Root Mean Square Forecast Error Research Articles

Poisson Incorporated Credibility Regression Modelling of Systematic Mortality Risk for Populations with Finite Data

This study considered the modeling of systematic mortality risk for populations with finite data using the Poisson incorporated Credibility regression model. For novelty, we have included the credibility regression approach to modelling mortality by assuming the number of annual deaths follow a Poisson distribution. Our model shows improvement in precision levels when estimating mortality risk compared to classical models used in European countries. We have illustrated that our model works optimally when using Kenyan mortality data, comparing male and female lives under the different strategies, thus making better predictions than the classical Lee–Carter (LC) and Cairns–Blake–Dowd (CBD) models. The mean absolute forecast error (MAFE), mean absolute percentage forecast error (MAPFE), root mean square error (RMSE), and root mean square forecast error (RMSFE) under the incorporated credibility regression model are much lower than the values obtained without incorporation of the Buhlmann credibility approach. The findings of this research will help insurance companies, pension firms, and government agencies in sub-Saharan countries model and forecast systematic mortality risks accurately. Finally, the results are essential in actuarial modelling and pricing, thus making life assurance products affordable for most people in low-income African countries.

Prognostications With Applications to the British Pound

This paper scrutinizes several exchange rate models, considers the effectiveness of their predictive performance after applying both parametric and nonparametric techniques to them, and chooses the forecasting predictor with the smallest root mean square forecast error (RMSE). Equation (34) displays empirical evidence consistent with a better example of an exchange rate model, although none of the evidence gives us a completely satisfactory forecast. In the end, the models’ error correction versions will be fit so that plausible long-run elasticities can be imposed on each model’s fundamental variables.

Forecasting Inflation with the Hybrid New Keynesian Phillips Curve: A Compact-Scale Global VAR Approach

ABSTRACTIn this article, the multihorizon predictive power of the Hybrid New Keynesian Phillips Curve (HNKPC) is analysed by making use of several close- and open-economy specifications for the headline inflation of six developed countries. The key element is the use of direct measures of inflation expectations – Consensus Forecast – embedded in a compact-scale Global VAR (GVAR) environment, becoming the baseline open-economy HNKPC (OE-HNKPC) specification. These OE-HNKPC point forecasts are evaluated using the Root Mean Squared Forecast Error (RMSFE) statistic and statistically compared with several benchmarks, including traditional atheoretical models. Several OE-HNKPC as well as a closed-economy HNKPC (CE-HNKPC) specifications are also analysed. The results indicate that in four out of six countries, the CE-HNKPC is the best forecasting model, whereas for the same countries, a parsimonious OE-HNKPC is the second-best alternative, and in most cases, outperforming traditional statistical benchmarks. The RMSFE is obviously affected by the unanticipated effects of the Great Financial Crisis (GFC), spoiling out the performance of a number of competing forecasts. However, when considering an evaluation sample just before the crisis, both the CE-HNKPC and the parsimonious OE-HNKPC still come out as the best forecasting models. Furthermore, these preferred models also do an excellent job tracking inflation better than the best atheoretical models during the GFC.

Algorithm based on local breeding of growing modes for convection-allowing ensemble forecasting

We propose a method based on the local breeding of growing modes (LBGM) considering strong local weather characteristics for convection-allowing ensemble forecasting. The impact radius was introduced in the breeding of growing modes to develop the LBGM method. In the local breeding process, the ratio between the root mean square error (RMSE) of local space forecast at each grid point and that of the initial full-field forecast is computed to rescale perturbations. Preliminary evaluations of the method based on a nature run were performed in terms of three aspects: perturbation structure, spread, and the RMSE of the forecast. The experimental results confirm that the local adaptability of perturbation schemes improves after rescaling by the LBGM method. For perturbation physical variables and some near-surface meteorological elements, the LBGM method could increase the spread and reduce the RMSE of forecast, improving the performance of the ensemble forecast system. In addition, different from those existing methods of global orthogonalization approach, this new initial-condition perturbation method takes into full consideration the local characteristics of the convective-scale weather system, thus making convection-allowing ensemble forecast more accurate.

Foreign Currency Prognostication: Diverse Tests for Germany

This paper uses a large variety of different models and examines the predictive performance of these exchange rate models by applying parametric and non-parametric techniques. For forecasting, we will choose that predictor with the smallest root mean square forecast error (RMSE). The results show that the better models are in equations (3), (10), (17), and (18), although none gives a perfect forecast. At the end, error correction versions of the models will be fit so that plausible long-run elasticities can be imposed on the fundamental variables of each model.

Extended-Range Ensemble Predictions of Convection in the North Australian Monsoon Region

Extended-range (<35 day) predictions of area-averaged convection over northern Australia are investigated with the Bureau of Meteorology’s Predictive Ocean-Atmosphere Model for Australia (POAMA). Hindcasts from 1980-2011 are used, initialised on the 1st, 11th and 21st of each month, with a 33-member ensemble. The measure of convection is outgoing longwave radiation (OLR) averaged over the box 120oE-150oE, 5oS-17.5oS. This averaging serves to focus on the intraseasonal and longer time scales, and is an area of interest to users. The raw hindcasts of daily OLR show a strong systematic adjustment away from their initial values during the first week, and then converge to a mean seasonal cycle of similar amplitude and phase to observations. Hence, forecast OLR anomalies are formed by removing the model’s own seasonal cycle of OLR, which is a function of start time and lead time, a usual practice for dynamical seasonal prediction. Over all hindcasts, the model forecast root-mean-square (RMS) error is smaller than the RMS error of persistence and climatological reference forecasts for leads 3-35 days. Ensemble spread is less than the forecast RMS error (i.e. under-spread) for days 1-12, but slightly greater than the RMS error for longer leads. Binning the individual forecasts based on ensemble spread shows a generally positive relationship between spread and error. Therefore, greater certainty can be given for forecasts with smaller spread.

Foreign Currency Forecasts: A Combination Analysis

This paper uses a large variety of different models and examines the predictive performance of these exchange rate models by applying parametric and non-parametric techniques. For forecasting, we will choose that predictor with the smallest root mean square forecast error (RMSE). The results show that the better model is equation (34), but none of them gives a perfect forecast. At the end, error correction versions of the models will be fit so that plausible long-run elasticities can be imposed on the fundamental variables of each model.

Quantitative evaluation of the impact of cloud transmittance and cloud velocity on the accuracy of short-term DNI forecasts

Ground based sky imaging and irradiance sensors are used to quantitatively evaluate the impact of cloud transmittance and cloud velocity on the accuracy of short-term direct normal irradiance (DNI) forecasts. Eight representative partly-cloudy days are used as an evaluation dataset. Results show that incorporating real-time sky and cloud transmittances as inputs reduces the root mean square error (RMSE) of forecasts of both the Deterministic model (Det) (16.3%∼ 17.8% reduction) and the multi-layer perceptron network model (MLP) (0.8% ∼ 6.2% reduction). Four computer vision methods: the particle image velocimetry method, the optical flow method, the x-correlation method and the scale-invariant feature transform method have accuracies of 83.9%, 83.5%, 79.2% and 60.9% in deriving cloud velocity, with respect to manual detection. Analysis also shows that the cloud velocity has significant impact on the accuracy of DNI forecasts: underestimating the cloud velocity magnitude by 50% results in 30.2% (Det) and 24.2% (MLP) increase of forecast RMSE; a 50% overestimate results in 7.0% (Det) and 8.4% (MLP) increase of RMSE; a ±30∘ deviation of cloud velocity direction increases the forecast RMSE by 6.2% (Det) and 6.6% (MLP).

The Role of Models with Deterministic Volatility and the Inflation: An Analysis of the G7 Economies

I propose a time-varying methodology for modeling and forecasting the dynamics of the Consumer Price Index (CPI) related to the G7 economies. In particular, I show the adequacy of AR(1)/GJR-GARCH(1,1) specifications and provide statistical support for considering methodologies with deterministic volatility. The root mean squared forecast error (RMSFE) as well as the mean absolute forecast error (MAFE) report the accuracy of this specification as an alternative class of univariate models. Therefore: (i) I measure the pseudo out-of-sample performance at several horizons ahead, from July 2007 and march 2009; (ii) I compare the accuracy of the methodology with existing univariate models; (iii) I show the divergence between the actual levels of the CPI related to the G7 economies, with respect to forecasts based on recursive methods.

A fast mosaic method for airborne images: the new Template-Convolution Speed-Up Robust Features (TSURF) algorithm

In this paper, we present a new feature extraction algorithm termed Template-Convolution Speed-Up Robust Features (TSURF), which uses template convolution to extract points of interest based on the Speed-Up Robust Features (SURF) algorithm. Feature extraction is applied to extract corresponding characteristics in overlapping fields from adjacent images. The characteristics include area, line, and point features. As the point feature is easy to compute and is invariant to image scale, rotation, intensity, and so on, we use it to register and mosaic images widely. By filtering redundant points of interest, TSURF can greatly reduce the running time and keep the mosaic quality good during real-time mosaicking. SURF and TSURF are applied to airborne images to compare the efficiency of each algorithm in constructing a mosaic. We calculate the average coordinate error and angle error for evaluating mosaic precision. We also use the average gradient, standard deviation, and forecast root mean-square error to compare the mosaic quality of SURF with that of TSURF. The first mosaic experiment consisting of 20 groups of airborne images showed that the mosaic speed of TSURF is three times faster than that of SURF and maintains comparative mosaic accuracy. In the second experiment, a series of continuous thumbnail images were mosaicked using the SURF and TSURF algorithms fully automatically. The TSURF speed was 63.40% faster than that of SURF and the accuracy remained consistent.

Does Banque De France Control Inflation and Unemployment?

We re-estimate statistical properties and predictive power of a set of Phillips curves, which are expressed as linear and lagged relationships between the rates of inflation, unemployment, and change in labour force. For France, several relationships were estimated eight years ago. The change rate of labour force was used as a driving force of inflation and unemployment within the Phillips curve framework. Following the original problem formulation by Fisher and Phillips, the set of nested models starts with a simplistic version without autoregressive terms and one lagged term of explanatory variable. The lag is determined empirically together with all coefficients. The model is estimated using the Boundary Element Method (BEM) with the least squares method applied to the integral solutions of the differential equations. All models include one structural break might be associated with revisions to definitions and measurement procedures in the 1980s and 1990s as well as with the change in monetary policy in 1994-1995. For the GDP deflator, our original model provided a root mean squared forecast error (RMSFE) of 1.0% per year at a four-year horizon for the period between 1971 and 2004. The same RMSFE is estimated with eight new readings obtained since 2004. The rate of CPI inflation is predicted with RMSFE=1.5% per year. For the naive (no change) forecast, RMSFE at the same time horizon is 2.95% and 3.3% per year, respectively. Our model outperforms the naive one by a factor of 2 to 3. The relationships for inflation were successfully tested for cointegration. We have formally estimated several vector error correction (VEC) models for two measures of inflation. In the VAR representation, these VECMs are similar to the Phillips curves. At a four year horizon, the estimated VECMs provide significant statistical improvements on the results obtained by the BEM: RMSFE=0.8% per year for the GDP deflator and ~1.2% per year for CPI. For a two year horizon, the VECMs improve RMSFEs by a factor of 2, with the smallest RMSFE=0.5% per year for the GDP deflator. This study has validated the reliability and accuracy of the linear and lagged relationships between inflation, unemployment, and the change in labour force between 1970 and 2012.

Forecast Combination Across Estimation Windows

In this article we consider combining forecasts generated from the same model but over different estimation windows. We develop theoretical results for random walks with breaks in the drift and volatility and for a linear regression model with a break in the slope parameter. Averaging forecasts over different estimation windows leads to a lower bias and root mean square forecast error (RMSFE) compared with forecasts based on a single estimation window for all but the smallest breaks. An application to weekly returns on 20 equity index futures shows that averaging forecasts over estimation windows leads to a smaller RMSFE than some competing methods.

Forecast Comparison of Nonlinear Time Series Models of Us GDP: A Bayesian Approach

This thesis utilizes modern Bayesian tools to evaluate the forecasting performance of two of the most widely used nonlinear time series models of post-war US GDP, the Markov Switching (MS) model and the Self-Exciting threshold autoregressive (SETAR) model. We develop a clear, empirical ground for model selection, forecast comparison and forecast combination in the context of nonlinear economic time series. The use of the Bayesian methodology introduces an immediate framework to deal with nonlinearities. This holds not only in estimation, by treating nuisance parameters as unknown random variables, and in testing, by avoiding the approximation of unknown distributions of likelihood ratio statistics in order to find evidence of nonlinearity, but also in the choice of the best model according to its forecasting potential. To our knowledge, the literature avoids welcoming existing Bayesian methods in forecasting and comparison of nonlinear time series models; all known attempts from a Bayesian perspective are consumed only to the estimation part. Here we propose to use predictive likelihoods, an easy to adopt and to interpret criterion, as an alternative to classical forecast evaluation criterions like the root mean squared forecast error (RMSE). The advantage of our approach is very clear in the nonlinear time series framework that we examine. Preservation of computational resources, efficiency in manipulation of nuisance parameters, and parameter uncertainty are fully incorporated while we improve over individual forecasts by implementing Bayesian Model Averaging.

Impact of including moisture perturbations on short‐range ensemble forecasts

We are developing a Short‐Range Ensemble Prediction (SREP) system based on the Eta Model for use over South America. The Eta Model SREP system uses the CPTEC global model Ensemble Prediction System (EPS) forecasts as initial and lateral boundary conditions. The objectives of this work are to verify the impacts of including moisture perturbations in the global EPS on the SREP and to evaluate the forecast quality from the resulting SREP. We compare the SREP constructed with and without moisture perturbations. We chose four cases of South Atlantic Convergence Zone events that produced heavy rainfall for the tests and evaluation. The Eta Model was set with a horizontal resolution of 10 km and integrated for 6 days. The mean errors of the forecasts based on the two perturbation methodologies are similar, which indicates that including moisture did not increase the forecast error. Precipitation forecasts showed major improvement when moisture perturbation was included. The root mean square error (RMSE) of the SREP ensemble mean forecast from both initial condition perturbations is smaller than the RMSE of the control run. The constructed SREP system exhibits forecast RMSE growth rate larger than the ensemble forecast spread, on the other hand, this difference is reduced compared to the driver global model ensemble forecast system.

The Role of Financial Variables in Predicting Economic Activity

Previous research has shown that the US business cycle leads the European cycle by a few quarters, and can therefore help predicting euro area GDP. We investigate whether financial variables provide additional predictive power. We use a VAR model of the US and the euro area GDPs and extend it to take into account common global shocks and information provided by selected combinations of financial variables. In- sample analysis shows that shocks to financial variables influence real activity with a peak around 4 to 6 quarters after the shock. Out-of-sample Root-Mean- Squared Forecast Error (RMFE) shows that adding financial variables yields smaller errors in forecasting US economic activity, especially at a five-quarter horizon, but the gain is overall tiny in economic terms. This link is even less prominent in the euro area, where financial indicators do not improve short and medium term GDP forecasts even when their timely availability, relative to a given GDP release, is exploited. The same conclusion is reached with a dataset of quarterly industrial production indices, although financial variables marginally improve forecasts of monthly industrial production. We argue that the findings that financial variables have no predictive power for future activity in the euro area relate to the unconditional nature of the RMFE metric. When forecasting ability is assessed as if in real time (i.e. conditionally on the information available at the time when forecasts are made), we find that models using financial variables would have been preferred in many episodes, and in particular between 1999 and 2002. Results from the historical decomposition of a VAR model indeed suggest that in that period shocks were predominantly of financial nature.

Upper bound criterion for testing the stability of root mean squared forecast error

The purpose of the present study was to develop a relationship between Restricted Cross Validity Predictive Power (RCVPP) and Root Mean Squared Forecast Error (RMSFE). Using the cross validity predictive power an upper bound criterion for root mean squared forecast error is developed to examine the stability over population.

Forecasting Fraser River flows and temperatures during upstream salmon migration

Mature salmon returning to spawn in their natal streams are sensitive to both river flows and temperatures. Enhancements to existing forecast models result in significant reductions in the root mean square (RMS) forecast errors for both flow and temperature in the semi-weekly 10-day forecasts made during the salmon migration season. The Fraser watershed model is replaced by a statistical model that projects future flows using the latest observation as an initial condition and a slope consistent with the historic rate of change. This new method reduced RMS errors by as much as 38%. When the model flows were adjusted iteratively by feeding the flow error back into the system, the average RMS forecast flow error was reduced from 18.7% to 6.4% in 2000 and from 16.8% to 7.4% in 2002. The coupled temperature model combines atmospheric forcing with transport and velocities from the flow models. When the temperature model was run using the iterative feedback scheme, the RMS forecast error was reduced from 0.85 °C to 0.59 °C in 2000 and from 1.18 °C to 0.94 °C in 2002. Key words: Fraser River, temperature model, flow model, data assimilation, salmon.