Nonparametric Forecasting Research Articles

Comparison of Parametric and Nonparametric Forecasting Methods for Daily COVID-19 Cases in Malaysia

Numerous research studies are currently examining various measures to control the transmission of COVID-19. One essential task in this regard is predicting or forecasting the number of infected individuals. This predictive capability is crucial for governments to allocate resources effectively. However, the most effective approach to handling time series problems between the parametric and non-parametric methods is unclear. The parametric method utilizes a fixed number of parameters to calculate the value. On the other hand, the non-parametric method increases its parameters along with the number of observations. To address the issue, we conducted a study comparing parametric and non-parametric models for time series forecasting, specifically using Malaysia's daily confirmed COVID-19 cases from 18/3/2020 to 30/12/2020. Since there have been limited comparisons of these models in time series forecasting, we believe our study is beneficial. We considered various models, including persistence, autoregression, ARIMA, SARIMA, single, double, and triple exponential smoothing, multi-linear regression, support vector regression, artificial neural networks (ANN), K-nearest neighbor regression, decision trees regression, random forest regression, and Gaussian processes regression models. Our study revealed significant characteristics of these methods, and we found that exponential smoothing methods were the most effective in capturing the level and trend of the data compared to other methods. Additionally, ANN had the least forecasting error among the machine learning methods. In conclusion, non-parametric methods are not suitable for predicting daily cases of Covid-19 in Malaysia. Enhancing the parametric methods will be preferable in the future.

Comparison of Parametric and Nonparametric Forecasting Methods for Daily COVID-19 Cases in Malaysia

Numerous research studies are currently examining various measures to control the transmission of COVID-19. One essential task in this regard is predicting or forecasting the number of infected individuals. This predictive capability is crucial for governments to allocate resources effectively. However, the most effective approach to handling time series problems between the parametric and non-parametric methods is unclear. The parametric method utilizes a fixed number of parameters to calculate the value. On the other hand, the non-parametric method increases its parameters along with the number of observations. To address the issue, we conducted a study comparing parametric and non-parametric models for time series forecasting, specifically using Malaysia's daily confirmed COVID-19 cases from 18/3/2020 to 30/12/2020. Since there have been limited comparisons of these models in time series forecasting, we believe our study is beneficial. We considered various models, including persistence, autoregression, ARIMA, SARIMA, single, double, and triple exponential smoothing, multi-linear regression, support vector regression, artificial neural networks (ANN), K-nearest neighbor regression, decision trees regression, random forest regression, and Gaussian processes regression models. Our study revealed significant characteristics of these methods, and we found that exponential smoothing methods were the most effective in capturing the level and trend of the data compared to other methods. Additionally, ANN had the least forecasting error among the machine learning methods. In conclusion, non-parametric methods are not suitable for predicting daily cases of Covid-19 in Malaysia. Enhancing the parametric methods will be preferable in the future.

Comparison of Parametric and Nonparametric Forecasting Methods for Daily COVID-19 Cases in Malaysia

Numerous research studies are currently examining various measures to control the transmission of COVID-19. One essential task in this regard is predicting or forecasting the number of infected individuals. This predictive capability is crucial for governments to allocate resources effectively. However, the most effective approach to handling time series problems between the parametric and non-parametric methods is unclear. The parametric method utilizes a fixed number of parameters to calculate the value. On the other hand, the non-parametric method increases its parameters along with the number of observations. To address the issue, we conducted a study comparing parametric and non-parametric models for time series forecasting, specifically using Malaysia's daily confirmed COVID-19 cases from 18/3/2020 to 30/12/2020. Since there have been limited comparisons of these models in time series forecasting, we believe our study is beneficial. We considered various models, including persistence, autoregression, ARIMA, SARIMA, single, double, and triple exponential smoothing, multi-linear regression, support vector regression, artificial neural networks (ANN), K-nearest neighbor regression, decision trees regression, random forest regression, and Gaussian processes regression models. Our study revealed significant characteristics of these methods, and we found that exponential smoothing methods were the most effective in capturing the level and trend of the data compared to other methods. Additionally, ANN had the least forecasting error among the machine learning methods. In conclusion, non-parametric methods are not suitable for predicting daily cases of Covid-19 in Malaysia. Enhancing the parametric methods will be preferable in the future.

Functional time series forecasting: Functional singular spectrum analysis approaches

AbstractWe introduce two novel nonparametric forecasting methods designed for functional time series (FTS), namely, functional singular spectrum analysis (FSSA) recurrent and vector forecasting. Our algorithms rely on extracted signals obtained from the FSSA method and innovative recurrence relations to make predictions. These techniques are model‐free, capable of predicting nonstationary FTS and utilize a computational approach for parameter selection. We also employ a bootstrap algorithm to assess the goodness‐of‐prediction. Through comprehensive evaluations on both simulated and real‐world climate data, we showcase the effectiveness of our techniques compared to various parametric and nonparametric approaches for forecasting nonstationary stochastic processes. Furthermore, we have implemented these methods in the Rfssa R package and developed a shiny web application for interactive exploration of the results.

Leveraging Geographically Distributed Data for Influenza and SARS-CoV-2 Non-Parametric Forecasting

The evolution of some epidemics, such as influenza, demonstrates common patterns both in different regions and from year to year. On the contrary, epidemics such as the novel COVID-19 show quite heterogeneous dynamics and are extremely susceptible to the measures taken to mitigate their spread. In this paper, we propose empirical dynamic modeling to predict the evolution of influenza in Spain’s regions. It is a non-parametric method that looks into the past for coincidences with the present to make the forecasts. Here, we extend the method to predict the evolution of other epidemics at any other starting territory and we also test this procedure with Spanish COVID-19 data. We finally build influenza and COVID-19 networks to check possible coincidences in the geographical distribution of both diseases. With this, we grasp the uniqueness of the geographical dynamics of COVID-19.

How will the greening policy contribute to China's greenhouse gas emission mitigation? A non-parametric forecast

On March 24, 2015, a political bureau meeting of the Communist Party of China Central Committee first proposed the political task of “greening” and placed unprecedented importance on the construction of an ecological civilization, aiming to guide China's economy and society toward green and low carbon development. This study aims to examine the impact of this “greening” policy on China's climate change mitigation. First, from an emissions reduction perspective, this study interprets greening as the process of constantly strengthening society's awareness and willingness regarding emissions reduction. Then, this study incorporates a carbon abatement willingness factor into a nonparametric model, and quantitatively simulates the impact of greening on carbon dioxide (CO2) emissions reduction in China. The results show that China can rapidly decrease its CO2 emissions in the early stages of greening. However, when greening passes a certain stage, it no longer affects CO2 emissions. Thus, the willingness to reduce emissions has a diminishing marginal effect on emissions reduction. Additionally, throughout the greening process, China is expected to reduce its CO2 emissions by 36.08%, or 3718.50 million tons. Finally, the impact of greening on China's CO2 emissions exhibits spatial variation, as its undeveloped western region can achieve greater CO2 emissions reductions by promoting greening. Base on the above results, corresponding policy implications are also provided at the end of this paper.

Prediction and Optimal Feedback Steering of Probability Density Functions for Safe Automated Driving

We propose a stochastic prediction-control framework to promote safety in automated driving by directly controlling the joint state probability density functions (PDFs) subject to the vehicle dynamics via trajectory-level state feedback. To illustrate the main ideas, we focus on a multi-lane highway driving scenario although the proposed framework can be adapted to other contexts. The computational pipeline consists of a PDF prediction layer, followed by a PDF control layer. The prediction layer performs moving horizon nonparametric forecasts for the ego and the non-ego vehicles' stochastic states, and thereby derives safe target PDF for the ego. The latter is based on the forecasted collision probabilities, and promotes the probabilistic safety for the ego. The PDF control layer designs a feedback that optimally steers the joint state PDF subject to the controlled ego dynamics while satisfying the endpoint PDF constraints. Our computation for the PDF prediction layer leverages the structure of the controlled Liouville PDE to evolve the joint PDF values, as opposed to empirically approximating the PDFs. Our computation for the PDF control layer leverages the differential flatness structure in vehicle dynamics. We harness recent theoretical and algorithmic advances in optimal mass transport, and the Schrödinger bridge. The numerical simulations illustrate the efficacy of the proposed framework.

Hotel revenue management for the transient segment: taxonomy-based research

PurposeThis paper aims to (1) organize the open literature on hotel revenue management systems, (2) compare practitioner systems in terms of functionality and (3) integrate (1)-(2) into research stream recommendations for the open literature with an empirical focus.Design/methodology/approachThe authors use Nickerson’s taxonomy development method from the field of information systems to build the taxonomy.FindingsNew forecasting areas include developing a metric for the degree of strategic fit of a hotel’s pricing strategy and using it in conjunction with quantifications of online reviews for predictions. New price optimization avenues include determining whether a lack of congruence between customer perceptions of fairness and trust and pricing history has a detrimental effect on overall hotel performance and determining which combinations of flexible products, decision-maker risk aversion, nonparametric forecasting and reference effect optimization features work best in which situations.Originality/valueThis is the first study to combine vendor activities outside the technical realms of forecasting and price optimization with an emphasis on the choice modeling technical framework. This study points to several promising studies using qualitative methods, action research and design science.

Automatic Grouping in Singular Spectrum Analysis

Singular spectrum analysis (SSA) is a non-parametric forecasting and filtering method that has many applications in a variety of fields such as signal processing, economics and time series analysis. One of the four steps of the SSA, which is called the grouping step, plays a pivotal role in the SSA because reconstruction and forecasting of results are directly affected by the outputs of this step. Usually, the grouping step of SSA is time consuming as the interpretable components are manually selected. An alternative more optimized approach is to apply automatic grouping methods. In this paper, a new dissimilarity measure between two components of a time series that is based on various matrix norms is first proposed. Then, using the new dissimilarity matrices, the capabilities of different hierarchical clustering linkages are compared to identify appropriate groups in the SSA grouping step. The performance of the proposed approach is assessed using the corrected Rand index as validation criterion and utilizing various real-world and simulated time series.

Nonparametric wind power forecasting under fixed and random censoring

We consider nonparametric forecasting of wind power for individual wind turbines, allowing for random right censoring as well as two-sided fixed censoring. We propose a very fast estimation algorithm and show that this estimator of the unknown regression function is uniformly consistent. We argue that the key statistical features of the proposed nonparametric regression framework, such as nonlinearities and fixed and random censoring, are all needed in order to properly capture the main characteristics of wind power production functions. We show by a simulation study that the asymptotic properties of the estimator also holds in finite samples. We provide an empirical illustration comparing the forecasting accuracy of the proposed nonparametric regression model to some of the existing and popular forecasting devices used for predicting short to medium term wind power production at the individual turbine level. The empirical results are generally very encouraging.

Forecasting with the Nonparametric Exclusion-from-Core Inflation Persistence Model Using Real-Time Data

This paper contributes to nonparametric forecasting techniques by developing three local nonparametric forecasting methods for the nonparametric exclusion-from-core inflation persistence model that are capable of utilizing revised real-time personal consumption expenditure and core personal consumption expenditure for 62 vintages. Local nonparametric forecasting provides forecasters with a way of parsing the data by permitting a low inflation measure to be included in other low inflationary time periods and vice versa. Furthermore, when examining real-time data, policy-makers can use the nonparametric models to help identify outliers and potential abnormal economic events and problems with the data such as an underlying change in volatility. The most efficient nonparametric forecasting method is the third model, which uses the flexibility of nonparametrics by making forecasts conditional on the forecasted value, which can be used for counterfactual analysis.

Direct Interval Forecast of Uncertain Wind Power Based on Recurrent Neural Networks

Interval forecast is an efficient method to quantify the uncertainties in renewable energy production. In this paper, the idea of prediction intervals (PIs) is employed to capture the uncertainty of wind power generation in power systems. The recurrent neural network (RNN) model is proposed to construct PIs with the lower upper bound estimation method, which is a powerful nonparametric forecast approach. In addition, a novel comprehensive cost function with a new PI evaluation index is designed with the purpose of enhancing the model training. To tune the parameters of RNN prediction model, the dragonfly algorithm with a linearly random weight update method is introduced as the optimization tool. The performance of the proposed prediction model is validated by a case study using a real world wind power dataset, and the comparative results show the superiority of the model.

Nonparametric Forecasting of Multivariate Probability Density Functions

The study of dependence between random variables is the core of theoretical and applied statistics. Static and dynamic copula models are useful for describing the dependence structure, which is fully encrypted in the copula probability density function. However, these models are not always able to describe the temporal change of the dependence patterns, which is a key characteristic of financial data. We propose a novel nonparametric framework for modelling a time series of copula probability density functions, which allows to forecast the entire function without the need of post-processing procedures to grant positiveness and unit integral. We exploit a suitable isometry that allows to transfer the analysis in a subset of the space of square integrable functions, where we build on nonparametric functional data analysis techniques to perform the analysis. The framework does not assume the densities to belong to any parametric family and it can be successfully applied also to general multivariate probability density functions with bounded or unbounded support. Finally, a noteworthy field of application pertains the study of time varying networks represented through vine copula models. We apply the proposed methodology for estimating and forecasting the time varying dependence structure between the S&P500 and NASDAQ indices.

Data-driven spectral decomposition and forecasting of ergodic dynamical systems

Abstract We develop a framework for dimension reduction, mode decomposition, and nonparametric forecasting of data generated by ergodic dynamical systems. This framework is based on a representation of the Koopman and Perron–Frobenius groups of unitary operators in a smooth orthonormal basis of the L 2 space of the dynamical system, acquired from time-ordered data through the diffusion maps algorithm. Using this representation, we compute Koopman eigenfunctions through a regularized advection–diffusion operator, and employ these eigenfunctions in dimension reduction maps with projectible dynamics and high smoothness for the given observation modality. In systems with pure point spectra, we construct a decomposition of the generator of the Koopman group into mutually commuting vector fields that transform naturally under changes of observation modality, which we reconstruct in data space through a representation of the pushforward map in the Koopman eigenfunction basis. We also establish a correspondence between Koopman operators and Laplace–Beltrami operators constructed from data in Takens delay-coordinate space, and use this correspondence to provide an interpretation of diffusion-mapped delay coordinates for this class of systems. Moreover, we take advantage of a special property of the Koopman eigenfunction basis, namely that the basis elements evolve as simple harmonic oscillators, to build nonparametric forecast models for probability densities and observables. In systems with more complex spectral behavior, including mixing systems, we develop a method inspired from time change in dynamical systems to transform the generator to a new operator with potentially improved spectral properties, and use that operator for vector field decomposition and nonparametric forecasting.

Simple noise-reduction method based on nonlinear forecasting.

Nonparametric detrending or noise reduction methods are often employed to separate trends from noisy time series when no satisfactory models exist to fit the data. However, conventional noise reduction methods depend on subjective choices of smoothing parameters. Here we present a simple multivariate noise reduction method based on available nonlinear forecasting techniques. These are in turn based on state-space reconstruction for which a strong theoretical justification exists for their use in nonparametric forecasting. The noise reduction method presented here is conceptually similar to Schreiber's noise reduction method using state-space reconstruction. However, we show that Schreiber's method has a minor flaw that can be overcome with forecasting. Furthermore, our method contains a simple but nontrivial extension to multivariate time series. We apply the method to multivariate time series generated from the Van der Pol oscillator, the Lorenz equations, the Hindmarsh-Rose model of neuronal spiking activity, and to two other univariate real-world data sets. It is demonstrated that noise reduction heuristics can be objectively optimized with in-sample forecasting errors that correlate well with actual noise reduction errors.

Hedge fund allocation: Evaluating parametric and nonparametric forecasts using alternative portfolio construction techniques

We propose a model for constructing Asian funds of hedge funds. We compare the accuracy of forecasts of hedge fund returns using an ordinary least squares (OLS) regression model, a nonparametric regression model, and a nonlinear nonparametric model. We backtest to assess these forecasts using three different portfolio construction processes: an “optimized” portfolio, an equally-weighted portfolio, and the Kelly criterion-based portfolio. We find that the Kelly criterion is a reasonable method for constructing a fund of hedge funds, producing better results than a basic optimization or an equally-weighted portfolio construction method. Our backtests also indicate that the nonparametric forecasts and the OLS forecasts produce similar performance at the hedge fund index level. At the individual fund level, our analysis indicates that the OLS forecasts produce higher directional accuracy than the nonparametric methods but the nonparametric methods produce more accurate forecasts than OLS. In backtests, the highest information ratio to predict hedge fund returns is obtained from a combination of the OLS regression with the Fung–Hsieh eight-factor variables as predictors using the Kelly criterion portfolio construction method. Similarly, the highest information ratio using forecasts generated from a combination of the nonparametric regression using the Fung–Hsieh eight-factor model variables is achieved using the Kelly criterion portfolio construction method. Simulations using risk-adjusted total returns indicate that the nonparametric regression model generates superior information ratios than the analogous backtest results using the OLS. However, the benefits of diversification plateau with portfolios of more than 20 hedge funds. These results generally hold with portfolio implementation lags up to 12months.

Bayesian nonparametric forecasting of monotonic functional time series

We propose a Bayesian nonparametric approach to modelling and predicting a class of functional time series with application to energy markets, based on fully observed, noise-free functional data. Traders in such contexts conceive profitable strategies if they can anticipate the impact of their bidding actions on the aggregate demand and supply curves, which in turn need to be predicted reliably. Here we propose a simple Bayesian nonparametric method for predicting such curves, which take the form of monotonic bounded step functions. We borrow ideas from population genetics by defining a class of interacting particle systems to model the functional trajectory, and develop an implementation strategy which uses ideas from Markov chain Monte Carlo and approximate Bayesian computation techniques and allows to circumvent the intractability of the likelihood. Our approach shows great adaptation to the degree of smoothness of the curves and the volatility of the functional series, proves to be robust to an increase of the forecast horizon and yields an uncertainty quantification for the functional forecasts. We illustrate the model and discuss its performance with simulated datasets and on real data relative to the Italian natural gas market.

Nonparametric forecasting of low-dimensional dynamical systems.

This paper presents a nonparametric modeling approach for forecasting stochastic dynamical systems on low-dimensional manifolds. The key idea is to represent the discrete shift maps on a smooth basis which can be obtained by the diffusion maps algorithm. In the limit of large data, this approach converges to a Galerkin projection of the semigroup solution to the underlying dynamics on a basis adapted to the invariant measure. This approach allows one to quantify uncertainties (in fact, evolve the probability distribution) for nontrivial dynamical systems with equation-free modeling. We verify our approach on various examples, ranging from an inhomogeneous anisotropic stochastic differential equation on a torus, the chaotic Lorenz three-dimensional model, and the Niño-3.4 data set which is used as a proxy of the El Niño Southern Oscillation.

Why preferring parametric forecasting to nonparametric methods?

A recent series of papers by Charles T. Perretti and collaborators have shown that nonparametric forecasting methods can outperform parametric methods in noisy nonlinear systems. Such a situation can arise because of two main reasons: the instability of parametric inference procedures in chaotic systems which can lead to biased parameter estimates, and the discrepancy between the real system dynamics and the modeled one, a problem that Perretti and collaborators call "the true model myth". Should ecologists go on using the demanding parametric machinery when trying to forecast the dynamics of complex ecosystems? Or should they rely on the elegant nonparametric approach that appears so promising? It will be here argued that ecological forecasting based on parametric models presents two key comparative advantages over nonparametric approaches. First, the likelihood of parametric forecasting failure can be diagnosed thanks to simple Bayesian model checking procedures. Second, when parametric forecasting is diagnosed to be reliable, forecasting uncertainty can be estimated on virtual data generated with the fitted to data parametric model. In contrast, nonparametric techniques provide forecasts with unknown reliability. This argumentation is illustrated with the simple theta-logistic model that was previously used by Perretti and collaborators to make their point. It should convince ecologists to stick to standard parametric approaches, until methods have been developed to assess the reliability of nonparametric forecasting.

Evaluating the effectiveness of parametric and nonparametric energy consumption forecasts for a developing country

This paper seeks to analyse and evaluate Sri Lanka's energy consumption forecasts, more specifically, electricity, petroleum, coal and renewable electricity consumption using a variety of parametric and nonparametric forecasting techniques. The Sri Lankan economy is emerging following the end of a prolonged civil war, and thus this topic is opportune as accurate forecasts of energy requirements are indispensable for sustaining the ongoing rapid economic expansion. We also consider evaluating the appropriateness of parametric and nonparametric energy forecasting methods for Sri Lanka. In addition, this paper marks the introductory application of SSA for forecasting in Sri Lanka, and the results from SSA are compared against the popular benchmarks of ARIMA, ETS, HW, TBATS, and NN. We find statistically significant evidence proving that the SSA model outperforms ETS and HW at forecasting renewable electricity consumption, and also, that the SSA model outperforms ARIMA and TBATS models at forecasting coal consumption. On average, the SSA model is found to be best for energy consumption forecasting in Sri Lanka whilst the Neural Networks model is second best.