DECIPHERING BUSINESS TRANSACTIONS FROM POINT PROCESS AND TIME SERIES PERSPECTIVES

Point process models are designed to scrutinize the timing of events or occurrences, primarily in continuous time. Their focus lies in modeling the probability of events transpiring at specific time points, giving rise to its name temporal point process. They are particularly efficacious when the precise timing of events holds paramount significance. Point process models offer a granular understanding of event occurrences and their interdependencies, adeptly capturing the stochastic nature of events and enabling the estimation of parameters related to event intensity or rate, which then can be used for predictions of future events. In the realm of business transactions, point process models find their forte in modeling events like customer arrivals at a physical store, website clicks, or order placements.

Time series models, in contrast, are instrumental in the analysis and forecasting of data points collected over time. They operate under the assumption that data points are temporally dependent, with the aim of discerning and predicting underlying patterns and trends. Time series models offer the ability to provide forecasts and predictions based on historical data (at fixed time intervals such as daily or monthly), capturing essential trends, seasonal variations, and other patterns critical for decision-making. Compared to point process models, they are relatively straightforward to implement and interpret. In the domain of business transactions, time series models find common application in finance, particularly for modeling stock prices, sales data, and other pertinent financial metrics. They can also be extended to various facets of transactions such as website traffic, customer orders, and more.

If we consider a hypothetical scenario involving an online retail platform like Shopee, with data on order placements with the corresponding timestamps shown below, a point process model would be indispensable for comprehending the timing of individual orders and modeling the intensity of order placements throughout the day.

From another perspective, if we have daily sales data which take the form shown as follows, a time series model would be instrumental in analyzing and forecasting future sales based on observed patterns, trends, and seasonality.

In practice, the choice between point process and time series models hinges on the specific nature of the data and the questions at hand. Point process models specialize in modeling the timing and intensity of individual events in continuous time followed by parameter estimations and predictions, while time series models excel at analyzing and forecasting aggregated data over fixed time intervals. Depending on the nature of the data and the research objectives, a synergistic blend of both approaches may prove advantageous, furnishing invaluable insights for understanding and optimizing business transactions, especially on platforms like Shopee and Lazada.