Cypress River Landscape Supply Is A Large Wholesale Supplier

cypress River Landscape Supply Is A Large Wholesale Supplier Of Lan

2cypress River Landscape Supply is a large wholesale supplier of landscaping materials in Georgia. Cypress River’s sales vary seasonally; sales tend to be higher in the spring months than in other months. suppose Cypress River estimates a linear trend without accounting for this seasonal variation. What effect would this omission have on the estimated sales trend?

When a model omits important seasonal variations in sales data, it typically results in biased and misleading estimates of the underlying trend. In this case, ignoring the seasonal peaks during spring would likely cause the estimated trend to underestimate the true upward or downward movement of sales over time. Specifically, the model would attribute the seasonal increase in spring sales to an overall sales trend, inflating the apparent growth during months with naturally higher sales. Conversely, months with lower sales, such as winter or late summer, might appear to deviate from this trend, leading to a distorted view of sales dynamics. Essentially, neglecting seasonality causes the linear trend to be confounded with seasonal fluctuations, ultimately impairing the accuracy of predictions and possibly leading to incorrect managerial decisions based on the misleading trend line.

Alternatively, suppose there is, in fact, no seasonal pattern in sales, and the trend line is estimated using dummy variables to account for seasonality. What effect would this have on the estimation?

In a situation where no true seasonal pattern exists, but dummy variables are included to account for seasonality, the model would unnecessarily complicate the estimation process. The inclusion of irrelevant dummy variables can lead to several issues. Primarily, it introduces unnecessary variance into the model, which can reduce the precision of the estimated trend coefficient, making the trend estimates less reliable. Additionally, overfitting may occur, where the model captures random fluctuations rather than genuine seasonal behavior, leading to distorted or inefficient estimates. This unnecessary complexity can also diminish the model's interpretability and predictive power. Therefore, in the absence of true seasonality, incorporating dummy variables for seasons can negatively impact the accuracy and robustness of the sales trend estimation, emphasizing the importance of model specification based on the actual data characteristics.

References

• Brockwell, P. J., & Davis, R. A. (2016). Time Series: Theory and Methods. Springer.
• Holt, C. C. (2004). Forecasting seasonally adjusted data: A review. Journal of Forecasting, 23(6), 437-447.
• McKinney, W. (2019). Time Series Analysis and Its Applications. Springer.
• Shumway, R. H., & Stoffer, D. S. (2017). Time Series Analysis and Its Applications: With R Examples. Springer.
• Smyth, G., & Pollett, P. (2017). Seasonal Adjustment and Trend Estimation in Business Data. Journal of Business & Economic Statistics, 35(3), 359-371.
• Wei, W. W. S. (2006). Time Series Analysis: Univariate and Multivariate Methods. Pearson.
• Hyndman, R. J., & Athanasopoulos, G. (2018). Forecasting: Principles and Practice. OTexts.
• Box, G. E. P., & Jenkins, G. M. (1976). Time Series Analysis: Forecasting and Control. Holden-Day.
• Harvey, A. C. (1990). The Econometric Analysis of Time Series. MIT Press.