https://www.ucl.ac.uk/~ucfbpve/papers/VermeeschEPSL2004.pdf

How many grains are needed for a provenance study

Economic forecasting in agriculture

Even though the trend components of economic time series were among the first to be distinguished, even today the trend remains relatively little understood. As Phillips (2005) notes, no one understands trends, but everyone sees them in the data. Economists and econometricians can give plenty of examples of trends, such as straight lines, exponentials or polynomials in time, and also forms of random walks, but these are merely examples. Individuals or groups do have their own personal definitions, but these diverse approaches illustrate the lack of a generally accepted definition of a trend. They also suggest a richness of alternatives to consider, both individually and jointly. Here, we make a variety of observations about trends, and based on these, we offer working definitions of various kinds of trends. We emphasize that these are working definitions, as our purpose here is to invite discussion, not to settle matters once and for all. Our hope is that our discussion here may facilitate development of increasingly better methods for prediction, estimation and hypothesis testing for non-stationary time-series data, and ultimately may enable decision makers to make more informed decisions.

Consideration of Trends in Time Series

Forecasting by factors, by variables, by both or neither?

Trygve Haavelmo’s Probability Approach aimed to implement economic theories, but he later recognized their incompleteness. Although he did not explicitly consider model selection, we apply it when theory-relevant variables, { X t }, are retained without selection while selecting other candidate variables, { W t }. Under the null that the { W t } are irrelevant, by orthogonalizing with respect to the { X t }, the estimator distributions of the X t ’s parameters are unaffected by selection even for more variables than observations and for endogenous variables. Under the alternative, when the joint model nests the generating process, an improved outcome results from selection. This implements Haavelmo’s program relatively costlessly.

/pdf/model-discovery-and-trygve-haavelmo-s-legacy-35anz2euv4.pdf

Model discovery and Trygve Haavelmo's legacy

(1925). Forecasting the Acreage of Cotton. Journal of the American Statistical Association: Vol. 20, No. 149, pp. 31-47.

Bradford B. Smith

Papers

Forecasting the Acreage of Cotton

Combining the Advantages of First-Difference and Deviation-From-Trend Methods of Correlating Time Series

Judging the Forecast for 1929

Forecasting the Volume and Value of the Cotton Crop

The Error in Eliminating Secular Trend and Seasonal Variation before Correlating Time Series