In the realm of project management consultancy services, the task of creating a comprehensive and precise budget is a delicate balancing act. It involves a nuanced comprehension of the financial landscape, a firm grasp of the client's unique needs, and a strategic application of economic principles to ensure an optimal distribution of resources.

Firstly, let's delve into the 'why' of the situation. A well-structured budget serves as a financial blueprint that guides the course of the consultancy project, dictating where capital will be allocated and how resources will be managed. It ensures financial control, accountability, and enhances the measurement of performance outcomes. Essentially, it provides a roadmap to financial efficiency and project success.

The ‘what’ of the budget is defined by the specific elements that it encapsulates. In project management consultancy, these typically include consulting fees, resource expenses, administrative costs, contingency reserves, and any other costs specific to the project. Each element must be carefully estimated and accounted for to culminate in a comprehensive budget.

Creating the budget commences with defining the project scope, which involves identifying the specific services the consultancy will offer. This can range from strategic advice and specialized expertise to the facilitation of project implementation. The scope forms the basis upon which the consultancy fees are determined. The notion of 'scope creep', a term used to describe the expansion of a project beyond its initial objectives, is intrinsically linked to budget management, as scope changes can significantly impact the project's cost.

The next step involves estimating the resource and administrative expenses. Resource expenses encompass all costs associated with the personnel, materials, and technologies necessary to execute the services stipulated in the project scope. Administrative costs, on the other hand, relate to overheads such as office supplies, communication costs, and utility bills.

Inevitably, every project encounters uncertainties that can lead to additional costs. This necessitates the allocation of a contingency reserve in the budget. The contingency reserve is essentially a safety net, ensuring that the budget can accommodate unforeseen expenses without jeopardizing the project's financial health.

The ‘who’ aspect of the situation refers to the various stakeholders involved in the budget creation process. This typically includes the project management consultant, the client, and any other parties involved in the project. Each party plays a crucial role in defining the project's scope, setting the consultancy fees, determining the resource allocations, and agreeing on the contingency reserve.

The ‘where’ and ‘when’ aspects of the situation are defined by the project's timeline and location. These factors can significantly influence the budget due to variations in cost of living, exchange rates, and market conditions. For instance, projects in metropolitan areas may incur higher resource and administrative costs compared to those in rural areas, and this must be factored into the budget.

The budget must be reviewed and updated regularly to ensure its relevance and accuracy. This is where the principles of control theory, an interdisciplinary branch of engineering and mathematics, come into play. Control theory provides a framework for managing dynamic systems, allowing the project management consultant to anticipate budget deviations and adjust accordingly.

The application of statistical techniques, such as regression analysis, can facilitate the budget review process by identifying trends and patterns in expenditure. This data can be utilized to forecast future costs and make informed adjustments to the budget.

In conclusion, the creation of a comprehensive budget for project management consultancy services is a task that demands meticulous planning, precise estimation, and continuous review. It involves a sophisticated interplay of financial forecasting, economic theory, and strategic resource allocation, resulting in a financial plan that underpins the trajectory of the project towards success. The budget serves as more than just a statement of probable expenditure; it is a strategic tool that guides the project's course, safeguards its financial health, and optimizes its performance outcomes.