Decision making in the economy demands tools to find the most effective, cost-affordable, and optimal solutions. Besides, there is a high necessity to have possible solutions not for tactic needs but for strategic as well. Business and economic analysts of all levels of economic management are eager to put up the user-friendly software, apps, or solutions to support their analytic and forecasting attempts. In the epoch of the claimed Industry 4.0, rapid digitization and on-line of recent quarantine events, the information systems, and any computer support is the best possibility and treasure. This paper is devoted to the idea of possible computer support for the analysis and forecasting of economic dynamics. Particular attention is paid to the time series modelling and detecting of its cyclic component. The majority of economic time series have the seasonality or other cycling inside of its dynamics, that could dramatically pervert the linear trend forecast or any other determinate direction of the trend. The proposed information system is quite user-friendly but the low error way provides a potential user with the tool of cyclic component forecasting. The methodology is grounded in the Assimakopouloscyclicity filter. The case of Denmark's GDP quarterly since 1995is presented to test and confirm the system's effectiveness in acquiring knowledge about the dynamics of the economic system. The sufficient accuracy of the implemented forecasting methods is presented.
A large proportion of open databases for the analysis are represented in the time series
view. There is often a need to analyze the main components of the time series: the
trend, seasonal, cyclic, and random components. The presence of each component is
explained by different reasons. The trend component that determines the direction of
process change is most often analysed in the time series. Its presence is usually
explained by demographic or technological factors. There are numerous opportunities
for trend modelling, in particular, the regression approach that allows different shapes
of a trend component modelling: linear, quadratic, exponential, and so on. It is also
Copyright © 2020 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
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possible to detect the magnitude of the trend by using certain smoothing methods: the
sliding average method, exponential smoothing [
It is no less common to exploit cycles and seasonal variations that show periodic changes over a certain period. For example, in agriculture and demography the modelling of monthly or quarterly fluctuations during the year, daily fluctuations during the week, and so on are in the scope. Some methods have been developed to highlight seasonal variations, including the Holt-Winters’ seasonal models and the seasonality index model. Econometrists often model seasonal fluctuations by adding some dummy variables to the regressions. It allows determining the effect of each season on the variable under study.
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As a rule, all parts of the time series that are not included in the trend or seasonal
component are referred to as the random component. There are some possibilities for
creating models for random component analysis, in particular ARMA models [
However, researchers do not always carefully examine how this random component is formed. For example, if a variable under study is affected by weather, which is currently very difficult or impossible to predict over a long period, then it is referred to as a random component. It also might include the effects of the cyclic component. This is uncertainty happens because, in practice, analysts rarely work with enough long time series reasoning by the significant changes in the methodology for collection and processing economic data. However, if such a series still exists, then it is necessary to detect a cyclic component (Fig. 1).
In practice, the cycle extraction from the trend causes considerable difficulties
caused by the interconnections. The trend shows a long-term change direction. Whilst
the cyclical component is a rhythmic fluctuation of indicators by a certain value,
which can be observed only for a rather long period. One of the approaches to isolate
cyclic sequence fluctuations is the Assimakopouloscyclicity filter [
The purpose of this paper is to propose an information system that based on an imported database could eliminate the cyclical fluctuations in time series and simultaneously detect both the magnitude of such fluctuations and other components of the series.
Structurally, the article consists of the following sections. The literature review presents an analysis of publications with methods for identifying the cyclic component in different fields, identifying their advantages and disadvantages. The methodology section describes the formal rules for allocating cyclic components in time series. The following section demonstrates the ability of an information system to split the time series into components. Finally, the last section provides conclusions. 2
The literature review on the cyclic component detection in the time series is quite vast. However, the main idea of this paper is to match the research gap in the studies of time series in the economic and social fields, along with the literature on the IT systems in the economy, particularly to put in the forecasting tools topic.
A significant problem in the economic situation forecasting and analyzing is to correctly identify the beginning of each phase of the cycles. This issue is still causing considerable debates among scientists because even under the modern development of statistical science, different researchers differently determine the presence of a new phase of the cycle. At present, there is no clear interpretation of the change in cycle phases, and therefore the cycle length. The latter magnitude is generally associated with the prime problems in the cycle formalization. Since even in retrospect there is no clear interpretation of the start and endpoint of the cycle: they are hardly determined.
Of course, the current state of issues provokes the necessity to develop a model for
determining the length of cycles and the time of their phase change. There were
attempts to develop such a mechanism using Markov chains [
In economics, the economic cycle refers to fluctuations with a fixed period. The
most important types of cycles [
The logic behind the proposed cycle lengths is determined only by the authors' understanding of the time it takes to change a particular product, production facility, or economic model. Still, it should be noted that all of these developments were based on data from the late XVII - early XX centuries. Though, the speed of economic change and new technologies launch has completely changed the idea of how the phases of the cycle change, what its real length is. Indeed, in the XVIII-XIXth centuries governments did not inspect the effects of cyclical fluctuations, and consequently did not respond to them. Then it says about the relative purity of scientific analysis of the crisis length. Yet, as early as the XXth century, following the Great Depression, governments began to use different mechanisms to avoid or eliminate the crisis. Such attention to crisis analyses could not affect the real economy and the behaviour of people who changed their expectations about the frequency of crisis and their devastating consequences. Although it did not lead to the complete abolition of the economic crisis, it has significantly changed the incidence and new expectations of people. In particular, if people previously feared crisis due to temporary loss of life and a rise in the cost of living, then today, the population expects only extremely dire crisis on a global scale with the devastating force like the 2020 pandemic coronavirus has shown.
Also, it should be understood that globalization is a process of synchronization in
crisis phenomena. The paper [
Accordingly, a particular problem of long-term forecasting is the allocation of cycles of different lengths. If all the cycles were of a predetermined length, if their objective manifestation was not impeded by numerous factors, then the possibility of mathematical determination of groups of cycles could be clear and simple. In fact, to determine the cycles of different lengths the researcher needs a sufficient number of observations. For example, to determine a cycle of 45-60 years (Kondratiev long waves), a series of at least 200-300 observations should be analyzed. Since the cycles are allocated with annual data, it is necessary to have the dynamics of some economic process at comparable prices for 300 years. That is a statistical challenge of any country in the world.
Thus, at the present stage of statistics, it is impossible to determine cycles with a large wavelength by mathematical methods alone. Having only more or less reliable and comparable observations over the last 100-120 years, one can speak of the allocation of small and medium cycles. However, it should be noted that the required statistics only exist in some countries. The geopolitical redistribution of the 1990s, the creation of new states, make it impossible to comprehensively analyze and test any method on real data.
This problem is not limited to economics. For instance, cyclical fluctuations are
present in the climate change on the planet. Nevertheless, due to the destructive
activities of mankind, increasing the carbonation of the economy, the impact of cycles
has significantly decreased compared to the global temperature increase trend, which
does not allow it to be distinguished by standard econometric methods. Global
warming and climate change have recently led to environmental, physical and medical
consequences, including extreme weather events. Compared to 1850, the average
temperature in the Northern Hemisphere has become higher by about 1.4 degrees Celsius,
and in the Southern Hemisphere by 0.8 degrees Celsius [
Afterwards, there is a assembly of studies dedicated to the cyclic fluctuations
modelling in the ecosystems to forecast chaos state (i.e. [
The major part of researches determines the cyclic component as regular or
periodic fluctuations around the trend, excluding the irregular component, revealing a
succession of phases of expansion and contraction [
At the same time, the realisation of time-series analyses for the economic
modelling is not exhausted just with tools of R, Eviews, Excel and other known software.
More and more companies are trying to support their analysts with quick, simple and
effective software that able to be helpful even for the person without deep
econometrics education, like logistics, marketing or production managers etc. Within the
artificial society, launching Industry 4.0 and the new era of robotization, there is a higher
demand on the computational intelligence that would be able to produce friendly
interface software with the application of the complicated but quite effective
fozzylogic-based computing, econometrics modelling, particularly time series modelling,
neurocomputing[
Highlight, that detecting of cycling is highly important for the economy. The
nature of the cyclicality of economic variables or political decisions is inherently linked
to the concept of the business cycle [
From the point of economic policy decisions, pro-cyclical discretionary economic
decisions stimulate the phases of the economic cycle - in case of uplift they stimulate
economic activity, in case of recession they cool the economy [
To highlight the cycles of an economic process, the first question that needs to be
answered is the trend characteristics of the dynamic process. Choosing a rational
forecasting strategy is one of the fundamental problems in any sector of the economy. The
arsenal of economic cybernetics methods contains a large number of various methods
of economic dynamics (time series) analysis which distinguishing feature is
considerable computational complexity and, as a consequence, the impossibility of practical
application without the use of modern software. The purpose of economic dynamics
analysis is the conceptualization of a comprehensive computer system to support the
forecasting ability. Mostly the researchers and economists are eager to obtain
qualitative conclusions about the nature of the system behaviour to predict it and then use the
results in the management of the economic system. Thus, the conceptual components
of the complex economic system analysis and forecasting are monitoring, forecasting
and subsequent management. This reflects the main stages of economic and
mathematical modelling (research, forecasting and management of the economic system)
and provides an integrated approach to the study of the economic system dynamics
and the use of its results [
As already mentioned, the allocation of cyclicity of time series fluctuations is an important practical task. First, it is necessary for macroeconomic research, because it is based on the analysis of the current economic cycle phase. Moreover, it enables to formulate an appropriate anti-cyclical or pro-cyclical government policy. Secondly, it is no less important to identify cyclical fluctuations for microeconomic modelling, in particular for the company sales analysis. At the same time, analysts often face a certain problem, which is the lack of long time series. This is due to the life cycle of the company, a particular product, accounting software, and so on. In any case, only a few firms can boast of having such long time series on which it would be realistic to distinguish cyclical fluctuations. Therefore, the model that allows this to be done with the least amount of observations, especially in automatic mode, should be valued by analysts quite highly.
In the literature review, it was pointed out that in fact there are not many effective models used to detect cyclic oscillations, and therefore the choice is narrowed to those that are able to work with short time series. We have chosen the Assimakopoulos filter, which independently determines the length of the cycle on the basis of calculations, and makes it possible to determine the cyclic component of the time series, using only the initial data series.
To present the information system we consider the Assimakopoulos method for allocation of cycles in the economic time series. The idea behind the cyclic isolation method is to eliminate cyclic effects based on the so-called -transformation. Such a filter can eliminate cyclic fluctuations of any length. Let the momentary trend in time t be equal trt yt 1 yt , t 1,T 1.
The new sequence is built by the rule:
yt 1 yt 1 ,if trt trt 1 0 and trt trt 1 max trk trk 1 , ~yt 2 k 2,T yt , in other cases.
It should be noted that this method does not apply to the linear trend series. We assume that the time series is believed to have a "pyramidal" structure. It is based on a straight line that refers to the simplest long-term trend. This line is superimposed on cyclical effects, starting with the longest end and ending with the shortest. In other words, the cyclic effects are superimposed on the trend line in a strictly decreasing order, depending on their length. This reasoning is consistent with the assumption that small cycles exist as part of long waves. Finally, the pyramid ends with the imposition of a random component.
p
max trt trt 1 tm1a,xT yt tm1a,xT yt t 2,T 1
The use of -transformation first eliminates the time series of the random component, then the shortest cycle, and ends with the trend selection. To use transformation to eliminate cyclic effects, we enter -index:
100
Step 1. Calculate the two additional observations to be added at the beginning and at the end of the time series.
Step 2: Initially estimate the length of the longest cycle that appears in the time series.
Step 3. Implement -transformation for a new time series derived from the original row by adding new elements in step 2.
Step 4. Calculate -index for each newly received time series.
Step 5. End the process when the time series p - index refers to the largest cycle estimate (as initially estimated in step 2). Thus, the time series obtained contain the trend of the initial time series.
Then a regression on the first and last n observations is constructed to obtain additional observations. Most commonly researchers use n 5 .
It should be noted that the above method eliminates the time series of all cyclic fluctuations whose length is less than selected in step 2. It cannot be guaranteed that the maximum possible cycle length will be selected.
It has been practically found that there is a relationship between the p - index and the length of the longest cycle, which can be determined from the time-series graph. It has been shown that the lk length of cycles using -transformation disappear if p k . The relationship between p and k for monthly data is the following: p = 1, the length of the eliminating cycle is equal to 5 (period of 5 months); p = 0.1, the length of the eliminating cycle is equal to 12 (seasonal cycles); p = 0.02, the length of the eliminating cycle is equal to 45-60 (period of 4-5 years); p = 0.007, the length of the eliminating cycle is equal to 80-125 (period of 7-10 years).
The above method can be widely used in forecasting a variety of economic information. It should be noted that generalization of known techniques can (as in the case of exponential smoothing) improve the accuracy of forecasts.
Thus, when running the program for the initial sequence (which is the database), the maximum and minimum values are calculated. Further, based on a simple linear regression (usually taking the step n = 5), the additional values are calculated having 0 and k + 1 positions, where k is the number of database elements. Based on the difference between the k-th and (k-1)-th element of the sequence, the trend is calculated. Based on the difference between the i-th and (i-1)-th value of the trend, the difference in the trends is counted. One can select the largest value of the trend difference by the module. Next, it is appropriate to use the formula that calculates theta-index: 1 N 1 p max L min L mia2x100 Tri Tri1
1 N 1 max L min L mia2x100 X i 2 X i1 X i2 where N –is the number of observations in the original time series, max L - min L – the difference between the maximum and the minimum value of the observations of the original series.
If the theta index is greater than 0.007, we can speak about the strong role of the random component in the sequence. Then a new smoothed sequence is calculated, each kth term of which is the arithmetic mean between the (k –1) and (k + 1) level of the previous sequence. This sequence will already be somewhat smoothed relative to the previous one. As far, it allows you to determine the value of the theta index for already calculated sequence. Since we are interested in the maximum deprivation of a given sequence of the cyclic component, the calculation was carried out until the difference between the theta indexes of the obtained and the previous sequence would be less than 0.01. 4
The program was developed by means of VBA for Microsoft Excel. When opening an application file, the user enters the standard Microsoft Excel file, where the original database has already been imported. However, users can download their data to run. When you make changes to the database, the user sees an application menu that appears automatically. There the analyst can either go directly to the analysis and get acquainted with the information about the program and its authors.
The application interface has been specifically designed to be concise so that the user can intuitively work with the program without confusion in different windows, tabs, and the like. The user can at any time start analyzing the time series, which is to derive the most smoothed sequence, which is a trend estimate, the value of the cyclic component, and a graph that reflects cyclic fluctuations relative to the trend. The program works for any size of the database, which is a significant advantage of it, and the process of work itself is fast, start-up-intuitive.
The system is not overloaded with the choice of different parameters, because the user only loads the required database, all parameters are calculated using the method Assimokoupolos within the code, so the user is completely burdened with the need for mathematical calculations. If the user is not familiar with the concept of theta index, it will be enough to see a graph that shows the cyclical fluctuations of the initial sequence relative to the trend, or he can read the instructions to the program.
Thus, one of the biggest advantages of this information system is its extraordinary ease of use. The user can make changes to the database if necessary to analyze another time series. The pressing "Go to Analysis" button is affordable even for a person who is unfamiliar with time series analysis, that makes the proposed IT decision users-friendly one. 5
As the case example, we propose a time series of the value of Denmark's GDP in millions of euros collected quarterly since 1995 (Fig. 2).
Running the program allows a user to make the necessary calculations (Fig. 3). The columns of the MS Excel sheet contain the name of each period, its ordinal number, the actual value of the time series, as well as two calculation columns: trend estimation and cyclic component estimation. Accordingly, if we subtract the value of the cyclic component from the real value, we can analyze the new time series without the influence of cyclicity. It is also possible to analyze separately the value of the column of the cyclic component, which allows us to find an economic justification for certain changes in the time series behavior.
Finally, one can construct a graph comparing the real value of the studied variable and the obtained forecast of the selected trend component (Fig. 4).
s e u l a V 80000,00 75000,00 70000,00 65000,00 60000,00 55000,00 50000,00 45000,00 40000,00 35000,00 30000,00
Trend component
Real value
In the last step, one can build the dynamics of the cyclic component of the time series (Fig. 5). This graph is based on the calculated column of the cyclic component in
3000,00 2000,00 1000,00
0,00 -1000,00 -2000,00 -3000,00
The graph allows determining the phase of economic growth from the beginning of observations until August 2008, when the global financial crisis began. But this growth was not homogeneous from 1996 to 2008. There were three small cycles: from January 1996 to April 1998, from May 1998 to April 2003, from May 2003 to December 2006. Finally, since 2007, the fourth cycle has come and ended with the financial crisis, that is, the end of a stronger long cycle. At the same time, the cyclical situation since 2009 has not been so clearly observed, because the governments of European countries, particularly Denmark, have pursued a stimulating fiscal and monetary policy, which has approved to be acyclic. But even under these conditions, the presented information system can identify three small uniform cycles of about 2 years in length, as well as the fourth wave with significant growth. If there had been no active state acyclic policy, a serious crisis would have been expected at the end of 2017 related to the end of the longer cycle. However, appropriate stimulus measures delayed the crisis. As it turned out for another short two-year cycle: the economic recession has been starting in the first quarter of 2020. Fig. 5 demonstrates the corresponding limits for the phases of the cycles, which can be determined from the data of the developed information system. It should be noted that this provides only a basis for the researcher for further analysis, as it is necessary to compare the obtained phase breakdown with the real economic or other factors that influenced the time series data. However, such an analysis must be individual in each case. For this paper example, it can be concluded that the lessons and consequences learned from the 2008 global financial crisis changed the size of short cycles (from about 3 to 2 years) but did not change the length of the longer cycle. Therefore, there were not 4 but 5 shorter cycles between crises.
As one can conclude, a series of cyclical fluctuations obtained employing the information system allows making as quite valuable conclusions, but also to predict the onset of economic, financial and other shocks. The better identification of cycles allows better policy reactions and enhances the attempts to predict naturally occurring cycles that is especially problematic if they are no longer naturally occurring. 6
The issue of allocation of the cyclic component is an important element of successful forecasting in all areas of activity. Correct allocation of the cyclic component in time series may be of interest to:
• governments and central banks to adopt changes to fiscal and monetary policies to avoid market distortions as a result of overproduction in certain sectors; • managers at firms to formulate more adequate sales and procurement plans for the warehouse, create timely advertising campaigns to increase profits; • ecologists to analyze climate change on the planet; • doctors to analyze the recurrence of epidemic diseases; • scientists to study a new class of time series voiding the cyclic component.
Obviously, further research should address how exactly economic and other cycles converge across countries, regions, industries. It will be able to provide information to shape relevant economic, environmental, health and social policies in the world.
The authors have created an information system that displays the smoothed sequence with the entered time series, which is a long-term trend, as well as the values of cyclic fluctuations with the further graphical display of the result. The program works simply and effectively, with repeated testing no problems were detected. This information system enables users to easily select cyclic fluctuations from an arbitrary time series. Obtaining this data allows researchers more often referring to the analysis of the cyclic component, motivating the study of dynamics and determining the factors that influence it.
With the help of the developed IT system, an example of a complex pre-forecast analysis of output time series in the field of economy is shown. The results of the application revealed the performance of the IT system and provided new knowledge about the objects of analysis and forecasting.
Acknowledgements. Paper is done in the framework of scientific faculty research 16КF040-04 "Steady-state security assessment: a new framework for analysis"(2016-2021), Taras Shevchenko National University of Kyiv (Ukraine)