Some misspecfication problems in long-memory time series models

Doctor of Philosophy in Mathematics

Estimation of leaf area in grapevine cv. Syrah using empirical models

Aiming to obtain empirical models for the estimation of Syrah leaf area a set of 210 fruiting shoots was randomly collected during the 2013 growing season in an adult experimental vineyard, located in Lisbon, Portugal. Samples of 30 fruiting shoots were taken periodically from the stage of inflorescences visible to veraison (7 sampling dates). At the lab, from each shoot, primary and lateral leaves were separated and numbered according to node insertion. For each leaf, the length of the central and lateral veins was recorded and then the leaf area was measured by a leaf area meter. For single leaf area estimation the best statistical models uses as explanatory variable the sum of the lengths of the two lateral leaf veins. For the estimation of leaf area per shoot it was followed the approach of Lopes & Pinto (2005), based on 3 explanatory variables: number of primary leaves and area of the largest and smallest leaves. The best statistical model for estimation of primary leaf area per shoot uses a calculated variable obtained from the average of the largest and smallest primary leaf area multiplied by the number of primary leaves. For lateral leaf area estimation another model using the same type of calculated variable is also presented. All models explain a very high proportion of variability in leaf area. Our results confirm the already reported strong importance of the three measured variables (number of leaves and area of the largest and smallest leaf) as predictors of the shoot leaf area. The proposed models can be used to accurately predict Syrah primary and secondary leaf area per shoot in any phase of the growing cycle. They are inexpensive, practical, non-destructive methods which do not require specialized staff or expensive equipment.