No lecture Tue Feb23. 

Fit f^(x) = a + bx + cx^2 + dx^3 + ex^4. 
Obtain estimates of a, b, c, d, e. 

Now suppose you fit f^x = a + bx + cx^2 + dx^3. 
Your estimates of a,b,c,d will be different! 
That's because the polynomial basis is not orthogonal! 

Projects. 
What should you do? 
Data problems. 
Do whatever is convenient to clean up your data, but acknowledge them in conclusion. 
Remove trend, 
look at the acf and pacf after removing trend, 
fit ARMA models. Pick the one with minimum AIC. 
Forecast with that ARMA? 
Interpret the coefficients of your fitted ARMA model. 
Are there features in your dataset, that are influencing these estimates? 
What do the ARMA fits and ACF and pacf telling you about your data? Smoothness? Predictability? 
Estimate the spectrum (non-parametrically and/or nonparametrically), and interpret the results. Are there significant cycles? Can you interpret the estimated spectrum in terms of how rough data are? Variation at different frequencies. 
Are there cycles you can remove and then re-estimate the spectrum? 
Forecast?