stationary if its statistical properties such as mean, variance remain constant over time. Time Series models are based on the assumption that the Time Series is stationary. Various techniques like differencing, log-differencing etc. are employed to make a non-stationary Time Series stationary. ARIMA model is a combination of differencing with auto-regression and a moving average model. ARIMA is an acronym for Auto-Regressive Integrated Moving Average (in this context, “integration” is the reverse of differencing).

We call this a non-Seasonal ARIMA(p, d, q) model, where

• ‘p’ is the order of the AR term. it refers to the number of Y lags which should be used as predictors.

• ‘d’ is the number of differencing required to make the time series stationary. It is the minimum amount of differentiation needed to render the sequence stationary, and if the time series is stationary already, then d = 0.

• ‘q’ is the order of the MA term. it refers to the number of lagged errors in the forecast that should go into the ARIMA model.

The objective of this paper is to fit a non-stationary ARIMA model to correctly recognize the stochastic mechanism of the time series of Covid-19 Daily Confirmed cases and forecast future values for the same.

Methodology

The best parameters of the ARIMA Model (suitable lags for the components of the AR and MA and the number of differencing required to induce stationarity) is determined for the Daily Confirmed Covid-19 Time Series data. The Auto Correlation (ACF) function and the Partial Auto Correlation (PACF) function are used to determine the best model.