Statistical modeling and forecasting of the level of interest rates. Interest Rate Forecasting

Rice. 9.6. parity band interest rates

in order to predict changes in legislation and in the conditions for concluding and executing contracts.

The following purposes of forecasting the exchange rate can be distinguished;

a) currency risk management.

This goal is leading, but not the only one; b) short-term financing decisions. The currency in which we borrow should have a desirably low interest rate and a tendency to weaken during the financing period; c) short-term investment decisions. The currency in which we place deposits or provide loans should have as high an interest rate as possible and tend to appreciate during the investment period; d) evaluation of long-term investment projects. If we are going to invest in another country, then the corresponding currency should ideally weaken. But if we invest funds within our own country for subsequent export, then it will be desirable to strengthen the corresponding currency;

e) assessment of long-term borrowings. In principle, the approach is the same as for short-term financing, but the implementation of this forecasting goal is much more difficult; f) management of the movement of income received* abroad. If the currency in which the income is received strengthens, then this income, most likely, should be repatriated, that is, taken out “home”. But if the opposite trend in the exchange rate is predicted, then it is best to reinvest them abroad.

The above list of goals shows the very significant impact that effective methods forecasting exchange rates on the profitability of international transactions. This determined the headquarters of the efforts and funds spent on solving the problem of their development. In the past period, an impressive arsenal of various forecasting methods has been created and extensive experience in their application has been accumulated.

The developed methods were based on theoretical studies on the movement of exchange rates carried out in the world financial science over the past decades, which were discussed above. Over the past twenty or thirty years, a large number of methods for assessing the future movement of exchange rates have been developed and practically tested. They are based on four basic approaches: 1) technical forecasting; 2) fundamental forecasting; 3) forecasting based on market expectations; 4) forecasting based on expert assessments.

The first two approaches come from two generally accepted forecasting methods, applied not only to exchange rates, but also to the prediction of many other socio-economic parameters. Features of their application in the currency markets are discussed in this section. The third approach is specific to forecasting exchange rates, so it will be given special attention. Finally, the fourth approach, which uses the intuitive opinions of experts, is rather obvious, and only some comments on the appropriateness of its application will be given below.

The approach based on technical forecasting can be formally represented as follows:

e(= a0 + a( x et_, + a2x ec_2 + + a „ x ec_ „, (9.17)

where e, is the change in the exchange rate in the forecast period t\

e, -2, ???, e, - " - changes in the exchange rate of the same currency in periods t - 1, t - 2, ..., t - p)

ak - statistical (weight) coefficients obtained by correlation-regression or other methods (k from 0 to n);

n is the number of past periods on the basis of which the forecast is built.

Technical forecasting has another name in the Russian version, namely forecasting based on time series. At present, quite a few new sophisticated methods of such forecasting have appeared, using a variety of non-linear functions of past and future data, graphical analysis fluctuations in the exchange rate, expert assessment of the possibility of carrying over from previous periods some patterns of the movement of this exchange rate, the so-called time series models, etc. Quite often, this really makes it possible to obtain satisfactory results. Nevertheless, in its essence, this approach assumes the admissibility of extrapolation, the extension of the development trends of a phenomenon that have developed in the past, into the future. From this premise both its possibilities and its limitations follow. The economic interpretation of the forecast is quite simple, but any significant change in the existing trends turns out to be detrimental to the quality of forecasting the future value of the exchange rate.

Fundamental forecasting, unlike technical forecasting, is based not on the extrapolation of the past trend of change in the exchange rate itself, but on the study of its dependence on various factors that are outside the foreign exchange market. In this regard, in the Russian-language litas, ratura, it is often also called factorial. In a formal form, this approach can be written as follows:

es \u003d aa + ahhi + ... + axP "(+ an ^ + y.x + - + an + tut1_u (9.18)

where хх, ..., хп," are the factors influencing the foreign exchange rate, the values ​​of which are also predicted for the period

y „, _ „ ..., ut," _, - factors affecting the foreign exchange rate, the values ​​of which can be calculated based on the actual data of the period t -

n, m - the number of factors of the first and second groups.

The selection of these two groups of factors is necessary, since it reflects the essence of the approach to forecasting the exchange rate. Indeed, the construction of factor models in the area under consideration should be based, first of all, on generally accepted theoretical considerations of the influence of certain parameters on the exchange rate.

The theory of Fisher's international effect discussed above defines a two-factor model in which the future value of the exchange rate depends on both the relative inflation rate and the comparative level of interest rates in the two countries between whose currencies the desired exchange rate is predicted. In this case, the inflation rates are taken for the period for which the forecast is made, i.e., they themselves must be predicted. You can also take the inflation rates for the previous period, for which they are already known. However, this requires appropriate justification, i.e., determining what is more statistically significant: the relationship of the movement of the exchange rate with the accompanying inflation rates or with those prevailing in the past period, and whether such a replacement will lead to a loss in the quality of the forecast.

As for interest rates considered as a factor in this theory, at first glance they are valid for the forecasting period and in this sense are unambiguously determined already at the beginning of the period, and therefore can be interpreted as a factor of the previous period. However, this is not quite true. The fact is that we usually make a forecast in advance, with some lead, which means that interest rates for the forecasting period are not yet known and must themselves be the subject of a forecast. As in the previous case, the rates of the previous period can also be considered as a factor, but here the same additional justification is required. Thus, the application of fundamental forecasting is associated with a number of problems, the degree of resolution of which directly affects the quality of the forecast.

Among these problems, first of all, it is necessary to pay attention to the following. The first is to find the periods for which the factors are taken. In this case, we are talking not only about the forecasting period and the period immediately preceding it. It is possible that the quality of the forecast may be higher if earlier periods are taken or if the model includes the values ​​of the same factor for several periods: 4 ^ - 1, ? - 2, etc. In particular, this may be appropriate when building a short-term forecast, for example, a month or a week ahead.

If it turns out to be justified to use the values ​​of the factors in the forecast period, then naturally the problem arises of how to obtain these values.

After resolving issues related to determining the required set of factors, problems arise in constructing a correlation-regression or some other relationship between the factors under consideration and the desired value. At the same time, there are traditional dangers of the process of constructing regression equations and, above all, the possibility of missing unaccounted for, but significant factors, which makes the model as a whole not quite adequate.

Finally, another very significant problem is the stability of the regression coefficients obtained as a result of calculating the regression equation. The instability and variability of these coefficients can stem from two main reasons. The first of them is that when the set of factors used or the method of calculating their values ​​is changed (for example, the calculation of this value for the period t or the same factor.

The second reason stems from the need to use predictive values ​​of factors in certain cases. Such a forecast cannot be absolutely accurate and, moreover, in most cases it is inappropriate to refine it, for example, to average it, since this leads to artificial smoothing of the obtained forecast values ​​of the exchange rate, which does not reflect the full complexity of the dependence under study.

In order to better understand the latter position and, in general, more clearly imagine the ways of using the economic interpretation of the results of fundamental forecasting, we will give an example.

Consider a two-factor fundamental forecasting model of the following form:

ec=a0+axxc+a2y1L, (9.19)

where x1 is the difference in interest rates between the two countries predicted for period I;

g/(_, - actual for the period? - 1 value of the difference in inflation rates between countries.

Assume that a statistically significant regression equation is obtained for this model

e(=0(2-0^c(+05y(_1. (9.20)

This equation can be interpreted in accordance with formulas (9.6) and (9.11) as follows.

Each percentage excess of the inflation rate in some conditional “our” country compared to the inflation rate in “another” country in the past period leads to a 0.5% increase in the direct exchange rate of “our” currency against the “other” currency in the forecast. - Ruem period. An increase in the direct exchange rate of "our" currency, i.e., an increase in the price of foreign currency, means a reduction in price, a weakening of "our" currency.

On the other hand, each percentage increase in the interest rate in "another" country compared to the interest rate in "our" country in the forecast period leads to a 0.6% depreciation of "our" currency in the same period and a corresponding appreciation of the foreign currency. .

Let us pay special attention to the conclusion obtained in the financial theory * and confirmed by the practice of countries with developed market economy. He ss| The point is that an increase in the interest rate in a country compared to other countries in a certain period (a year, a month) leads, ceteris paribus, to upward pressure, i.e., to an appreciation of the currencies of this country in the same period. However, we note that the same increase | can lead, on the contrary, to downward pressure, to a depreciation of this currency in the next period? + 1.

After the necessary explanations, we introduce some initial values ​​taken! into the factor model. Suppose that the actual value of the difference between | inflation rates in the two countries under consideration in period 1 amounted to! 1%. This means that the inflation rate in our country was higher. Let's do it! the same assumptions about the values ​​of the difference in interest rates obtained as a result of some calculations for the forecast period. These input values ​​| are given not by one number, but by a certain set of them, a distribution with an indication! we eat for each of them the probability of implementation. Relevant data are given in table. 9.4. |

Table 9.І Forecast values ​​of the difference in interest rates Forecast variant number Forecast value for the variant, % Probability of the implementation of the variant, % 1 -4 10 2 -5 60 3 -6 30 As can be seen from the table. 9.4, in all options, the interest rate in “our* country is lower than in “another”, but the possible difference is not the same. In addition, the probability of implementation of each of the options is not the same. We emphasize that this principle of presenting forecast information is quite common, and moreover, it corresponds to modern ideas about financial risk as an objectively existing uncertainty of future results and many other economic parameters.

The results of the exchange rate forecast will also be presented in three versions, which are shown in Table. 9.5.

As can be seen from Table. 9.5, both higher inflation and lower interest rates in "our" country lead to a weakening of "our" currency, which, depending on the possible size of the fall in interest rates, or, more precisely, on the predicted degree of their lagging behind the level of interest rates in "other" country, can be 3.7% with a probability of 60%,

Table 9.5

Forecast values ​​of the exchange rate Option number «„ + »L,., «А e, Probability of implementation of the variant, % 1 0.7 2.4 bl 10 2 0.7 3.0 3.7 60 3 0.7 3.6 4.3 30 and also 4.3% - with a probability of 30% and 3.1% - with a probability of 10%. Some average value can also be calculated ( expected value) exchange rate changes 3.1

x 0.10 + 3.7 x 0.60 + 4.3 x 0.30 = 3.82.

This value will take place when the average, mathematically expected forecast value of the gap in interest rates equal to 5.2% is realized.

Let us now turn to the consideration of the third approach in the field of forecasting the exchange rate, which is very different from the first two, since it uses a fundamentally different methodology and technique for forecasting calculations. This approach is based on the use of interest rate parity theory. The leading problem in its application to forecasting is the degree to which the forward rate matches the future spot rate. The fundamental possibility of coincidence or closeness of these courses sufficient for forecasting is determined by the following two circumstances.

The first is that the forward rate is a value derived from market expectations about the future current rate of banks and other firms that provide forward services. The specialists of these banks and firms have best knowledge relevant foreign exchange markets, since they are professionally worked on, and, in addition, are interested in minimizing the difference between the calculated forward rates and the spot rates that actually occur in the future, since this reduces the risk of providing forward services.

The second circumstance is that the convergence of forward and future current rates is ensured by the processes of market self-regulation. The latter is based on currency-percentage arbitrage: from a theoretical point of view, zero profitability of arbitrage operations can be achieved, which means the equilibrium state of the market segment under consideration. Of course, complete equilibrium or, as they say, the state of a perfect financial market is achievable only in the ideal. Nevertheless, the measure of achieving equilibrium determines the measure of justification for applying the method of forecasting the exchange rate based on market expectations.

Let us now turn to the problems of the practical use of the described methods, taking into account the real limitations that exist in the economic system.

In a number of countries, extensive studies have been carried out on the quality of forecasts obtained using different methods. Evaluating the results of these studies in an integrated manner, two main conclusions should be pointed out. First, none of the methods gives sufficiently accurate forecasts in the statistical sense. Almost always there is a statistically significant bias of the prognostic estimate in relation to the actual one. Second, the smallest bias in most studies was forecasting based on market expectations.

Singling out this method as giving on average the minimum forecast error, it must be emphasized that this does not negate the expediency of using other methods in certain circumstances. At brief periods forecasting (day, week), the method of technical forecasting becomes preferable, if only for the reason that on ryi! kah developed countries there simply are no representative quotes of interest rates for such short periods. With an increase in the duration of these periods (a year or more), macroeconomic factors of the movement of the exchange rate are manifested to a greater extent and, accordingly, the method of fundamental forecasting becomes more important.

It should also be borne in mind that for practical application the forecasting method based on market expectations must meet three fundamental conditions under which it works: 1) there are no sufficiently significant restrictions on the movement of money between the markets under consideration; 2) the vast majority of foreign exchange transactions are purely financial in nature and do not serve the processes of movement of goods or the provision of non-financial services; 3) commercial banks play a decisive role in the market, in any case, their total financial positions are not inferior to those of the central banks of those countries for whose markets this approach is applied. These conditions are met for countries with developed market economies, and this determines the fundamental possibility of forecasting based on this method.

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1 18 S.A. Poluyakhtov, V.A. Belkin S.A. Poluyakhtov, V.A. Belkin UDC Kondratieff cycles of the interest rate as the basis for predicting its dynamics Abstract. Based on extensive statistical material, the article proves the hypothesis that cyclical fluctuations in the bank interest rate on loans are determined by cycles of solar activity. On this basis, it is possible to predict the interest rate in the medium and long term, and, consequently, the future state of the global and Russian economies. summary. Extensive statistic material helped the authors to prove the hypothesis that cyclical fluctuations of the bank credit interest rate are determined by solar cycles. These facts make it possible to forecast an interest rate in a medium-term and long-term perspective and consequently to predict the future economic situation in the world and in Russia as well. Keywords. bank interest rate cyclicality, solar activity cycles, cyclical development of the economy, economic crisis forecasting, bank interest rate forecasting. key words. Cyclical fluctuations of the bank credit interest rate, solar cycles, cyclical development of economy, forecast of economic crisis, forecast ofbank interest rate. The global financial crisis again exposed the problem of inadequate forecasting of the main economic indicators and, consequently, an overly optimistic view of governments various countries on the future economic situation in the world. One of the reasons for this situation is the lack of forecasts for one of the most important economic indicators of the bank interest rate. In his article “On Interest Rate Forecasts”, S. Moiseev notes that “if abroad interest rates are well predictable even without central bank forecasts, then in Russia there is a lack of information about the future dynamics of the money market. Guessing interest rates is one of the most complex analyzes and, as a rule, estimates of future rates are not included in consensus forecasts and surveys of professional forecasters. Not being able to get percentage forecast from official sources, many economists decide to forecast it themselves. However, the forecasting methods available today are either too primitive or so time-consuming that they are inaccessible to most of them. Therefore, we propose to develop a method for forecasting interest, based on its relationship with solar activity cycles (hereinafter referred to as SA), which will give a more accurate forecast without any labor-intensive calculations, which will allow any economic entity to apply it. Bulletin of the Turkmen State University No. 11

2 Kondratieff cycles of the interest rate As a starting point, we accept the hypothesis of V.A. Belkin that “cyclical fluctuations of the main macroeconomic indicators, including such as the unemployment rate, inflation rate and average loan rate, the national currency exchange rate, the deficit (surplus) of the consolidated budget, are determined by cycles of solar activity” . To test this hypothesis for the period from 1947 to July 2010, we took average annual data on the Wolf numbers, which are proportional to the number of sunspots on the solar disk and characterize SA. For the same period, the prime rate was taken as the bank interest rate that affects the state of the world economy (the interest rate closest to the risk-free rate). Next, we built graphs of changes in these indicators over time (Fig. 1). As this chart shows, since 1968, the cycles of the prime rate have been largely determined by the cycles of the SA. Rice. Fig. 1. Dynamics of changes in the average annual Wolf numbers and the prime rate rate It is worth noting some features of the cyclical nature of the SA and the prime rate rate. Thus, the growth phase of SA lasts an average of 4 years, and the decline phase lasts 7 years, the total duration of the cycle is 11 years on average. That is, the SA cycle has a sharp rise and a smooth decline. At the same time, during the CA growth phase, there is also a growth phase of the bank interest rate, and when the CA cycle reaches its peak, the interest rate immediately or after 1 year also reaches its maximum value. During the CA decrease phase, the bank interest rate also decreases simultaneously. However, about one or two years before the next CA low, the bank interest rate reaches its next high. So far, we cannot accurately determine the reason for the repeated cycle of the bank rate within the SA cycle and can only make assumptions or hypotheses. ECONOMY

3 20 S.A. Poluyakhtov, V.A. Belkin To get rid of the influence of short-term fluctuations in the prime rate, we calculated the average values ​​of the analyzed indicators over the years at the inflection points of the SA cycle curve and plotted the corresponding graphs (Fig. 2). It can be seen from this diagram that the 11-year cycles of the SA sufficiently coincide with the cycles of the bank interest rate (the correlation coefficient is 79%), which coincide with the cycles of C. Juglar. That is, the growth of SA leads to an increase in the prime rate and, as a result, at the maximum points to an economic crisis. Thus, it is the cyclical activity of the sun that is the key factor determining the change in the bank interest rate. Also, the revealed relationship reveals true reason the cyclicity of this indicator and the development of the world economy as a whole. Let's show that such rates as LIBOR, EURIBOR change almost synchronously with the prime rate. Thus, we will prove that SA cycles determine the dynamics of bank interest around the world, and not just in the United States. Rice. Fig. 2. Dynamics of changes in the average annual Wolf numbers and the prime rate at the inflection points (extremums) of the solar activity curve To study the relationship between prime rates and LIBOR, we chose the LIBOR rate for loans up to one year. The values ​​for it were taken from the economic statistics website MORTGAGE-X. Below is a diagram that clearly shows the dynamics of synchronous changes in the average annual prime rate and LIBOR rates (for up to one year) (Fig. 3). Bulletin of the Turkmen State University No. 11

4 Kondratieff cycles of the interest rate Fig. 3. Changes in the average annual prime rate and LIBOR rates (for up to one year) To investigate the relationship between the prime rate and EURIBOR, the EURIBOR rate for loans up to one year was chosen. The values ​​for it were taken from the ItIsTimed website. Next, we built a diagram that clearly shows the dynamics of a highly synchronous change in the average annual prime rate and EURIBOR rates (for a period of up to one year) (Fig. 4). In the years the EURIBOR rate changed synchronously with the prime rate, but with a time delay (lag) of about 1 year. Rice. 4. Dynamics of changes in the average annual prime rate and EURIBOR rates (for a period of up to one year) ECONOMICS

5 22 S.A. Poluyakhtov, V.A. Belkin The presented diagrams clearly and convincingly prove the high degree of synchronization of changes in the main international interest rates LIBOR and EURIBOR and the prime rate. Thus, the relationship between SA and the prime rate that we have proven can be extended to other interest rates, in particular, LIBOR and EURIBOR. Based on the result obtained, as well as the forecast of the 24th SA cycle (Fig. 5), it is possible to develop a forecast for the value of the prime rate. The next peak of CA is expected in 2013, and, therefore, we can expect an increase in the prime rate until 2013, and in 2013. we predict another maximum of this rate and the subsequent global financial crisis. Of course, the actual activity of the Sun in the 24th cycle may differ from the predicted one, since these cycles vary somewhat in duration (9-11 years). In this case, there will be some corresponding shift in time of the indicated date of the next prime rate high and the global economic crisis. Rice. 5. Forecast of the 24th cycle of solar activity Figure 5 shows that the next SA minimum should occur around 2020. Consequently, around 2018 there will be another increase in interest rates, and then in 2019 and 2020. a slowdown in US real GDP growth or an economic crisis. In order to give a more accurate forecast of the value of the prime rate in 2013, let's turn to N. Kondratiev's theory of waves, on the basis of which 5 economic cycles are identified, about a year long: Bulletin of the Turkmen State University Heritage No. 11

6 Kondratieff cycles of interest rates cycle from 1790 to 2 cycle from to years. 3 cycle from to years. 4 cycle from to years. Cycle 5 with Kondratiev cycles are subject to all major macroeconomic indicators, including the bank prime rate interest rate. At the same time, at the end of the cycle, the rate reaches its maximum value. To confirm our hypothesis, let us analyze the diagram shown in Fig. 1. It shows that the penultimate minimum of economic indicators of the world economy was in 1982 and was accompanied by a maximum of the bank interest rate, which we propose to call the Kondratiev maximum of the prime rate (K-rate). Before the K-rate, there was an increase in the prime rate, after a decrease. We propose to call these cycles large prime rate cycles. According to research by Japanese scientist Shimanaka Yuji, confirmed by the Japan Economic Research Center (JERC) and published in The Wall Street Journal of 1999, one Kondratieff cycle equals five SA cycles, or 55 years. Based on this theory and the fact that two SA cycles took place between 1982 and 2010, it can be assumed that 2010 is the inflection point of the large prime rate cycle and will continue to grow. Consequently, the local maximum prime rate in 2013 will be higher than the local maximum of this indicator in 2009 and will be approximately at the level of the local maximum of 2000. Thus, the prime rate in 2013 will reach its intermediate next maximum in the medium term at the level of 8-9%, which with a high degree of probability will lead to another global financial crisis (Fig. 6). Rice. 6. Kondratieff cycle of the prime rate and its forecast until 2020 ECONOMICS

7 24 S.A. Poluyakhtov, V.A. Belkin Similarly, the local maximum of the prime rate in 2018 will be higher than the local maximum of this indicator in 2013, but lower than the local maximum of this indicator in 1989, that is, its value will be approximately at the level of 10% (Fig. 6 ). Based on the fact that changes in the prime rate are in sync with changes in LIBOR and EURIBOR interest rates, we can expect a corresponding increase in these rates to 6% and 5%, respectively, in 2013 and LIBOR at 8.5% in 2018. Since 2003, due to the globalization of the world economy and the high involvement of the Russian economy in it, there has been a synchronization of US GDP and Russian GDP with a higher volatility of Russian GDP. Consequently, a change in the prime rate inevitably leads to a similar change in the Russian bank interest rate on loans, so by 2013 in Russia the bank interest rate on loans issued to legal entities for a period of up to 1 year will also grow to the level of 2000 and will be 18 -20% per annum. Solar activity peaks will continue to lead to an increase in the Russian bank interest rate on loans and, accordingly, to another financial crisis. The result obtained is extremely important not only for government officials, but also for the entire economically active population, since on its basis it is possible to make long-term investment decisions and objectively assess the future development of the country's economy. As an explanation of the reason for the revealed connection, one can cite the studies of the great Russian scientist A. Chizhevsky, who argued that psychopathic epidemics, panic moods, mass hysteria, hallucinations, etc., as well as modification of the nervous excitability of the neuropsychic tone are closely related to SA cycles. Cyclical fluctuations of the above pessimism and optimism lead to cyclical fluctuations in the value of the risk payment, which is taken into account in the interest rate, and to its cyclical fluctuations. So, as a result of this study: A high degree of connection between SA cycles and the bank interest rate was revealed using the prime rate as an example; It is proposed to introduce into scientific circulation the concepts of the Kondratieff cycle of the bank rate (on the example of the prime rate) and the Kondratieff maximum (minimum) of this rate; A medium- and long-term forecast of the next highs in the prime rate and global financial crises has been developed; A high degree of synchronism in the dynamics of prime rate, LIBOR, EURIBOR rates is shown; A medium-term forecast has been developed for the next highs in LIBOR, EURIBOR rates and the Russian interest rate on loans in 2013. Bulletin of the Turkmen State University No. 11

8 Kondratieff cycles of the interest rate References 1. Moiseev S. “On the forecast of the interest rate” URL: post/124329/ 2. Belkin V. A. Relationship between cycles of solar activity and cycles of main macroeconomic indicators // Social and economic development of Russia in the post-crisis period : national, regional and corporate aspects: Sat. m-catching 27 intl. scientific-practical. conferences Part 1, Chelyabinsk: UrSEI AT and SO, C; 3. Statistical data of the Center for Data Analysis on the Influence of the Sun (Belgium) URL: 4. Data from the economic statistics website MORTGAGE-X URL: com 5. Data from the ItIsTimed website URL: php 6. NASA research data URL: solnechnyiy-prognoz/ 7. Korotaev A. V., Tsirel S. V. Kondratieff waves in world economic dynamics / System monitoring. Global and regional development / Ed. ed. D. A. Khalturina, A. V. Korotaev. M.: Librokom/URSS, C URL: cliodynamics.ru/download/m02korotayev_tsirel_kondratyevskie_volny.pdf 8. The Union of Intelligible Associations // Configuring: Transformative policy cycles (9. Chizhevsky A. L. Earth echo of solar storms. 2nd ed. M.: Thought, pp. EKO N O M I K A

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• Specialty HAC RF08.00.13
• Number of pages 149