Содержание
- 2. The problem of forecasting companies’ cash flows is important in the growing uncertainty of the business
- 3. Methods of Cash Flow Forecasting
- 4. Revenues as a Key Element to be Forecasted Revenues generated by various centers of financial responsibilities
- 5. Fuzzy Time Series (1) When discussing fuzzy time series {Ỹ(t)}, it should be noted that such
- 6. Fuzzy Time Series (2) By studying a time series in a fuzzy dynamic environment one is
- 7. Stages for forecasting with Fussy Time Series (1)
- 8. Stages for forecasting with Fuzzy Time Series (2) At the first stage, the boundaries of the
- 9. Stages for forecasting with Fuzzy Time Series (3) At the third stage of the analysis, a
- 10. Stages for forecasting with Fuzzy Time Series (4) In order to define the fuzzy set Аi
- 11. Stages for forecasting with Fuzzy Time Series (5) At the fourth stage, conversion of numerical values
- 12. Stages for forecasting with Fuzzy Time Series (6) At the sixth stage, conversion of fuzzy values
- 13. Using the Method for Cash Flows Predicting According to the proposed method, boundaries of the universal
- 14. Variables and Their Values very low level of revenue gain (VLLRG); low level of revenue gain
- 15. Conversion of Fuzzy Sets Let us define a fuzzy set Аi within the universal set U
- 17. Revenues Forecasting
- 18. Conclusion The proposed forecasting method based on fuzzy sets is an addition to the existing quantitative
- 20. Скачать презентацию
The problem of forecasting companies’ cash flows is important in the
The problem of forecasting companies’ cash flows is important in the
It is also discussed in the literature (Kaplan, Ruback, 1995; Fridson, Alvarez, 2009; Cheng, Czernkowski, 2010; Pae, Yoon, 2012; Ruppert, 2017)
One of the main objectives of forecasting is to enhance the enterprise's ability to react to changes of the external environment that might affect the performance
Motivation
Methods of Cash Flow Forecasting
Methods of Cash Flow Forecasting
Revenues as a Key Element to be Forecasted
Revenues generated by various
Revenues as a Key Element to be Forecasted
Revenues generated by various
The resulting forecast is based on data obtained on all levels of research starting with the macroeconomic level and down to the level of enterprise. At this stage, variants of macroeconomic and microeconomic dynamics are compared, and the enterprise's response scenarios to changes of the internal and external environments are developed.
Due to the modern volatility of global and national economies, the significance of forecasting, in general, and enterprise revenue forecasting, in particular (being part of the budgeting process) is greater than ever.
The models mentioned above are limited, to some extent, and often, their use does not make it possible to obtain the desired result due to certain inherent risks and errors.
Fuzzy Time Series (1)
When discussing fuzzy time series {Ỹ(t)}, it should
Fuzzy Time Series (1)
When discussing fuzzy time series {Ỹ(t)}, it should
In this case, we used the assumption that the components of the series Xt have linguistic values, and Ỹ(t) is a fuzzy function with argument t which values have fuzzy verbal variables “high”, “average”, “low”, etc.
The use of logical-linguistic variables makes it possible to take into account qualitative factors that enable to recognize the uncertainty
Empirical data of the time series {Y(t)} must be designated. These are selected with account to the objective of study (revenue of the enterprise, per-capita income, GDP, etc.)
Fuzzy Time Series (2)
By studying a time series in a fuzzy
Fuzzy Time Series (2)
By studying a time series in a fuzzy
Xt = {µX t (ui)/ui},
where Xt is fuzzy range; µXt(ui) is membership function; and t is argument of the function; and the following conditions are met:
ui∈ U; µXt (ui) ∈[0, 1].
The conditions considered signify that every point within the interval of ui will be a member of the set Xt and have the degree of membership of:
µXt (ui) = µi (t),
where µi (t) are given numbers, i=; 1, t = [1, 2,…].
Thus, the complete set or range of number axis will appear as:
U = (u1, u2, …, um),
where ,ui, i = 1,m.
The fuzzy set of X of the universal set of U may be defined as:
X = {(μx(u1)/u2), (μx(u1)/u2), …, (μx(um)/um)},
where μx(ui) is the membership function which puts its elements ui as a set of real numbers within the segment of [0, 1] indicating the degree of membership of elements ui in the set of X, μx(ui)∈ [0, 1];“/” designates the membership of the value μx in the element um.
Stages for forecasting with Fussy Time Series (1)
Stages for forecasting with Fussy Time Series (1)
Stages for forecasting with Fuzzy Time Series (2)
At the first stage,
Stages for forecasting with Fuzzy Time Series (2)
At the first stage,
At the second stage, the defined universal U set is divided into intervals having equal length.
Stages for forecasting with Fuzzy Time Series (3)
At the third stage
Stages for forecasting with Fuzzy Time Series (3)
At the third stage
very low level of increment of the forecasted indicator (VLLIFI);
low level of increment of the forecasted indicator (LLIFI);
average level of increment of the forecasted indicator (ALIFI);
stationary level of increment of the forecasted indicator (SLIFI);
normal level of increment of the forecasted indicator (NLIFI);
high level of increment of the forecasted indicator (HLIFI); and
very high level of increment of the forecasted indicator (VHLIFI).
Stages for forecasting with Fuzzy Time Series (4)
In order to define
Stages for forecasting with Fuzzy Time Series (4)
In order to define
Thus, by consistently adopting the average value ui of middle point of the intervals as the value of variable V we can develop the following representation of fuzzy sets:
А1 = {(/u1), (/u2), (/u3), (/u4), (/u5), (/u6), (/u7)}
А2 = {(/u1), (/u2), (/u3), (/u4), (/u5), (/u6), (/u7)}
А3 = {(/u1), (/u2), (/u3), (/u4), (/u5), (/u6), (/u7)}
А4 = {(/u1), (/u2), (/u3), (/u4), (/u5), (/u6), (/u7)}
А5 = {(/u1), (/u2), (/u3), (/u4), (/u5), (/u6), (/u7)}
А6 = {(/u1), (/u2), (/u3), (/u4), (/ u5), (/u6), (/u7)}
А7 = {(/u1), (/u2), (/u3), (/u4), (/ u5), (/u6), (/u7)}.
Stages for forecasting with Fuzzy Time Series (5)
At the fourth stage,
Stages for forecasting with Fuzzy Time Series (5)
At the fourth stage,
At the fifth stage, forecasting of the studied indicator is done using fuzzy logic symbols.
To forecast the value of increment of the studied indicator for the period of t resulting in the fuzzy set of F(t)), fuzzy relation matrix R(t) must be calculated. This matrix is determined by intersecting the matrix of fuzzy increment of the studied indicator N(t) for the period of (t-1) and the matrix of fuzzy increments of the studied indicator S(t) for the periods of (t-2), (t-3), (t-4), (t-5), (t-+).Therefore:
In this case F(t) = [max(r11, r21, …, ri1) max(r12, r22, …, ri2) … max(r1j, r2j, …,rij)].
Stages for forecasting with Fuzzy Time Series (6)
At the sixth stage,
Stages for forecasting with Fuzzy Time Series (6)
At the sixth stage,
where µt(ui) are the values of membership function for the considered year and uсрi are coordinates of points dividing intervals of equal length into equal parts ui that belong to the universal U set.
In order to obtain the value of the forecasted indicator, the value of the forecasted increment must be added to its value for the last period.
Using the Method for Cash Flows Predicting
According to the proposed method,
Using the Method for Cash Flows Predicting
According to the proposed method,
Variables and Their Values
very low level of revenue gain (VLLRG);
low level
Variables and Their Values
very low level of revenue gain (VLLRG);
low level
average level of revenue gain (ALRG);
stationary level of revenue gain (SLRG);
normal level of revenue gain (NLRG);
high level of revenue gain (HLRG); and
very high level of revenue gain (VHLRG).
Conversion of Fuzzy Sets
Let us define a fuzzy set Аi within
Conversion of Fuzzy Sets
Let us define a fuzzy set Аi within
А1 = {(1/u1), (0,97/u2), (0,87/u3), (0,75/u4), (0,63/u5), (0,53/u6), (0,43/u7)}
А2 = {(0,97/u1), (1/u2), (0,97/u3), (0,87/u4), (0,75/u5), (0,63/u6), (0,53/u7)}
А3 = {(0,87/u1), (0,97/u2), (1/u3), (0,97/u4), (0,87/u5), (0,75/u6), (0,63/u7)}
А4 = {(0,75/u1), (0,87/u2), (0,97/u3), (1/u4), (0,97/u5), (0,87/u6), (0,75/u7)}
А5 = {(0,63/u1), (0,75/u2), (0,87/u3), (0,97/u4), (1/u5), (0,97/u6), (0,87/u7)}
А6 = {(0,53/u1), (0,63/u2), (0,75/u3), (0,87/u4), (0,97/ u5), (1/u6), (0,97/u7)}
А7 = {(0,43/u1), (0,53/u2), (0,63/u3), (0,75/u4), (0,87/ u5), (0,97/u6),(1/u7)}.
Revenues Forecasting
Revenues Forecasting
Conclusion
The proposed forecasting method based on fuzzy sets is an addition
Conclusion
The proposed forecasting method based on fuzzy sets is an addition
Application of forecasting using the fuzzy set method and linear model demonstrated that the fuzzy set method made it possible to bring average approximation error down by 13.7%.
This allows for the conclusion that forecast accuracy is increased