Optimal forecasting accuracy using Lp-norm combination

A well-known result in statistics is that a linear combination of two-point forecasts has a smaller Mean Square Error (MSE) than the two competing forecasts themselves (Bates and Granger in J Oper Res Soc 20(4):451–468, 1969). The only case in which no improvements are possible is when one of the single forecasts is already the optimal one in terms of MSE. The kinds of combination methods are various, ranging from the simple average (SA) to more robust methods such as the one based on median or Trimmed Average (TA) or Least Absolute Deviations or optimization techniques (Stock and Watson in J Forecast 23(6):405–430, 2004). Standard regression-based combination approaches may fail to get a realistic result if the forecasts show high collinearity in several situations or the data distribution is not Gaussian. Therefore, we propose a forecast combination method based on Lp-norm estimators. These estimators are based on the Generalized Error Distribution, which is a generalization of the Gaussian distribution, and they can be used to solve the cases of multicollinearity and non-Gaussianity. In order to demonstrate the potential of Lp-norms, we conducted a simulated and an empirical study, comparing its performance with other standard-regression combination approaches. We carried out the simulation study with different values of the autoregressive parameter, by alternating heteroskedasticity and homoskedasticity. On the other hand, the real data application is based on the daily Bitfinex historical series of bitcoins (2014–2020) and the 25 historical series relating to companies included in the Dow Jonson, were subsequently considered. We showed that, by combining different GARCH and the ARIMA models, assuming both Gaussian and non-Gaussian distributions, the Lp-norm scheme improves the forecasting accuracy with respect to other regression-based combination procedures.

Arterial Stiffness Preceding Diabetes

Rationale: Previous studies on the relationship between diabetes and arterial stiffness were mostly cross-sectional. A few longitudinal studies focused on one single direction. Whether the association between arterial stiffness and diabetes is bidirectional remains unclear to date. Objective: To explore the temporal relationship between arterial stiffness and fasting blood glucose (FBG) status. Methods and Results: Included were 14 159 participants of the Kailuan study with assessment of brachial-ankle pulse wave velocity (baPWV) from 2010 to 2015, and free of diabetes, cardiovascular and cerebrovascular diseases, and chronic kidney disease at baseline. FBG and baPWV were repeatedly measured at baseline and follow-ups. Cox proportional hazard regression model was used to estimate hazard ratios and 95% confidence intervals (CIs) of incident diabetes across baseline baPWV groups: <1400 cm/s (ref), 1400≤ baPWV <1800 cm/s, and ≥1800 cm/s. Path analysis was used to analyze the possible temporal causal relationship between baPWV and FBG, among 8956 participants with repeated assessment of baPWV and FBG twice in 2010 to 2017. The mean baseline age of the observed population was 48.3±12.0 years. During mean 3.72 years of follow-up, 979 incident diabetes cases were identified. After adjusting for potential confounders, the hazard ratio (95% CI) for risk of diabetes was 1.59 (1.34–1.88) for the borderline arterial stiffness group and 2.11 (1.71–2.61) for the elevated arterial stiffness group, compared with the normal ideal arterial stiffness group. In the path analysis, baseline baPWV was associated with follow-up FBG (the standard regression coefficient was 0.09 [95% CI, 0.05–0.10]). In contrast, the standard regression coefficient of baseline FBG for follow-up baPWV (β=0.00 [95% CI, −0.02 to 0.02]) was not significant. Conclusions: Arterial stiffness, as measured by baPWV, was associated with risk of developing diabetes. Arterial stiffness appeared to precede the increase in FBG.

ANTITRUST DAMAGES IN FINANCIAL MARKETS

I briefly review the standard regression methods used to estimate damages in antitrust actions, and I analyze how these would be applied to cases in financial markets. I consider applications to three different financial market cases. The first is the NASDAQ odd-eighths litigation, where existing antitrust methods closely resemble the analyses published in the academic literature on this issue. The second type of case is bond market antitrust litigation, where the expert faces an additional hurdle because they have to estimate bid-ask spreads. The third type of case is related to the LIBOR manipulation scandal. I analyzed why existing methods provide a poor fit for the LIBOR damage calculations. Lastly, I evaluate IPO issuance fees as an example of price clustering in financial markets that has not let to antitrust litigation.

Some competing nonresponse adjustment estimators

The nonresponse adjustment estimator, derived in this paper by standard regression tools, is surprising by its form. The weights of the new estimator, called the f-estimator, are (general) inverses of the respective weights in the classical linear calibration estimator and propensity adjusted estimator. In a simulation experiment on real data, the new estimator is the best for several study variables.

Are Pain and Suffering Awards (Un-)Predictable? Evidence from Germany

This paper assesses the widely held belief that damages for pain and suffering are random or arbitrary. In detail, we investigate whether damages for pain and suffering are systematically affected by individual-, injury- and procedural-specific characteristics and how important these factors are relative to each other. To uncover the predictability of these awards, we rely on a sample of German damages for pain and suffering awards including 2.244 verdicts. By estimating a standard regression model we observe that final awards are systematically influenced by the injury’s conditions, by the court level the case is brought in and by the engagement of a lawyer. Our findings let us conclude that damages for pain and suffering and the respective assessment process within the German judicial system are largely reasonable and transparent rather than random.

A Nonlinear Rank Regression Method for Ensemble Kalman Filter Data Assimilation

It is possible to describe many variants of ensemble Kalman filters without loss of generality as the impact of a single observation on a single state variable. For most ensemble algorithms commonly applied to Earth system models, the computation of increments for the observation variable ensemble can be treated as a separate step from computing increments for the state variable ensemble. The state variable increments are normally computed from the observation increments by linear regression using the prior bivariate ensemble of the state and observation variable. Here, a new method that replaces the standard regression with a regression using the bivariate rank statistics is described. This rank regression is expected to be most effective when the relation between a state variable and an observation is nonlinear. The performance of standard versus rank regression is compared for both linear and nonlinear forward operators (also known as observation operators) using a low-order model. Rank regression in combination with a rank histogram filter in observation space produces better analyses than standard regression for cases with nonlinear forward operators and relatively large analysis error. Standard regression, in combination with either a rank histogram filter or an ensemble Kalman filter in observation space, produces the best results in other situations.

Pengaruh Kondisi Internal Pertanian Terhadap Sistem Pertanian Terintegrasi Padi Sawah dengan Ternak Kerbau dan Pengembangan Wilayah di Kabupaten Humbang Hasundutan

Penelitian ini bertujuan mengetahui pengaruh kondisi internal pertanian terhadap sistem pertanian terintegrasi padi sawah dengan ternak kerbau dan pengembangan wilayah di Kabupaten Humbang Hasundutan. Metode analisis dengan R/C ratio dan pemodelan persamaan struktural (Structural Equation Modeling). Hasil penelitian; a) sistem pertanian terintegrasi padi sawah dan ternak kerbau lebih efisien dibandingkan usahatani non integrasi (R/C integrasi 2,4795 > R/C non-integrasi), b) Kondisi internal pertanian berpengaruh positif signifikan terhadap sistem pertanian terintegrasi dengan bobot regresi standar 0.52,p<0.001, c) Kondisi internal pertanian berpengaruh langsung tidak signifikan terhadap pengembangan wilayah dengan bobot regresi standar 0.24, p < 0.001; c) Kondisi internal pertanian berpengaruh tidak langsung terhadap pengembangan wilayah melalui sistem pertanian terintegrasi padi sawah dan ternak kerbau sebesar 0.28, total pengaruh kondisi internal pertanian terhadap pengembangan wilayah sebesar 0.52. Berdasarkan hasil penelitian disarankan agar: a) pemerintah daerah melakukan pelatihan kepada petani yang mengelola pertanian sistem integrasi agar lebih baik, b) pemerintah memperhatikan kelanyakan sarana prasarana pertanian, khususnya fasilitas jalan, irigasi, c) pemerintah menyediakan bibit berkualitas, penyuluhan tentang beternak yang baik, d) pemerintah melakukan pelatihan terhadap petani dalam mengembangkan usahataninya sehingga pendapatan meningkat dan berdampak pada pengembangan wilayah, e) pemerintah membantu petani untuk mendapatkan modal usahatani yang lebih fleksibel dan harga output yang stabil. This study aims to determine the effect of agricultural internal conditions on the integrated agricultural system between paddy field and buffalo livestock on the Humbang Hasundutan regional development. Using R / C ratio and Structural Equation Modeling, this study finds that a) the integrated agricultural system is more efficient than the non-integrated ones, with the integration R / C = 2.4795 that is higher than the non-integration one, b) Internal agricultural conditions have significant positive effects on integrated farming systems with standard regression weights of 0.52 and p <0.001, c) Internal conditions of agriculture have a direct and insignificant effect on regional development with a standard regression weight of 0.24 and p <0.001; c) Internal conditions of agriculture have an indirect effect on regional development through an integrated farming system of paddy rice and buffalo livestock of 0.28, and total effect of internal agricultural conditions on regional development of 0.52. Based on the results it is suggested that: a) the regional government should conduct training to improve the farmers agricultural integration system management, b) the government should pay attention to the maintenance of agricultural infrastructure, especially road facilities, irrigation, c) the government provides quality seeds, good information about raising livestock , d) the government should conduct trainings to support the development of farmers’ business and income increases, which at the end impacts the regional development, e) the government helps farmers to obtain more flexible farming capital and stable output prices.