Скачать презентацию

Идет загрузка презентации. Пожалуйста, подождите

Презентация была опубликована 2 года назад пользователемТимофей Тарханов

1 1 Another useful model is autoregressive model. Frequently, we find that the values of a series of financial data at particular points in time are highly correlated with the value which precede and succeed them. Autoregressive models

2 2 Models with lagged variable Dependent variable is a function of itself at the previous moment of period or time. The creation of an autoregressive model generates a new predictor variable by using the Y variable lagged 1 or more periods.

3 3 The most often seen form of the equation is a linear form: where: y t – the dependent variable values at the moment t, y t-i (i = 1, 2,..., p) – the dependent variable values at the moment t-i, bo, bi (i=1,..., p) – regression coefficient, p – autoregression rank, e t – disturbance term.

4 4

5 5 A first-order autoregressive model is concerned with only the correlation between consecutive values in a series. A second-order autoregressive model considers the effect of relationship between consecutive values in a series as well as the correlation between values two periods apart.

6 6 The selection of an appropriate autoregressive model is not an easy task. Once a model is selected and OLS method is used to obtain estimates of the parameters, the next step would be to eliminate those parameters which do not contribute significantly.

7 7 (The highest-order parameter does not contribute to the prediction of Yt) (The highest-order parameter is significantly meaningful)

8 8 using an alpha level of significance, the decision rule is to reject H 0 if or if and not to reject H 0 if

9 9 Some helpful information:

10 10 If the null hypothesis is NOT rejected we may conclude that the selected model contains too many estimated parameters. The highest-order term then be deleted an a new autoregressive model would be obtained through least- squares regression. A test of the hypothesis that the new highest-order term is 0 would then be repeated.

11 11 This testing and modeling procedure continues until we reject H 0. When this occurs, we know that our highest-order parameter is significant and we are ready to use this model.

12 12 Example 1

13 13

14 14

15 15

16 16

17 17

18 18 We have to estimate the parameters of the first-order autoregressive model: and then check if Beta1 is statistically significant.

19 19

20 20 Example 2

21 21

22 22

23 23

24 24 Autogregressive Modeling Used for Forecasting Takes Advantage of Autocorrelation 1st order - correlation between consecutive values 2nd order - correlation between values 2 periods apart Autoregressive Model for pth order: Random Error

25 25 Autoregressive Modeling Steps 1. Choose p: 2. Form a series of lag predictor variables Y i-1, Y i-2, … Y i-p 3. Use Excel to run regression model using all p variables 4. Test significance of B p If null hypothesis rejected, this model is selected If null hypothesis not rejected, decrease p by 1 and repeat your calculations

Еще похожие презентации в нашем архиве:

Готово:

Econometrics. Econometrics is "the application of mathematics and statistical methods to economic data" and described as the branch of economics "that.

Econometrics. Econometrics is "the application of mathematics and statistical methods to economic data" and described as the branch of economics "that.

© 2017 MyShared Inc.

All rights reserved.