Bivariate (multivariate) analysis. Aim: to estimate the model: Y t =b*X t + N t ; b= the regression coefficient expressing the effect of X on Y N t =noise term (error term), including other causes of Y besides X.
Aim: to estimate the model:
Yt=b*Xt + Nt;
b= the regression coefficient expressing the effect of X on Y
Nt=noise term (error term), including other causes of Y besides X
The differencing reduces the risk of spurious correlations, since an omitted variable is more likely to be correlated with the explanatory variable due to common trends than as a result of synchronization in the yearly changes.
Plot (scattergram) Yt against Xt to detect outliers
Are the series stationary? If not: difference both X and Y; Xt = Xt-Xt-1Plot (scattergram) Yt against Xt to detect outliers. Remedies: shorten series; dummy variable
have a temporal structure that is modelled
through AR and/or MA-parameters:
Nt= Nt-1+ et. The residuals et= white noise.
If the residuals ≠ white noise (but
autocorrelated), the estimate of b will be
unbiased, but the SE of b will be
Thus, we must identify and estimate a model
Yt=b*Xt + Nt ;don’t include any noise parameters.
2. Identify the structure of the noise term on the basis of the ACF and PACF of the residuals.
3. Re-estimate the model including noise parameters.
4. Diagnostic test of the model: are the residuals white noise. If not: modify the noise parameters on the basis of the ACF and PACF of the residuals, and re-estimate the model.
Alkuttot=public (bars etc) alcohol consumption
1. twoway (line alkuttot year) if year>1955
2. twoway (line assaultrate year) if year>1955
/Trending: should difference, but analyse raw data as an exercise /
3. generate alkutdif=d.alkuttot
4. generate assaultdif=d.assaultrate
5. twoway (scatter assaultdif alkutdif)
6. corrgram assaultdif, lags(20)
7. corrgram alkutdif, lags(20)
8.arima alkutdif, arima(1,0,0)
9.predict resass, r
10. corrgram resass, lags(20)
12. arima assaultrate alkuttot, arima(0,0,0)
13. predict resmod1, r
14. arima assaultrate alkuttot, arima(1,0,0)
15. predict resmod2, r
16. corrgram resmod2, lags(20)
17. arima assaultrate alkuttot, arima(0,1,0)
18. predict resmod3, r
19. corrgram resmod3, lags(20)