Forecasting Lost Sales Based On Time Series Data And County

Forecasting Lost Sales Based on Time Series Data and Countywide Sales

The Carlson Department Store was severely impacted by a hurricane that occurred on August 31, resulting in a closure that lasted four months, from September through December. This incident has raised critical questions concerning the estimation of revenue lost due to the closure, as well as potential claims for additional compensation based on increased subsequent sales. To address these issues, data analysis of prior sales trends, both at the individual store level and on the countywide scale, is necessary. The goal is to generate reliable forecasts of what sales would have been without the hurricane and to evaluate whether post-storm sales exceeded normal expectations, indicating possible excess storm-related business activity.

The analysis involves three primary tasks: first, estimating the sales Carlson would have achieved in the closed months if the hurricane had not occurred; second, forecasting what the countywide department store sales should have been during these months without the disaster; and third, quantifying the store’s lost sales during the closure period. Finally, the analysis must assess if increased sales post-storm are statistically significant to warrant a claim for excess storm-related sales. The data provided include historical sales figures for Carlson’s store, overall countywide department store sales, and total sales for the four months during which Carlson’s was closed.

Paper For Above instruction

The recent hurricane that struck the region had a profound impact on the operations of Carlson Department Store, leading to an unprecedented closure from September through December. To effectively analyze the financial implications of this event, it is essential to establish a benchmark of what sales levels would have been if the disaster had not occurred. This process involves applying time series forecasting techniques to historical sales data, analyzing patterns, seasonality, and trends to project what the store’s sales might have been during the closure period.

Data on Carlson's past sales over the previous 48 months present a valuable resource for developing such forecasts. One common approach involves decomposing the historical data into trend, seasonal, and irregular components. Techniques such as exponential smoothing (e.g., Holt-Winters method) or ARIMA models enable quantifying these components and generating out-of-sample forecasts. Given the seasonal nature of retail sales, particularly around the holiday season, incorporating seasonal adjustment into the models is critical. For example, the observed increase in December sales, often driven by holiday shopping, should be appropriately modeled to avoid underestimating or overestimating the expected sales during that month.

Simultaneously, estimating countywide department store sales during the same period can help contextualize Carlson's performance relative to the broader market. The county sales data, spanning several years, can be modeled similarly to forecast what the total sales would have been without the hurricane, accounting for overall trends and seasonal fluctuations. For this purpose, a multivariate analysis might be employed, using the historical relationship between Carlson’s sales and countywide sales to improve the accuracy of the store-specific forecast. Regression models or cointegration analysis can be utilized to capture this relationship, thereby refining the estimates of what the store's sales should have been during the closure period.

To estimate the lost sales attributable to the hurricane, the predicted sales figures serve as the baseline. Subtracting the actual sales during September through December from these baseline forecasts yields estimates of the sales lost because of the closure. It is important to acknowledge that irregularities, such as promotional events or economic shifts, might influence sales beyond normal patterns. Therefore, confidence intervals or prediction intervals around the forecasts should be computed to assess the uncertainty associated with these estimates.

Beyond calculating lost sales, it is essential to analyze whether the post-hurricane period experienced any excess sales that surpass what would be expected based on historical trends. This involves comparing actual countywide department store sales during September to December with forecasted values. If actual sales significantly exceed predictions, it could indicate increased business activity driven by factors such as recovery efforts, promotional campaigns, or storm-related demand surges.

Performing statistical hypothesis tests, such as t-tests on deviations between observed and forecasted sales, can help establish if the excess sales are statistically significant. Additionally, lift charts or response rate analyses provide insights into the effectiveness of targeted marketing strategies in the recovery phase, potentially justifying claims for storm-related compensation that accounts for these anomalous sales increases.

In summary, the comprehensive analysis combines time series forecasting, regression modeling, and statistical testing to quantify the sales lost due to the hurricane, contextualize the store's performance relative to broader market trends, and evaluate the presence of excess storm-related sales. Accurate estimates will enable Carlson Department Store to substantiate its claim for damages and explore opportunities for strategic recovery initiatives.

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