# Construction of the model change of employment over working age in the Tomsk region, taking into account seasonal fluctuations

One of the most important areas of study of the problem of well-being of the older generation is to study the activity of the working population of retirement age. A significant factor affecting the labor activity is a seasonal component. The employment of retirees is not constant at different periods - activity is cyclical fluctuations. This is important to study the influence of the seasonal component for the

Simulation of seasonal variation is carried out for the economically active and the economically inactive population of Tomsk region in the working age. The sample set is the data for each month of the economically active population, including employed and unemployed in the period from 2011 to 2013. The seasonally adjusted construction of the additive time series model was chosen as a modeling approach. In the other words each value of the time series is represented as the sum of the trend, seasonal and random components. There is constant oscillation amplitude, so the general view of the model is as follows: Y=T+S+E

Where T - trend component; S - seasonal component; E - random component.

It should also be noted that the most important task in the classical study of economic time series is the identification and statistical evaluation of the main trends in the development of the studied process, detecting the presence of seasonal variations in the range of people of retirement age, and deviations from it. Figure 1 shows the dynamics of the number of employed persons over the working age over the period from 2012 to 2014.

Figure 1. Dynamics of employment over working age in the period from 2012 to 2014

The construction of model changes in the number of employed older generation represents the calculation of all the above components for each time series. The following steps are offered to build this model:

1. Baseline statistics are aligned by moving average;

2. The influence of the seasonal component S on empirical data is calculated;

3. Excluding the impact of seasonality on statistics, analysis of the impact of the trend and the random variable T + E in the additive model;

4. Selection of the best analytical description of the trend component, taking into account the effect of the random component of T + E;

5. Trend and random components are calculated in the model;

6. Forecast values of deferred employed people over the working-age population with the resulting model.

When analyzing the data of the economically active population of working age, seasonal variations with frequency of 12 were shown, because the number of employed people is much higher in July than in January. Thus, the analyzed factor reaches a peak in winter and summer.

Excluding the impact of the seasonal component and subtracting its value from each level of the original time series, we obtain the value T + E = Y-S. In this case, the data contain a trend component and a random component only. Fig. 2 shows the dynamics of these components of the indicator changes in the employment of the elderly population: the original data Y, data with excluded the impact of the seasonal component Y-S, data with excluded the impact of random components T + S, trend component T only. Figure 3 shows the quantitative impact of seasonal and random components for each moment all the time during the analyzed period.

Figure 2 Changes in the statistics, the data with the excluded impact of seasonal and random components, as well as the trend of employment of the elderly population of the Tomsk region

Dynamic of statistics is showing the impact of the magnitude of the seasonal component in the overall level of employment. Curves Y and YS have a slight resemblance - the maximum level of influence of the seasonal component is close to 2,000 jobs. This random component has little effect on the overall activity of the population of working age. Curves Y and S + T are almost the same - the maximum level of influence of the random components does not exceed 1000. Therefore, we can conclude that the degree of influence of seasonal variation than the random variable 2 times.

Figure 3. Dynamics of seasonal and casual component in the analysis of the employment of the elderly population

Figure 3 shows the dynamics of changes in the seasonal and random components in the overall level of employment of persons older than working age. Thus, it can be concluded that the maximum value of the random component of the absolute value is approximated to 1500. The impact of the seasonal component in the overall level of economic activity of pensioners in absolute value exceeds 4,000.

It is necessary to align the analytical series T + E by a linear trend to determine the effect of directly trend component T. Substituting in this equation the values t = 1, 2, ..., 16, we find the levels of T for each time point, substituting the values t = 1, 2, ..., 16 in this equation. We can find the value of a number of levels obtained by the additive model. To do this, it is necessary to add the values of the seasonal component for the respective months to the levels of T.

Figure 4 shows the dynamics (after excluding the seasonal component) and the trend of the economic activity of the population of retirement age. The trend looks upward straight y = 13,93x + 40752. There has been an increase in the activity of the slow pace of work - the number of employed persons over the working age increased by only 1% for two years.

Figure 4 Changes in employment over working age after excluding the seasonal component for the period from 2012 to 2014

An important component is the comparison of the initial statistical data and data after excluding the impact of the random component to identify the seasonal fluctuations in employment over working age. On the same graph we should postpone the actual values of levels of time series and theoretical received under an additive model. Random component in the total number of employed persons over the working age does not exceed 1,000 jobs.

Figure 5 Dynamics of changes in employment over working age (the original data and the data with eliminated the random variable)

We should apply the method of the sum of squares obtained the absolute errors to assess the quality of the constructed model. The coefficient of determination is equal to 0.922102183. Thus, we can say that the combined model has built 92% of the total variation of levels of time series of the number of employed people over the working-age population.

According to the results of this work there are following conclusions:

- Modeling the dynamics of change in the number of employed people over working age allowed to obtain estimates of the seasonal component under the additive model. For example, with an annual increase in employment of 0.5% must be taken into account that in July of each year, increasing of the number of jobs in 2000 are required due to the increase of labor activity.
- This makes it possible to use the data seasonal adjustment in the assessment of income of the older generation, which in turn affects the welfare of the population.

The ratio of the labor market in the region are increasingly will be determined by the social activity and social mobility of persons older than working age. The package of measures to preserve their economic activity takes into consideration the influence of the seasonal component in the overall level of activity of people of retirement age. In a situation of decreasing working-age population important activity seems to maintaining employment and social activity of the elderly generation.