A Quantitative approach to modelling and forecasting New South Wale’s class 3720 industry turnover figures post COVID-19
Limkheang Heng
2024-05-10
Abstract
In this report, we will be quantitatively modelling and forecasting the turnover for New South Wale’s pharmaceutical and toiletry wholesale industry by using 2 methods: Exponential smoothing (ETS) and Auto-Regressive Integrated Moving Average (ARIMA). In the first half, we will go wrangle and provide a brief visualisations and time series characteristics of the turnover data. In addition, we will transform the data using a log transformation and apply the appropriate differencing. Then we will go through the process of selecting our models’ parameters and train our model using a test set consisting of the COVID-19 ending period data. We will conduct residuals diagnostic on the models to draw attention to the COVID-19 effects on the effectiveness of forecasting. In the second half, we train each of our best ETS and ARIMA model using the full turnover data (up to December 2022) to conduct out of sample forecast (up to December 2024) and compare our predictions against actual turnover.
We conclude that COVID-19 had a big impact on both forecasting methods. During the periods immediately after COVID-19 (December 2021), it is found that both forecasting methods severely underestimate the turnover figures. The rebound of demand is not fully capture and while the models trained on data up to December 2022 performed better, an overcorrection of turnover estimation is likely. With all this, we suggest a cautious approach when it comes to relying on forecasts as the full effects of COVID-19 has still not been seen.
1. Statistical features of the data
Plotting the data, the y-axis represents the turnover figures and x-axis represents the time period in years. The turnover figures are the turnover for New South Wales’ phamaceutical, comsetic and toiletry goods retailing.
Looking at the plot generated from the data-set, we can observe a general upward trend throughout the given time period. Looking more closely we can see that there are multiple periods where the trend is slowing down before going up again in the following periods. From this we can assume there to be a hint of cyclic behaviors within the data. Interestingly, during and after the COVID-19 pandemic starting in 2020, we can observe a greater increase in turnover year by year. An explanation for this could be the hoarding of pharmaceutical and toiletry goods during the initial shock of the pandemic, followed by a pented up desire to consume cosmetic goods after pandemic measures were lifted.
In addition, we can observe the presence of seasonality from year to year. At the beginning the level of seasonality is not as substantial as the end of the time series as we can observe higher peaks and deeper troughs by the end. We can use a seasonal plot to further analyse the seasonality.
From the seasonal plot generated. We can observe that the seasonality within the data intensifies as time goes on. In the beginning, we can barely see the seasonality in the data, the orange lines are pretty flat throughout besides an upward tick in December. However, this seasonal behavior grew as the time series progresses. From the 1990s to the 2000s, we observe strong seasonal behaviors. Turnover seems to be lower at the first half of the year but increases in the second half before peaking in December.
From the sub-series plot, we can observe the turnovers of each month throughout the time series in seperate plots. We can see an increasing trend over every month throughout the time period. This means turnover has increased consistently during every month throughout the years. We can observe the seasonal pattern that aligns with what we observed from our previous seasonal plot, sales are higher in the second half of the year and typically peak in December.
Overall, we can observe a time series with a trend, multiplicative seasonality and multiplicative errors. We can see that the turnover across the pharmaceutical, cosmetics, and toiletry industry in New South Wales has steadily increased over time. The rate of the increase seems to be constant. We can observe some unusual noise beginning in 2020, the trend afterward appears to increase at a higher rate than previous periods. This may be the result of the mass consumption of items during the initial panic of the pandemic and its lingering effects on demand and thus may not be a long term change in turnover trends. Furthermore, the turnover is seasonal; could be attributed to increasing demand in certain periods such as for Christmas in December. In addition the general trend has some cyclic behaviors that could be linked to the economic and business cycle of Australia.