Forecast Error Statistics Research Articles

A Transcendental LASSO Function for Combining Machine Learning and Statistical Model Forecasts

The aim of the study is the development of methodology for accurate estimation of electric vehicle demand; which is paramount regarding various aspects of the firms decision-making such as optimal price, production level, and corresponding amounts of capital and labor; as well as supply chain, inventory control, capital financing, and operational expenses management. The forecasting methods utilized include statistical techniques (autoregressive integrated moving average [ARIMA], and polynomial regression), machine learning (nonlinear autoregressive neural network [NAR]), deep learning (long short-term memory [LSTM]), hybrid and combination forecasting. With regard to the latter method, our study experiments with four different combining model approaches, including the introduction of an original, novel combining method with the employment of a transcendental LASSO function, which is used to form combinations of forecasts generated by the NAR, ARIMA, and polynomial regression models. The LASSO-based combining model proved superior to all other models, for the majority of forecast error statistics; where the root mean square error (RMSE) and mean absolute percentage error (MAPE) values are 4.5% and 8% respectively lower than the average level of the component model forecasts. The major implications of our empirical findings are that greater accuracy in demand forecasting can be achieved with a combining model approach, rather than reliance on any particular, singular model. Furthermore, given its superior performance, the employment of the studys LASSO-based combining model to forecast electric vehicle demand may lead to optimal firm decision-making over a range of organizational facets, which is predicated on accurate demand function estimation.

A Mini‐Batch Stochastic Optimization‐Based Adaptive Localization Scheme and Its Implementation in NLS‐i4DVar

AbstractThis paper proposes a mini‐batch stochastic optimization‐based adaptive localization scheme for computing the “optimal” localization radius in data assimilation (DA) applications. After constructing a cost function of the localization radius by estimating forecast and observation error statistics, a mini‐batch stochastic gradient descent method with a novel sampling strategy is proposed to minimize the cost function. The proposed stochastic optimization algorithm is further incorporated into the DA method NLS‐i4DVar (the nonlinear least squares integral correcting four‐dimensional variational DA method), which was developed by the authors in Tian et al. (2021, https://doi.org/10.1029/2021EA001767). It is utilized to compute the “optimal” covariance localization radii adaptively and flow‐dependently inside NLS‐i4DVar. The computational cost of NLS‐i4DVar with the proposed adaptive localization scheme only increases slightly due to the use of the mini‐batch stochastic optimization algorithm. Numerical experimental results using the shallow‐water equations demonstrate that NLS‐i4DVar with the proposed adaptive localization scheme shows substantial performance improvement over the standard NLS‐i4DVar method.

A new global ocean ensemble system at the Met Office: Assessing the impact of hybrid data assimilation and inflation settings

AbstractWe have developed a global ocean and sea‐ice ensemble forecasting system based on the operational forecasting ocean assimilation model (FOAM) system run at the Met Office. The ocean model Nucleus for European Modelling of the Ocean (NEMO) and the community ice code (CICE) sea‐ice model are run at 1/4 resolution and the system assimilates data using a three‐dimensional variational assimilation (3DVar) version of NEMOVAR. This data assimilation (DA) system can perform hybrid ensemble/variational assimilation. A 36‐member ensemble of hybrid ensemble variational assimilation systems with perturbed observations (values and locations) has been set up, with each member forced at the surface by a separate member of the Met Office Global–Regional Ensemble Prediction System (MOGREPS‐G). The unperturbed member is forced by atmospheric fields from the Met Office operational numerical weather prediction (NWP) deterministic system. The system includes stochastic model perturbations and a relaxation to prior spread (RTPS) inflation scheme. A control run of the system using an ensemble of 3DVars is shown to be generally reliable for Sea‐Level Anomaly (SLA), temperature, and salinity (the ensemble spread being a good representation of the uncertainty in the ensemble mean), although the ensemble is underspread in eddying regions. The ensemble mean gives a 4% reduction in error in SLA compared with the deterministic 3DVar system currently used operationally. The system was tested with different weights for the ensemble component of the hybrid background‐error covariance matrix and different inflation factors. The best results, in terms of short‐range forecast error and ensemble reliability statistics, were obtained with hybrid three‐dimensional ensemble variational DA (3DEnVar). The RTPS inflation scheme is shown to be beneficial in producing an appropriate ensemble spread in response to hybrid DA. 3DEnVar with an ensemble hybrid weight of 0.8 leads to a reduction of 20% (5%) in the ensemble mean error for SLA (profile temperature and salinity) compared with an ensemble of standard 3DVars.

ANALYSIS AND FORECASTABILITY OF MARKET MODEL: EVIDENCE FROM PAKISTANI MARKET INDEX AND EMERGING MARKET INDEX

Purpose of the Study: This study examines and analyzes the influence of the Market Model on the Market Level Return (KSE-100 index) and the Emerging Market Level Return (MSCI Index).
 Methodology: The study has employed the sample data of the companies’ representatives of the Oil and Gas Sector of Pakistan from July 2001 to June 2018 respectively. For estimation, the Panel Regression techniques are employed followed by the Forecast Error Statistics for the in-sample forecast ability of the variables under study.
 Main Findings: The results of the study depict that the Market Model comprising of the Market Value Financial Ratios strongly influences the returns of the Emerging Market Index relative to the Market Level Return respectively. Similarly, the predictive power of the Market Model is more influential at the Emerging Market Level Return but not less at Market Level Return.
 Application of the Study: The findings of the study suggest that the domestic and foreign investors may consider the Market Value Financial Ratios for the valuation and estimation of asset prices. Moreover, the local authorities may take robust steps to continuously reforms in the Energy Mix policy to enhance local as well as foreign investment.
 Novelty/Originality of this study: The prime novelty of the study is to analyze the market model based on Market Value Financial Ratios to forecast the Market Level Return and Emerging Market Index Returns using three standard symmetric measures; root mean square error (RMSE), the mean absolute error (MAE), the mean absolute percentage error (MAPE) and the Theil inequality coefficient (TIC) respectively.

Forecast Impact of FORMOSAT‐7/COSMIC‐2 GNSS Radio Occultation Measurements

AbstractThe FORMOSAT‐7/COSMIC‐2 GNSS‐RO mission was launched on June 25, 2019, and it has provided a large increase in the number of GNSS‐RO observations available for operational numerical weather prediction (NWP) in the latitude band between ±40°. A key aim of this mission has been to improve the GNSS‐RO measurement quality in the lower and middle troposphere. In this study, we summarize the impact of the FORMOSAT‐7/COSMIC‐2 measurements in two independent NWP systems, which are now assimilating these measurements operationally. These are the United States Navy Global Environmental Model (NAVGEM) and the European Center for Medium‐Range Weather Forecasts (ECMWF) Integrated Forecasting System (IFS). Both systems employ a 4‐dimensional variational system (4D‐Var), and assimilate GNSS‐RO bending angles. The experiments cover the period January to March 2020. The impact of the FORMOSAT‐7/COSMIC‐2 measurements is assessed using improvements in short‐range forecast departures to other observations such as radiosonde and radiances, forecast error statistics against a verifying analysis, and adjoint based Forecast Sensitivity to Observation Impact (FSOI) estimates. The FORMOSAT‐7/COSMIC‐2 measurement has a clear impact on stratospheric temperatures and winds in the tropics. A novel finding is that the measurements also improve the tropical tropospheric humidity fit to radiosondes, and the fit to tropospheric radiances sensitive to humidity. To date, the impact of GNSS‐RO on humidity has been difficult to demonstrate in well constrained, operational NWP systems assimilating the full suite of observations. The results are achieved with a conservative assimilation approach which extended the quality control and observation error assignments used for the previous COSMIC receivers; further, possible improvements to the assimilation strategy are noted.

Background Error in WRF Model

WRF model have been tuned and tested over Georgia’s territory for years. First time in Georgia theprocess of data assimilation in Numerical weather prediction is developing. This work presents how forecasterror statistics appear in the data assimilation problem through the background error covariance matrix – B, wherethe variances and correlations associated with model forecasts are estimated. Results of modeling of backgrounderror covariance matrix for control variables using WRF model over Georgia with desired domain configurationare discussed and presented. The modeling was implemented in two different 3DVAR systems (WRFDA andGSI) and results were checked by pseudo observation benchmark cases using also default global and regional BEmatrixes. The mathematical and physical properties of the covariances are also reviewed.

Impact of Refractivity Profiles from a Proposed GNSS-RO Constellation on Tropical Cyclone Forecasts in a Global Modeling System

Abstract A global observing system simulation experiment (OSSE) was used to assess the potential impact of a proposed Global Navigation Satellite System (GNSS) radio occultation (RO) constellation on tropical cyclone (TC) track, maximum 10-m wind speed (Vmax), and integrated kinetic energy (IKE) forecasts. The OSSE system was based on the 7-km NASA nature run and simulated RO refractivity determined by the spatial distribution of observations from the original planned (i.e., including both equatorial and polar orbits) Constellation Observing System for Meteorology, Ionosphere, and Climate-2 (COSMIC-2). Data were assimilated using the NOAA operational weather analysis and forecasting system. Three experiments generated global TC track, Vmax, and IKE forecasts over 6 weeks of the North Atlantic hurricane season in the North Atlantic, east Pacific, and west Pacific basins. Confidence in our results was bolstered because track forecast errors were similar to those of official National Hurricane Center forecasts, and Vmax errors and IKE errors showed similar results. GNSS-RO assimilation did not significantly impact global track forecasts, but did slightly degrade Vmax and IKE forecasts in the first 30–60 h of lead time. Global forecast error statistics show adding or excluding explicit random errors to RO profiles made little difference to forecasts. There was large forecast-to-forecast variability in RO impact. For two cases studied in depth, track and Vmax improvements and degradations were traced backward through the previous 24 h of assimilation cycles. The largest Vmax degradation was traced to particularly good control analyses rather than poor analyses caused by GNSS-RO.

MODEL-BASED VS. PROFESSIONAL FORECASTS: IMPLICATIONS FOR MODELS WITH NOMINAL RIGIDITIES

We compare model forecast error statistics with forecast error statistics of professional forecasts. We look at a standard sticky-prices–wages model, concluding that it delivers too strong a theoretical forecastability of the variables under scrutiny, at odds with the data (professional forecasts). We argue that the lack of compatibility between the model and professional forecasts results from trying to fit inflation (which is probably nonstationary) to a model that assumes inflation is stationary. A modified version of the model, one with a varying inflation target, delivers a better fit in terms of forecastability.

How is the Balance of a Forecast Ensemble Affected by Adaptive and Nonadaptive Localization Schemes?

Abstract This paper investigates the effect on balance of a number of Schur product–type localization schemes that have been designed with the primary function of reducing spurious far-field correlations in forecast error statistics. The localization schemes studied comprise a nonadaptive scheme (where the moderation matrix is decomposed in a spectral basis), and two adaptive schemes: a simplified version of Smoothed Ensemble Correlations Raised to a Power (SENCORP) and Ensemble Correlations Raised to a Power (ECO-RAP). The paper shows, the author believes for the first time, how the degree of balance (geostrophic and hydrostatic) implied by the error covariance matrices localized by these schemes can be diagnosed. Here it is considered that an effective localization scheme is one that reduces spurious correlations adequately, but also minimizes disruption of balance (where the “correct” degree of balance or imbalance is assumed to be possessed by the unlocalized ensemble). By varying free parameters that describe each scheme (e.g., the degree of truncation in the schemes that use the spectral basis, the “order” of each scheme, and the degree of ensemble smoothing), it is found that a particular configuration of the ECO-RAP scheme is best suited to the convective-scale system studied. According to the diagnostics this ECO-RAP configuration still weakens geostrophic and hydrostatic balance, but overall this is less so than for other schemes.

Univariate forecasting of Indian exchange rates: a comparison

The objective of this paper is to search for a univariate forecasting model that can provide the most accurate forecasts of monthly exchange rates of Indian rupee over the period August 1994-April 2014. A random walk model is used as the benchmark model. Using Box-Jenkins methodology, ARIMA structures of exchange rates are identified. The presence of heteroscedastic variance of ARIMA residuals has been accomplished through the re-estimation of ARIMA models including autoregressive conditional heteroscedasticity (ARCH)/generalised autoregressive conditional heteroscedasticity (GARCH) parameters. From the estimated models, in-sample (April 1994-July 2010) and out-of-sample (August 2010-April 2014), forecasts for 1-, 3- and 6-month horizon are generated. The forecasting ability of the estimated models is accessed by forecast error statistics. The paper finds that in general the random walk model outperforms ARIMA and ARCH/GARCH models for forecasting exchange rates of Indian rupee under the in-sample and the out-of-sample period.

Mood dynamics in bipolar disorder.

The nature of mood variation in bipolar disorder has been the subject of relatively little research because detailed time series data has been difficult to obtain until recently. However some papers have addressed the subject and claimed the presence of deterministic chaos and of stochastic nonlinear dynamics. This study uses mood data collected from eight outpatients using a telemonitoring system. The nature of mood dynamics in bipolar disorder is investigated using surrogate data techniques and nonlinear forecasting. For the surrogate data analysis, forecast error and time reversal asymmetry statistics are used. The original time series cannot be distinguished from their linear surrogates when using nonlinear test statistics, nor is there an improvement in forecast error for nonlinear over linear forecasting methods. Nonlinear sample forecasting methods have no advantage over linear methods in out-of-sample forecasting for time series sampled on a weekly basis. These results can mean that either the original series have linear dynamics, the test statistics for distinguishing linear from nonlinear behaviour do not have the power to detect the kind of nonlinearity present, or the process is nonlinear but the sampling is inadequate to represent the dynamics. We suggest that further studies should apply similar techniques to more frequently sampled data.Electronic supplementary materialThe online version of this article (doi:10.1186/s40345-014-0011-z) contains supplementary material, which is available to authorized users.

Scaling of GNSS Radio Occultation Impact with Observation Number Using an Ensemble of Data Assimilations

Abstract An ensemble of data assimilations (EDA) approach is used to estimate how the impact of Global Navigation Satellite System (GNSS) radio occultation (RO) measurements scales as a function of observation number in the ECMWF numerical weather prediction system. The EDA provides an estimate of the theoretical analysis and short-range forecast error statistics, based on the ensemble “spread,” which is the standard deviation of the ensemble members about the ensemble mean. This study is based on computing how the ensemble spread of various parameters changes as a function of the number of simulated GNSS RO observations. The impact from 2000 up to 128 000 globally distributed simulated GNSS RO profiles per day is investigated. It is shown that 2000 simulated GNSS RO measurements have an impact similar to real measurements in the EDA and that the EDA-based impact of real data can be related to the impact in observing system experiments. The dependence of the ensemble statistics on observation error statistics assumed when assimilating the data, rather than the actual observation errors, is emphasized. There is no evidence of “saturation” of forecast impact even with 128 000 GNSS RO profiles per day. However, this result is a well-known consequence of always improving the theoretical analysis and short-range forecast error statistics when adding new observations that are assumed to have uncorrelated observation errors. In general, it is found that 16 000 GNSS RO profiles per day have around half the impact of 128 000 profiles, based on the reduction of ensemble spread values where the GNSS RO measurements have the largest impact.

Stochastic interest rate volatility modeling with a continuous-time GARCH(1, 1) model

In this work, we develop a continuous-time GARCH(1, 1) (COGARCH(1, 1)) model driven by a NIG-Lévy process in order to analyze the volatility characteristics of Turkish interest rates. To our knowledge, this is the first work considering NIG-COGARCH modeling of interest rate data that utilizes the indirect inference method for parameter estimation. The discrete-time GARCH(1, 1) model has been used as a skeleton for building the NIG-COGARCH(1, 1) model. Daily interest rates on the Turkish two-year maturity treasury bond for the period between 02/01/2006 and 31/12/2010 have been used for the analysis. The empirical results show that the NIG-COGARCH(1, 1) model successfully captures the volatility clustering and heavy-tailed behavior of the interest rate returns and yields better in-sample estimations for conditional volatility in terms of forecast error statistics than the discrete-time model.

Impact of Wind Forecast Error Statistics Upon Unit Commitment

Driven by a trend towards renewable forms of generation, in particular wind, the nature of power system operation is changing. Systems with high wind penetrations should be capable of managing the uncertainty contained within the wind power forecasts. Stochastic unit commitment with rolling planning and input scenarios, based on wind forecasts, is one way of achieving this. Here, a scenario tree tool is developed which allows forecast error statistics to be altered and facilitates the study of how these statistics impact on unit commitment and system operation. It is shown that the largest individual impact on system operation is from the inclusion of variance and that variance, kurtosis, and skewness together produced the error information with the lowest system cost. Similar impacts for inaccurate error statistics are observed but generalization of these results will need more studies on a range of test systems.

A Hybrid Background Error Covariance Model for Assimilating Glider Data into a Coastal Ocean Model

Abstract A hybrid background error covariance (BEC) model for three-dimensional variational data assimilation of glider data into the Navy Coastal Ocean Model (NCOM) is introduced. Similar to existing atmospheric hybrid BEC models, the proposed model combines low-rank ensemble covariances with the heuristic Gaussian-shaped covariances to estimate forecast error statistics. The distinctive features of the proposed BEC model are the following: (i) formulation in terms of inverse error covariances, (ii) adaptive determination of the rank m of with information criterion based on the innovation error statistics, (iii) restriction of the heuristic covariance operator to the null space of , and (iv) definition of the BEC magnitudes through separate analyses of the innovation error statistics in the state space and the null space of . The BEC model is validated by assimilation experiments with simulated and real data obtained during a glider survey of the Monterey Bay in August 2003. It is shown that the proposed hybrid scheme substantially improves the forecast skill of the heuristic covariance model.

Ensemble prediction for nowcasting with a convection-permitting model – II: forecast error statistics

Ensemble prediction for nowcasting with a convection-permitting model – II: forecast error statistics

A method for merging flow-dependent forecast error statistics from an ensemble with static statistics for use in high resolution variational data assimilation

The background error covariance matrix, B, is often used in variational data assimilation for numerical weather prediction as a static and hence poor approximation to the fully dynamic forecast error covariance matrix, P f. In this paper the concept of an Ensemble Reduced Rank Kalman Filter (EnRRKF) is outlined. In the EnRRKF the forecast error statistics in a subspace defined by an ensemble of states forecast by the dynamic model are found. These statistics are merged in a formal way with the static statistics, which apply in the remainder of the space. The combined statistics may then be used in a variational data assimilation setting. It is hoped that the nonlinear error growth of small-scale weather systems will be accurately captured by the EnRRKF, to produce accurate analyses and ultimately improved forecasts of extreme events.

Ensemble prediction for nowcasting with a convection-permitting model – II: forecast error statistics

A 24-member ensemble of 1-h high-resolution forecasts over the Southern United Kingdom is used to study shortrange forecast error statistics. The initial conditions are found from perturbations from an ensemble transform Kalman filter. Forecasts from this system are assumed to lie within the bounds of forecast error of an operational forecast system. Although noisy, this system is capable of producing physically reasonable statistics which are analysed and compared to statistics implied from a variational assimilation system. The variances for temperature errors for instance show structures that reflect convective activity. Some variables, notably potential temperature and specific humidity perturbations, have autocorrelation functions that deviate from 3-D isotropy at the convective-scale (horizontal scales less than 10 km). Other variables, notably the velocity potential for horizontal divergence perturbations, maintain 3-D isotropy at all scales. Geostrophic and hydrostatic balances are studied by examining correlations between terms in the divergence and vertical momentum equations respectively. Both balances are found to decay as the horizontal scale decreases. It is estimated that geostrophic balance becomes less important at scales smaller than 75 km, and hydrostatic balance becomes less important at scales smaller than 35 km, although more work is required to validate these findings. The implications of these results for high-resolution data assimilation are discussed.

Multivariate fractionally integrated APARCH modeling of stock market volatility: A multi-country study

Tse (1998) proposes a model which combines the fractionally integrated GARCH formulation of Baillie, Bollerslev and Mikkelsen (1996) with the asymmetric power ARCH speciflcation of Ding, Granger and Engle (1993). This paper analyzes the applicability of a multivariate constant conditional correlation version of the model to national stock market returns for eight countries. We flnd this multivariate speciflcation to be generally applicable once power, leverage and long-memory efiects are taken into consideration. In addition, we flnd that both the optimal fractional difierencing parameter and power transformation are remarkably similar across countries. Out-of-sample evidence for the superior forecasting ability of the multivariate FIAPARCH framework is provided in terms of forecast error statistics and tests for equal forecast accuracy of the various models.

Multivariate Fractionally Integrated APARCH Modeling of Stock Market Volatility: A Multi-Country Study

Tse (1998) proposes a model which combines the fractionally integrated GARCH formulation of Baillie, Bollerslev and Mikkelsen (1996) with the asymmetric power ARCH specification of Ding, Granger and Engle (1993). This paper analyzes the applicability of a multivariate constant conditional correlation version of the model to national stock market returns for eight countries. We find this multivariate specification to be generally applicable once power, leverage and long-memory effects are taken into consideration. In addition, we find that both the optimal fractional differencing parameter and power transformation are remarkably similar across countries. Out-of-sample evidence for the superior forecasting ability of the multivariate FIAPARCH framework is provided in terms of forecast error statistics and tests for equal forecast accuracy of the various models.