Time Series Model Estimation

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Time Series Model Estimation. Outline for this lectureReview the first times series lecture Discuss model estimation Demonstrate how to estimate Time Series (AR) models with SimetarInterpretation of model resultsHow you forecast the results for an AR model. . Time Series Model Estimation. Plot

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Time Series Model Estimation

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1. Time Series Model Estimation Materials for this lecture Read Chapter 15 pages 30 to 37 Lecture 7 Time Series.XLS Lecture 7 Vector Autoregression.XLS

2. Time Series Model Estimation Outline for this lecture Review the first times series lecture Discuss model estimation Demonstrate how to estimate Time Series (AR) models with Simetar Interpretation of model results How you forecast the results for an AR model

3. Time Series Model Estimation Plot the data to see what kind of series you are analyzing Make the series stationary by determining the optimal number of diferences based on =DF() test, say Di,t Determine the number of lags to use in the AR model based on =AUTOCORR(), say Di,t =a + b1 Di,t-1 + b2 Di,t-2 +b3 Di,t-3+ b4 Di,t-4 Create all of the data lags and estimate the model using OLS

4. Time Series Model Estimation An alternative to estimating the differences and lag variables by hand and using a regression package, use Simetar Simetar time series function is driven by a menu

5. Time Series Model Estimation Read the results like a regression Beta coefficients are provided like OLS SE of Coef used to calculate t ratios to determine which lags are significant For goodness of fit refer to AIC, SIC and MAPE Can restrict out variables

6. Time Series Model Estimation Dickey-Fuller test indicates whether the data series used for the model, Di,t , is stationary and if the model is D2,t = a + b1 D1,t the DF it indicates that t stat for b1 is < -2.90 Augmented DF test indicates whether the data series Di,t are stationary, if we added a trend to the model and one or more lags Di,t =a + b1 Di,t-1 + b2 Di,t-2 +b3 Di,t-3+ b4 Tt SIC indicates the value of the Schwarz Criteria for the number lags and differences used in estimation Change the number of lags and observe the SIC change AIC indicates the value of the Aikia information criteria for the number lags used in estimation Change the number of lags and observe the AIC change Best number of lags is where AIC is minimized Changing number of lags also changes the MAPE and SD residuals

7. Time Series Model Forecasting Assume a series that is stationary and has T observations of data so estimate the model as an AR(0 difference, 1 lag) Forecast the first period ahead as YT+1 = a + b1 YT Forecast the second period ahead as YT+2 = a + b1 YT+1 Continue in this fashion for more periods This ONLY works if Y is stationary, based on the DF test for zero lags

8. Time Series Model Forecasting What if D1,t was stationary? How do you forecast? First period ahead forecast is D1,T = YT – YT-1 D^1,T+1 = a + b1 D1,T Add the calculated D1,T+1 to YT YT+1 = YT + D^1,T+1 Second period ahead forecast is D^1,T+2 = a + b D^1,T+1 YT+2 = YT+1 + D^1,T+2 Repeat the process for period 3 and so on This is referred to as the chain rule of forecasting

9. For Model D1,t = 4.019 + 0.42859 D1,T-1

10. Time Series Model Forecast

11. Time Series Model Estimation Impulse Response Function Shows the impact of a 1 unit change in YT on the forecast values of Y over time Good model is one where impacts decline to zero in short number of periods

12. Time Series Model Estimation Impulse Response Function will die slowly if the model has to many lags Same data series fit with 1 lag and a 6 lag model

13. Time Series Model Estimation Dynamic stochastic Simulation of a time series model

14. Time Series Model Estimation Look at the simulation in Lecture 6 Time Series.XLS

15. Time Series Model Estimation Result of a dynamic stochastic simulation

16. Vector Autoregressive (VAR) Models VAR models a time series models where two or more variables at thought to be correlated and together they explain more than one variable by itself For example forecasting Sales and Advertising Money supply and interest rate Supply and Price We are assuming that Yt = f(Yt-i and Zt-i)

17. Time Series Model Estimation Take the example of advertising and sales AT+i = a +b1DA1,T-1 + b2 DA1,T-2 + c1DS1,T-1 + c2 DS1,T-2 ST+i = a +b1DS1,T-1 + b2 DS1,T-2 + c1DA1,T-1 + c2 DA1,T-2 Where A is advertising and S is sales DA is the difference for A DS is the difference for S In this model we fit A and S at the same time and A is affected by its lag differences and the lagged differences for S The same is true for S affected by its own lags and those of A

18. Time Series Model Estimation Advertising and sales VAR model

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