The article considers the possibility and expediency of using the apparatus of the theory of wavelets to conduct analysis of banking activities. The authors determine separate stages of the complex application of various tools on the theory of wavelets to analyze the activities of banks based on retrospective data. Among these stages are: decomposition of the initial data by their approximating coefficients and coefficients of detail, and the use of wavelet coherence.
Indicated the importance of conducting a retrospective analysis to reveal hidden relationships in the data structure that determine certain aspects of banking. The advantages of using the tools of the theory of wavelets from the point of view of analyzing the activities of banks based on their statistical data are highlighted. Among these advantages the authors highlight the possibility of studying the relationships between data over time and determining the depth of such relationships. It is noted that this can be done in one research window.
Particular attention is focused on the analysis of the reciprocity between the volume of funds in deposit accounts and the volume of loans granted, as one of the key parameters for conducting banking activities. The reciprocity between the volumes of funds in deposit accounts and the volumes of loans granted is revealed in accordance with the volumes of administrative expenses and equity of banks. It is noted that retrospective analysis allows us to identify the consequences of the onset of unwanted events and prevent them in the future.
To carry out a corresponding analysis, the content of constructing a description of spatial wavelet coherence is disclosed. Such a description makes it possible to take into account a larger number of parameters than classical approaches for calculating wavelet coherence. This expands the boundaries of the relevant analysis, allows you to explore various mutual influences between individual banks in terms of their individual indicators for banking activities. Such an analysis allows to determine not only the reciprocity between individual indicators of banking activity, but also the depth of influence between individual banks, taking into account such indicators of their activity. Concrete examples are given that prove the feasibility and likelihood of applying the proposed approaches to the analysis of banking activities.

Keywords:wavelet coherence, banking, time series, deposits, loans, administrative expenses, equity

The article considers the conceptual foundations of the functioning of institutions for support and promotion of the development of small and medium businesses. The author defines the significance of such institutions, and the value of their product, that is, the services for small and medium entrepreneurship (SME), which allows a better understanding of the main functional and applied role and purpose of these entities.
Given the lack of trust from the population of Ukraine for government agencies and organizations, the presence of a number of problems in the SME support system, and especially the inadequate legislative regulation of the status and definition of the functions of the main performers of SME development policy, the article notes that this area needs a qualitative institutional change.
The study uses the methods of analysis and synthesis, comparison, generalization, and induction and tests the methodology of Canvas Business Model strategic planning of the activities of SME support entities.
Guided by the principle of functionalism, the author conventionally groups the SME support institutions into five main types: business support funds, business centers, business incubators, business innovation centers, and business associations. For each type of SME support institution, the main functional purpose and, accordingly, the main type of operational activity are specified. There are proposals that allow understanding the essence, the functional and applied role and the mission of individual elements of the SME support infrastructure. In practical terms, they can be used in state purpose-oriented programs to promote the development of small and medium businesses in order to qualitatively improve the final product for SME.
The author develops a model of the activity for a typical SME promotion entity, which is applicable, can be adapted to specific conditions and is flexible over time. Strategic planning of the entity’s activities based on the methodology of Canvas Business Model allows defining both the value of the product (services for SME), as well as the general value of the entity’s activities, which is extremely important in the SME support system.
It is emphasized that each institution of the SME promotion infrastructure performs an important social function. The key values recommended following for SME support institutions are trust, partnership, and righteousness.

Keywords:institution, SME support system, value, Canvas Business Model