Divergent profiles and generating profiles: an original univariate forecasting model

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The purpose of this study is to present a global uni-variate forecasting model, which runs on the basis of a series of data points acquired periodically for each unit observed. The examples of units that we will be using in this article may come from any type of population: companies, bank accounts, distribution outlets, and so on, depending on the approach used: general economic studies by the public sector, marketing and financial analyses by private companies, banks and other trade sectors. Note that the basic hypotheses of the forecasting model are universal enough to be used in a wide range of applications. One mandatory condition for the model to run properly is that each individual unit being studied be given only one permanent identifying number. Individual data can be chosen among a broad range of quantitative variables, such as number of employees, salaries, revenues, profits, account balances, sold quantities, etc., but are not limited to them. We will call "y" the variable representing any possible variable in the applications.

Extraits

[...] The test is applied to every row from the transition matrix times in total. It brings 8 partial, sometimes inconsistent, contradictory answers to the question: the transition matrix invariable over while we are looking for a definitive and global and unicunique answer. To find this answer, we suggest to calculate the arithmetic or the geometric mean of the 8 χ²i values, and then to look for this mean value in the table. (Note that the geometric mean is always inferior to the arithmetic one). [...]

[...] This approach is expected to help a progressive understanding of the model. A computer application procedure of the model can be ordered from the Author. Summary 1 The simple model 1.1 The concept of evolution profile 1.2 The divergence concept 1.3 The convergence Implicit characteristics and fundamental hypotheses of the Model 1.5 Recurrent forecasting process 1.6 Algebraic presentation of the model 1.7 Asymptotic properties of the model 1.8 Fundamental hypothesis test 1.9 Application to seasonal data 1.10 Final step : forecasting of the observed variable 1.11 Long profiles 1.12 Corrections of data imperfections 2 The complete model - The concept of evolution profile extended to the unit presences-absences 2.2 Definition of creation and cessation 2.3 The divergence laws of the Complete model 2.4 - Interpretation of the profile 2.5 - The concept of generating profile 2.6 - Calculation of the generating effect by profile 2.7 - The recurrent process of the complete model 2.8 - Forecasting the variable 2.9 - Generating effects calculated from a short history 2.10 - The lags in generating effects 1 The simple model 1. [...]

[...] The divergence law of every profile is then a property of the whole population. Therefore, the whole population owns 8 divergence laws. If this population is stable, the 8 laws are constant over time. In order to ensure to create the conditions under which the fundamental assumption is valid, and be able to apply the model properly ,properly, it will often be necessary to break down the global population into homogeneous sub-groups according to their known dynamics. Examples : Case of a short term forecast on customers' purchase trends , where the period is the month and the variable is the revenue .revenue. [...]

[...] Let us call the proportion of units moving from the state at date to the state at date. The divergence law associated to the Ei profile can be written in the form of a row vector, which is: where every pij is ( 0 the sum of terms of the row is equal to 1 since it is a distribution without unit entries or exits between t and t+1. So, we can write : and j from 1 to 8 The same rationale applies successively to the 8 defined states. [...]

[...] The methodology consists in attributing to each number of units per profile as calculated previously, a mean value of the observed variable, per future period. Take t0, t1, t2 as the three last consecutive dates of observation. For each of the 8 profiles, let us calculate the mean over the subset of units which compose it. So we calculate 8x3 average values. Let us write as the mean values of the j profile at t0, t1 and t2. For each profile let us then calculate the index : where Ij characterizes the angle at t1 of the profile j (see Chart 1). [...]