<title>UK Covid-19 Cases Forecasting Project (ARIMA)</title>

UK Covid-19 Cases Forecasting (ARIMA Model)

Project Overview

This project delivers a time series analysis and short-term forecasting of daily UK Covid-19 case counts using ARIMA models, based on data from January 1, 2020 to June 14, 2020. All analysis was conducted in IBM SPSS, aiming to assess stationarity, build a parsimonious ARIMA model, and forecast cases for the period 15–21 June 2020.

Dataset Description

• Source: UK government daily Covid-19 cases data.
• Period: 1 January 2020 – 14 June 2020
• Frequency: Daily (time series, no missing days)
• Variables: Date, Number of new cases
• Forecast window: 15–21 June 2020 (out-of-sample)
• File Provided: Covid19_uk.xlsx

Analysis Workflow

1. Data inspection and cleaning
2. Check for stationarity (ACF & PACF of original series)
3. Difference the series and confirm stationarity
4. Model identification (ARIMA parameter selection)
5. Model estimation and diagnostics
6. Forecasting for the next 7 days
7. Model evaluation (MAE, MSE, residual analysis)

1. Assessing Stationarity

The ACF of the original series shows strong, slowly decaying autocorrelation, indicating non-stationarity. The PACF has a strong lag-1 spike, typical for AR processes.

After first-order differencing, the ACF cuts off rapidly and the PACF shows reduced spikes, confirming the series is now stationary.

2. Model Selection and Identification

• The series was best modelled using an ARIMA(1,1,0) process: 1 autoregressive term, 1 difference, 0 MA.
• Model parameters were significant and model fit judged by AIC/BIC.
• Comparison to ARIMA(0,1,0) and ARIMA(1,1,1) showed that ARIMA(1,1,0) is most parsimonious for short-term forecasting.

3. Forecasting Results

The ARIMA(1,1,0) model was used to forecast cases for 15–21 June 2020.

• Forecast values: 1470, 1468, 1480, 1488, 1497, 1506, 1515
• Upper & lower confidence intervals provided for each date.

Figure: Observed daily cases (red) with ARIMA(1,1,0) forecast for 7 days (blue).

4. Model Diagnostics & Fit

• MAE: 365.5
• MSE: 526,452.5
• RMSE: 725.57
• R-squared: 0.878
• Stationary R-squared is low due to non-stationarity of the raw series (corrected by differencing)

Figure: ACF of residuals confirms no remaining autocorrelation.

5. Interpretation and Discussion

• The ARIMA(1,1,0) model tracks the downward trend in daily Covid-19 cases as of June 2020.
• All parameters are statistically significant; diagnostics confirm model adequacy.
• Residuals are uncorrelated and near zero mean, supporting forecast validity.
• Alternative models (ARIMA(0,1,0) and (1,1,1)) were not significantly better or overfit.

6. Conclusion

The chosen ARIMA(1,1,0) model provides a simple and effective means to forecast daily Covid-19 cases over short windows, supporting public health planning with honest evaluation and error bounds. Forecast accuracy (MAE ≈ 365, RMSE ≈ 726) is reasonable given the data volatility. For future work, incorporating exogenous predictors or using more recent data may further improve accuracy.

References & Files

• Covid19_uk.xlsx (original data)
• SPSS .sav and output files (available upon request)
• All visualizations and tables produced in IBM SPSS