# Statistical methods of forecasting the economy

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## Product description

laboratory practice and four current control

"The use of models of growth curves in economic forecasting"

To calculate the K = 10

All fields are required assignments marked in yellow

1. quarterly data are available on the company´s profits (thous.).

Table 1. Baseline

t yt (thous.) t yt (thous.) t yt (thous.)

1 80.4 6 115.2 + K + K + K 11 147.4

2 TO 7 + 88.3 118.4 155.2 + 12 K + K

3 TO 8 + 92.0 127.1 169.8 + 13 K + K

4 98.5 + K + K 9 131.3 14 176.7 + K

5 109.9 10 136.9 + K + K + K 15 192.4

The graphical analysis in MS Excel examine the component structure of the time series (the trend component and random).

Explain the possibility of using the models of growth curves of polynomial type (I and II order) and the exponential model to describe the dynamics of this series.

2. Assuming that the trend can be described by a number

I) the linear model;

II) parabolic model,

III) the exponential model

to determine the coefficients of these models by the method of least squares (OLS) (exponential model must be brought to a linear form logarithms). To simplify the calculations, do the transfer of the origin in the middle of a number of speakers.

3. Compare selected models using the graphical analysis in MS Excel.

To do this on the same graph picture the empirical data and theoretical values \u200b\u200bobtained for I, II and III models.

4. Compare the model built on the characteristics of precision: average

absolute error of the module and the mean relative error of

module. Check the adequacy of the source data models on the criterion

Durbin-Watson. Make a conclusion about the "quality" of the obtained models, determine the most appropriate model (has the least mistakes and adequate baseline data on the criterion Durbin-Watson).

5. Calculate the best model using point forecast for the period of pre-emption L = 1.

Laboratory workshop.

Table 1.1.Opredelenie coefficients of the linear model of MNCs transfer

the origin in the middle of a number of speakers.

Baseline. coord. the original data transfer NK in mid. For linear. models for parabens.

models for the show. model. Ln -natural logarithm to the "e". calculation of the parameters of the theoretical trends in the three models.

t! yt (thous.) t yt * t t2 yt * t2 t4 Ln (yt) Ln (yt) * t

(Linear).

(Parabens.)

(The show.)

1 80.4 + K -7

2 88.3 + K -6

3 92.0 + K -5

4 98.5 + K -4

5 109.9 + K -3

6 115,2 + K -2

7 118.4 + K -1

8 127.1 0 K +

9 TO 1 131.3 +

10 136.9 + K 2

11 147.4 + K 3

12 155.2 + K 4

13 169.8 + K 5

14 176.7 + K 6

15 192.4 7 + K

\$ 8

Forecast

= ----- ----- Forecast Forecast = ----- =

When calculating the parameters of all models of the summation is carried out in t, obtained after migration of the origin in the middle of the series.

The linear model:

a0 = ------

a1 = ------

The forecast profit in the next quarter: + ---- ---- ---- * ---- = thousand.

a0 a1 t

Parabolic Model:

The forecast profit in the next quarter: ---- + ---- + ---- * ---- * ---- = ---- thousand.

a0 a1 t a2 t2

Exponential model:

Since OLS - linear estimation method will take the natural logarithm of the left and right of the function. After taking the logarithm function became linear.

Designating; ; write

The forecast profit in the next quarter: ---- * ---- * ---- = ---- thousand.

Table 1.2.Raschet accuracy characteristics of the linear model.

yt (thous.) (line.) (thous.)

80.4 + K

88.3 + K

92.0 + K

98.5 + K

109.9 K +

115.2 K +

118.4 K +

127.1 K +

131.3 K +

136.9 K +

147.4 K +

155.2 K +

169.8 K +

176.7 K +

192.4 K +

Sum

........

Monitoring №1

1.Tendentsiya changes in the average annual number of industrial production personnel described by the model of the enterprise:. According to the model the average growth rate of population was as follows:

a) 2.2%; b) 31%; c) 22%; g) 12.2%; d) 102.2%.

2.Godovaya dynamics of the company´s profit model is described:

According to the model, the average annual growth of profit is:

a) 6.4 b) -6,4 c) 372.2 g) 72.2

3.Ezhekvartalnaya dynamics of the interest rate of the bank for 5 quarters is presented in the table below:

The forecast of the interest rate of the bank at 6 quarter, calculated using the average growth rate is equal to:

a) 11.1%; b) 11.8%; a) 10, 9%; g) 11.5%; d) 11.6%.

4.Urovni time series vary from approximately constant growth rate. Prediction one step forward using the average growth rate can be calculated by the formula:

5.Dinamika time series is close to a linear development. Prediction two steps forward by the average of the absolute gain can be calculated using the formula:

Monitoring №2

1. Introduction levels of time series (t = 1,2, ..., n) as:

Where ut -trendovaya component; cyclic component; st-seasonal component; a random component that corresponds to the model:

a) the multiplicative; b) an additive; c) mixed type; d) an adaptive

2. Presentation of levels of the time series (t = 1,2, ..., n) as: where ut-trend component; cyclic component; st-seasonal component; a random component that corresponds to the model:

3. For a description of periodic oscillations with a period of three months is used:

a) the seasonal component; b) random component;

c) the trend component; d) cyclical component.

4.Predstavlenie levels of the time series (t = 1,2, ..., n) as:

Where ut -trendovaya component; cyclic component; st-seasonal component; a random component that corresponds to the model:

a) the multiplicative; b) an additive; c) mixed type; d) an adaptive

5. For the description of periodic oscillations with a period of five years is used:

a) the seasonal component; b) random component;

c) the trend component; d) cyclical component.

Monitoring №3

1.Znachenie Durbin-Watson test for time series residuals e1, e1, ..., en is given by:

2. After the transfer of the origin of a number of speakers in the middle of the coefficient a1 is a linear model:

3. For the estimation of the unknown polynomial coefficients used:

a) the method of successive differences; b) the method of least squares;

c) the method of characteristics increments; g) the method of moments.

4. Durbin-Watson criterion is used to:

a) check the properties of random residual component;

b) test the hypothesis that the distribution of the normal number of residues;

c) autocorrelation in the residuals.

5. The system of normal equations for the parabolic model includes:

a) three equations with three unknowns;

b) two equations with three unknowns;

c) two equations with two unknowns.

Monitoring №4

1.Model exponential smoothing is determined by the recurrence formula:

2.In the exponential smoothing model parameter adaptation ? can be equal to:

a) 1.9; b) 99; c) 0.1; g) 1.5; d) 2.

3.Model Holt - Winters used to predict the time series:

a) a multiplicative seasonality; b) with additive seasonality;

c) an exponential trend; g) with a damping trend.

4.Kolichestvo adaptation parameters used in the model of linear growth C. Holt, is:

a) 2; b) 3; c) 1; g) 4.

5. If the calculated criterion value Durbin-Watson d is below the lower critical value table d1, then:

a) the model is not adequate to the real process of this criterion;

b) the actual process of the model is adequate on this criterion;

c) there was insufficient evidence to make a decision

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