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Research in to the structure of the inflation time series in the Republic of Belarus at present

14.04.2013 – It has been known that any time series is formed under the influence of various factors. Traditionally, the following groups of factors are singled out: permanent, seasonal and irregular ones [1, 2, and 6]. The permanent factors are explained through a trend, or a trend-cyclical component. The seasonal factors are included in the seasonal component. The irregular component encompasses the influence of different random (extemporaneous) factors.

Below is a general view of the multiplicative model of a time series:

                                             Y=TC·S·E                                                           (1)

This model implies that each level of a time series can be presented as a product of the trend-cyclical (TC), seasonal (S) and irregular (E) components.

The most important tasks are to determine the seasonal factor of inflation and analyze the “core inflation”, which is identified through eliminating the seasonal factor as well as random factors (for example, energy sources price advance or change of administered prices). As a result, the core inflation is reflected in the trend-cyclical component of inflation, which is generated under the influence of long-term and medium-term factors.

In order to study the structure of the time series of the consumer price index for the period of January 2000 through October 2005, it would be reasonable to use variant X-11 of the seasonal decomposition Census II [3-5], which is a development of the classical seasonal decomposition. This method was developed in the US Census Bureau and has won itself a name.

Table 1 contains an analysis of the structure of the inflation time series based on variant X-11 of the seasonal decomposition Census II.

Table 1

Seasonal decomposition of the inflation time series for the period of 2000-2005

Continuance of Table 1


The first column contains the actual values of the consumer price index. The second one depicts the estimated values of the seasonal component for each particular month. The third column reflects the calculated values of the time series adjusted for seasonality (or, otherwise, cleared of seasonality). The forth column contains the values of the trend-cyclical component calculated with the help of Henderson curve. And, finally, the fifth column contains the values of the irregular component.

The presence of seasonality in the inflation time series is statistically significant (Table 2).

Table 2

Test for the presence of seasonality in the inflation time series


In general, the influence of the seasonality factor shows rather explicitly (Figure 1, Table 3), which enables the following conclusions.

Figure 1. Seasonal wave of inflation in the economy of the Republic of Belarus in 2000-2005

Table 3

Estimate of the seasonal component of inflation for each month in 2000-2005

First, in Figure 1 it is evident that with the course of time the amplitude of seasonal oscillation dies out. Thus, while in January 2000 inflation increased by 2,3% due to the seasonality factor, in January 2005 it came up only by 1,9% (Table 3).

Secondly, inflation traditionally goes up in autumn and winter time, and it goes down in spring and summer. As an example, let us consider the seasonal wave in 2004 (Table 3, Figure 2). Thus, the most inflation-dangerous months were January (due to the seasonality factor, inflation grew by 1,9%), December (1,1%) and November (0,7%). Besides, due to the seasonality factor, inflation went up in October (0,1%) and February (0,1%). In all the other months, starting from March, the seasonality factor caused inflation to go consistently down. This positive process reaches its utmost in summer time, especially in August (-1,4%).


Figure 2. Seasonal wave of inflation in the economy of the Republic of Belarus in 2004

As the analysis shows, the retardation of inflationary development in spring and summer is caused mainly by the seasonal price fluctuations for horticultural products, as well as by the decrease in the growth intensity of production costs in this period of the year.

Table 4 depicts the forecast of the seasonality factor for one year. It is assumed that, in general, the seasonality factor dynamics next year will not change a lot and will be similar to the ones last year.

Table 4

Forecast of the seasonal component of inflation in 2005-2006

Thirdly, it is prominent that in January 2004 the value of the consumer price index cleared of seasonality was 99,9% (Table 1), that is to say that prices, for the first time within the exploration period, decreased (!) by 0,1%. The situation revealed itself even more distinctly in January of the current 2005 – prices went down by 1,2% at a sweep, and the core inflation value (trend-cyclical component) proved to be the lowest for the whole exploration period – 100,9%.
Figure 3. Inflation time series cleared of seasonality and trend-cyclical component of inflation

Thereafter, however, the situation took a turn for the worse. In February-April 2005 the core inflation remained the same – 100,9%, and in May-October it was 101,0% (Figure 3, Table 1). Figure 4 depicts the irregular component of inflation.

Figure 4. Irregular component of inflation

Starting in 2003 the Ministry of Statistics and Analysis of the Republic of Belarus has been conducting official assessment of core inflation. When calculating the core consumer price index, horticultural products are excluded from the list of food products, as their prices are subject to seasonal fluctuation. The goods which prices are controlled by the bodies of state administration are also excluded from the list. When calculating the core inflation in 2003, 52 items altogether were excluded (out of 377 items in the consumer goods and services basket). The ratio of consumer goods and services excluded from the calculation of the core consumer price index came up to 27,8%.

Table 5 reflects the dynamics of gross inflation, core inflation and trend-cyclical component. It is worth while noting that in 2004 both estimates of the “core inflation” were practically the same (official assessment was 14,9%, and the trend-cyclical component of inflation was 15,2%) and they exceeded a bit the gross inflation value (14,4%).

The excess of core inflation over gross inflation stems from the strengthening of administrative control over price formation in 2004. Thus, for instance, in 2003 consumer prices grew by 25,4%. The administered prices among them grew by 44,9%, or became 1,8 times higher (Table 6). As a result, the growth of administered prices provided 10,1 of 25,4 per cent points of inflation (Table 7). Its contribution to the total price advance accounted for 39,8% (Table 8).

In 2004 the situation radically changed: with the growth of consumer prices by 14,4%, administered prices grew by 10,2%. As a result, their direct contribution to inflation decreased – 3,4 of 14,4 per cent point, which means that the role of administered prices in the total consumer price advance came up to 23,6%, or 16,2 per cent points less than in 2003 (Tables 7 and 8). The current year demonstrates a similar effect – with the growth of consumer prices in January-October 2005 by 5,6%, administered prices increased by 4,4%.

Such dynamics leads to accumulation of inflation potential and serious imbalances of economy. Thus, according to the data of Table 6, the inflation potential in 2004 (the difference between the values of net inflation and gross inflation) was estimated as 2,4% (16,8%-14,4%), in the current 2005 it is estimated as 0,8% (6,4%-5,6%), which totals 3,2%. That is if, for instance, in October 2005 the accumulated inflation potential (3,2%) had blown off all at once, then the current inflation in January-October would have made not 5,6%, but 9,0%, or 1,6 times more.

The same evidence is given by the dynamics of the trend-cyclical component in 2005 – 0,9-1,0% per month, or 10,0% for the period January-October, which is 1,8 times more than the official gross inflation value (Table 5). The dynamics of prices for horticultural products also come under notice – 15,3% in January-October 2005 (Table 6). Taking into account the seasonal character of horticultural products, one can conclude that by the end of 2005 this value will, probably, exceed 20-25%. Note that complex consideration of the seasonal factor creates the necessary prerequisites for the development of measures to mitigate the negative consequences of seasonal price fluctuations for certain goods and services.

In general, according to the author’s estimates, with the possible worsening of the situation, the potential inflation rate may exceed the official figure more than twice.

So, administrative price regulation leads to the accumulation of inflation potential, enhances imbalance and instability of inflationary developments, encourages considerable loosening and deformation of the existing economic system to the worse and bears certain risks of destabilization of the situation in the future.

The main task of the anti-inflationary economic policy at present is to balance the growth rate of administered and non-regulated prices, to achieve coherent price changes for certain goods and services (in particular, horticultural products, municipal housing services, etc.) with the general dynamics of inflationary developments, to decrease the total volatility and secure smoother dynamics of prices within a year, as well as to limit the growth rate of core inflation caused by long-term and medium-term factors.


1. Austin, J. S. (1981) How to Use and Interpret Seasonal Factors, Business Economics, 16, no. 4.

2. Burman, J. P. (1979) Seasonal adjustment - A Survey, Forecasting, Studies in Management Science, 12.

3. Findley, D. F., Monsell, B. C., Shulman, H. B., Pugh, M. G. (1988) Sliding Spans Diagnostics for Seasonal and Related Adjustments, Statistical Research Division Report No.CENSUS/SRD/RR-86/18, Bureau of the Census.

4. Shiskin, J., Young, A.H., Musgrave, J.C. (1967) The X-11 variant of the census method II seasonal adjustment program, Technical paper no. 15, Bureau of the Census.

5. Wallis, K. F. (1974). Seasonal adjustment and relations between variables, Journal of the American Statistical Association, 69.

6. Zellner, A., ed. (1978) Seasonal Analysis of Economic Time Series, U.S. Department of Commerce, Bureau of the Census.

Author: analyst Alexander Mukha

Source: BusinessForecast.by

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