Using additive regression models for short-term forecasting of financial macro-indicators and assessing the potential for financing megaprojects

Kuznetsov Nikolay Chief Researcher at the Institute for Economic Policy and Economic Security Problems at Financial University under the Government of the Russian Federation 125167, Russia, Moscow, Leningradsky prosp., 49/2 nkuznetsov@outlook.com Other publications by this author

Introduction

The need to obtain forecast estimates of various financial indicators at the macro level exists today in many areas of activity. Without such forecasts, the state cannot form adequate socio-economic, monetary, fiscal and other policies, and corporations cannot develop strategies for their long-term development, investment and attraction of financing.

At the same time, there is still a discussion among professionals about which forecasting method and which predictive model gives the highest quality results (see, for example, the analysis carried out in ^{[1, 2]}). However, the majority of experts agree on one thing – financial forecasts are extremely difficult to build. Firstly, because financial processes are characterized by high dynamics and a high degree of uncertainty. Being under the influence of a large number of various factors that simply cannot be fully taken into account within the framework of a mathematical model, they have a difficult-to-predict trend change, cyclical and seasonal effects, as well as significant volatility ^[3]. And secondly, because the data of financial statistics reflecting these processes, respectively, are characterized by non-linearity, non-stationarity, the presence of outliers and anomalies ^[4], as well as in some cases omissions in the data and the lack of closure in the series of dynamics, which is due to the peculiarities of the formation and calculation of the corresponding indicators, and repeatedly complicates their synchronization. At the same time, all these features have been further strengthened recently due to the deterioration of the global geopolitical situation.

This state of affairs requires the use of modern self-learning models for building financial forecasts, that is, such models that could self-correct in the process of forecasting, adapting to changes in the initial data. Various variants of such models are being developed and used by both Russian ^[5] and foreign ^[6] financial institutions. And, nevertheless, research on this issue is still far from being completed and therefore relevant.

In this paper, the use of additive regression models for forecasting macro-level financial indicators is considered. As examples, the problem of short-term forecasting of the dynamics of gross domestic product (GDP) and money supply (M2), as well as their subsequent use to assess the level of monetization of the country's economy, as one of the factors determining the potential of the state to attract financing for the implementation of projects of structural modernization of the economy, is considered.

Additive regression models for forecasting financial indicators

Additive regression models (AR models) are a separate type of statistical models (also related to machine learning methods) based on one-dimensional smoothing of data followed by the construction of nonparametric regression. This approach was first proposed in 1981 ^[7] and since then has proven to be more flexible and more convenient in comparison with the previously used standard linear regression ^[8].

According to the AP model approach, the prediction result (each individual element of the set Y, with dimension n) is determined by adding several independent components (see Table 1):

The selection of component parameters is made on the basis of available statistical data using some method known from the literature (for example, a reverse fitting algorithm).

Table 1. Key components of the AR model (compiled by the author)

Different practical implementations of AR models may have a different set of components (as a rule, less wide in comparison with the one presented above). Overview Several examples of popular AR models used today for making forecasts in the field of finance are given in the table (see Table 2). It can be seen that each of them has both advantages and disadvantages. The choice of a particular model largely depends on the characteristics of the data under study, as well as the goals of forecasting.

Table 2. Examples of popular AR models used to predict financial indicators (compiled by the author based on ^[8])

A common disadvantage of all the above models is their situation-dependent nature. To ensure the quality of the received forecasts, their scrupulous initial adjustment is necessary, often achieved only by adjusting, optimizing the initial data or making corrective corrections. In turn, this creates difficulties with the subsequent interpretation of the results obtained. For this reason, their effective use is often inaccessible to specialists in the subject area (financiers, economists) and requires the involvement of specialists in mathematical modeling, data analysis and machine learning. Unfortunately, the latter, in turn, may not have deep knowledge of economics and finance, which allows them to formulate and argue their own conclusions. As a result, this leads to the inability to fully use modeling tools due to the general distrust of the results of the models.

In this paper, we used a model from the open source library Prophet, developed for Python and R languages by Facebook's Core Data Science team ^[9]. The core of the Prophet procedure is implemented in the probabilistic programming language Stan ^[10] using the principles of Bayesian statistics. According to the tests carried out, this library works well with data series with pronounced seasonal and trend effects, is resistant to data absence and trend shifts, copes well enough with outliers, and in general has a significantly lower error compared to other methods of automatic time series forecasting ^[11].

From the point of view of practical application, the most important distinguishing quality of the Prophet library is that in order to use it, an analyst does not need a deep knowledge of mathematical methods and predictive modeling, there is no need for a preliminary in-depth study of the initial data series, bringing it to a stationary form, selecting initial approximations and hyperparameters of the algorithm, etc. All this greatly facilitates the use of the model, making it accessible to applied practitioners in the field of economics and finance, and not just mathematicians or analysts.

Building short-term forecasts of financial macro indicators using the AR model

As an example, let's consider the problem of short-term forecasting of the dynamics of gross domestic product (GDP) and money supply (M2) based on data for the last 10 years (from January 2013 to December 2022 inclusive).

The necessary historical data are presented in the reports of the Federal State Statistics Service (Rosstat) "Gross Domestic Product (in current prices)" ^[12] and "Money supply M2 (national definition)" ^[13]. It should be noted here at once that these data are presented with different frequency (GDP – quarterly values with an increasing total as of the end of the quarter, M2 – monthly fixed values as of the end of the month), and also that there are no data for February-December 2018 and October-November 2022 in the statistics of the M2 indicator. These circumstances would significantly complicate the construction of a forecast in the case of using any method other than Prophet. Let's make a forecast of GDP and M2 indicators by the end of 2023 (see Figure 1 and Figure 2, respectively).

Figure 1. Forecast of the dynamics of the GDP indicator (calculated by the author)

Figure 2. Forecast of the dynamics of the M2 indicator (calculated by the author)

Thus, according to the revised forecast, the possible GDP growth in 2023 (relative to 2022) is unlikely to exceed 3.6% (which will be equivalent to RUB 158.7 trillion). However, at the same time, there is a high probability of near-zero growth or even a drop in GDP by an amount of about -2.9% (that is, up to 148.9 trillion rubles). Thus, even taking into account the crisis situation, our country still has a certain probability of fulfilling the originally laid plans for economic development ^[14], however, the risks of slipping into recession are also high. At the same time, the value of the average absolute percentage prediction error (MAPE) calculated according to the common methodology for assessing the quality of forecasts ^[8] was 6.3%, which is a sign of a sufficiently high quality of the constructed forecast.

At the same time, the latest version of the medium-term forecast published by the Bank of Russia at the time of writing ^[15] presents a significantly narrower forecast corridor, on the one hand assuming a more conservative GDP growth (no more than 2.5%), but at the same time not suggesting its fall at all. This discrepancy can be explained by the fact that the considered forecast model reflects the inertial development, that is, the dynamics of changes in indicators in the conditions of maintaining the existing trends of factor dependencies and the absence of serious financial, external and internal political "disturbances". The forecast of the Bank of Russia also takes into account the likely regulatory impacts, which are not always obvious and obvious to an outsider.

At the same time, according to the projected forecast, the volume of money supply will steadily increase. If the current trends continue, by the end of 2023, the value of the M2 monetary aggregate may increase by 19.7%, reaching the value of 84.9 trillion rubles. At the same time, the likely growth spread is from 17.7% to 21.7%. In this case, the value of the average absolute percentage prediction error (MAPE) ^[8] is 1.5%, which is a sign of a very high quality forecast. Also, the forecast we received almost completely coincides with the medium-term forecast of the Bank of Russia ^[15], which assumes an increase in the money supply by 17-21%.

Assessment of the financing potential of structural modernization projects of the economy

Having forecast values of GDP and M2 indicators, it becomes possible to assess one of the most important indicators of the national economy – its monetization coefficient, better known in foreign literature as the "Marshall coefficient" ("Marshallian K") and defined as the ratio of money supply (M2) to gross domestic product (GDP) ^[16]:

Note that for the correctness of the calculation, it is necessary to use the M2 value averaged over a period similar to the period of calculation of GDP.

The monetization coefficient reflects the degree to which the economy is provided with money (that is, its saturation with liquid assets capable of performing the functions of a means of payment) and, in fact, allows linking the financial and real sectors of the economy in a single model.

World practice shows that in a market economy, monetization at a level of at least 50% is necessary to ensure the normal operation of economic agents. A decrease in monetization below this threshold leads to a decline in the economy, an increase in barter and offsets due to the lack of a full-fledged possibility of monetary settlements, as well as the growth of the shadow sector of the economy, settlements in which are carried out through alternative financial instruments (for example, cryptocurrencies). To ensure full-fledged investments in fixed assets, the level of monetization of the economy should no longer be lower than 80%. The generally accepted benchmark of monetization for developed countries is the level of 150% ^[16].

A number of scientists have proved that the high monetization of the economy allows to reduce interest rates on loans and increase their availability ^[17], increase the liquidity and capitalization of the financial market ^[18], and, what is especially important in our situation, to stabilize inflation and stimulate economic growth ^[19]. The latter becomes especially important in view of the ambitious goals outlined by the Government for the modernization and restructuring of the country's economy, the implementation of which is based on large-scale national programs and federal projects (megaprojects) ^[20].

The table (see Table 3) shows data on the monetization of the economy of various countries for 2020, structured and classified in accordance with the above approach.

Table 3. The level of monetization of the economy of some countries (compiled by the author on the basis of ^[16])

The level of monetization largely determines the ability of the state to borrow money on the domestic market ^[21]. It can be seen that our country in 2020 belonged to countries with low monetization of the economy, which indicates a limited opportunity for the country to increase its domestic debt.

According to the forecasts of GDP and M2 indicators, the expected level of monetization of the Russian economy in 2023 will increase and may reach 62%. However, in the current economic conditions, due to the closure of access to international capital markets and partial blocking of reserves, this growth may not be enough to ensure full and timely financing of declared national projects and government programs. Thus, it is very likely that the plans announced by the Government of our country for the structural modernization of the national economy will experience a shortage of funding, which may jeopardize the possibility of their implementation on time. On the contrary, an increase in the level of monetization of the economy will contribute to the growth of investment activity within the country and will create the volume of "long money" (that is, long-term investments) needed today, while reducing the cost of lending.

Thus, the Central Bank of the Russian Federation and the Ministry of Finance of the Russian Federation today face a difficult compromise task – if the conditions for targeting inflation are met, to ensure targeted regulation of the volume of money supply with bringing the monetization of the economy to the required level.

It should be noted here that these tasks have a different horizon – the task of targeting inflation is of a short-term nature (should be solved now), while the task of ensuring sustainable development by saturating the economy with money can be smoothly stretched over time. In this regard, an important role should be assigned to the regulatory function designed to ensure compliance with the targeted nature of the monetary issue and blocking the possibility of liquidity flow to the market of speculative instruments (currency, derivatives, etc.) or to foreign financial markets, and not allowing this money to go into the sphere of final consumption, thereby increasing demand and, accordingly, inflation. One of the possible directions of this could be, for example, the introduction of a segmental reserve ratio, lowered for the industrial sector (to stimulate production growth) and increased for the consumer sector (to contain inflation).

Conclusion

Thus, additive regression models are an effective tool for forecasting macro-level financial indicators. At the same time, the situation in which our country finds itself today has only increased the value of forecast data, making the speed and ease of obtaining them the key to timely and adequate response to emerging new challenges.

The used Prophet library has shown sufficient accuracy, allowing not only to simulate the dynamics of individual indicators (GDP or M2), but also to obtain an indirect assessment of our country's potential for financing its economic development.

It is established that despite the possibility of positive economic dynamics, the level of monetization of the economy remains low and may be a hindering factor for the development of the country. This situation obviously goes against the Government's plans to modernize the national economy. In order to correct the situation, it is necessary to continue improving the monetary policy pursued by the state.