Reading List for October

Some suggestions for the coming month:

• Franses, P. H., 2016. A note on the mean absolute scaled error. International Journal of Forecasting, 32, 20-22.
• Gorroochurn, P., 2015. On Galton's change from 'reversion' to 'regression'. American Statistician, in press.
• Holan, S. H., R. Lund, and G. Davis, 2010. The ARMA alphabet soup: A tour of ARMA model variants. Statistics Surveys, 4, 232-274.
• Liu, S., H. Wu, and W. Q. Meeker, 2015. Understanding and addressing the unbounded "likelihood" problem. American Statistician, 69, 191-200.
• McCracken, M. W. and S. Ng, 2015.  FRED-MD: A monthly database for macroeconomic research. Journal of Business and Economic Statistics, in press.
• Müller, U. K. and M. W. Watson, 2015. Low-frequency econometrics. NBER Working Paper No. 21564.

© 2015, David E. Giles

Thanks, Dan!

Quite out of the blue, Dan Getz kindly sent me a nice LaTeX version of my hand-written copy of "The Solution", given in my last post.

Dan used the ShareLaTeX site - https://www.sharelatex.com/ .

So, here's a nice pdf file with The Solution.

Thanks a million, Dan - that was most thoughtful of you!

© 2015, David E. Giles

The Solution

You can find a solution to the problem posed in yesterday's post here.

I hope you can read my writing!

p.s.: Dan Getz kindly supplied a LaTeX version - here's the pdf file. Thanks, Dan!

© 2015, David E. Giles

Try This Problem

Here's a little exercise for you to work on:

We know from the Gauss-Markhov Theorem that within the class of linear and unbiased estimators, the OLS estimator is most efficient. Because it is unbiased, it therefore has the smallest possible Mean Squared Error (MSE) within the linear and unbiased class of estimators. However, there are many linear estimators which, although biased, have a smaller MSE than the OLS estimator. You might then think of asking: 

“Why don’t I try and find the linear estimator that has the smallest possible MSE?”

(a) Show that attempting to do this yields an “estimator” that can’t actually be used in practice.

(You can do this using the simple linear regression model without an intercept, although the result generalizes to the usual multiple linear regression model.)

(b) Now, for the simple regression model with no intercept, 

         y_i = β x_i + ε_i       ;     ε_i ~ i.i.d. [0 , σ²] ,

find the linear estimator, β* , that minimizes the quantity:

h[Var.(β*) / σ²] + (1 - h)[Bias(β*)/ β]² , for 0 < h < 1.

Is  β* a legitimate estimator, in the sense that it can actually be applied in practice?

The answer will follow in a subsequent post.

© 2015, David E. Giles

September Reading List

• Abeln, B. and J. P. A. M. Jacobs, 2015. Seasonal adjustment with and without revisions: A comparison of X-13ARIMA-SEATS and CAMPLET. CAMA Working Paper 25/2015, Crawford School of Public Policy, Australian National University.
• Chan, J. C. C. and A. L. Grant, 2015. A Bayesian model comparison for trend-cycle decompositions of output. CAMA Working Paper 31/2015, Crawford School of Public Policy, Australian National University.
• Chen, K. and K-S. Chan, 2015. A note on rank reduction in sparse multivariate regression. Journal of Statistical Theory and Practice, in press.
• Fan, Y., S. Pastorello, and E. Renault, 2015. Maximization by parts in extremum estimation. Econometrics Journal, 18, 147-171.
• Horowitz, J., 2014. Variable selection and estimation in high-dimensional models. Cemmap Working Paper CWP35/15, Institute of Fiscal Studies, Department of Economics, University College London.
• Larson, W., 2015. Forecasting an aggregate in the presence of structural breaks in the disaggregates. RPF Working Paper No. 2015-002, Research Program on Forecasting, Center of Economic Research, George Washington University.

© 2015, David E. Giles