Differential geometry in statistical inference

Everywhere around the globe, the hot topic of discussion today is the ongoing and fast-spreading coronavirus disease (COVID-19), which is caused by the severe acute respiratory syndrome coronavirus 2 (SARS-COV-2). Earlier detected in Wuhan, Hubei province, in China in December 2019, the deadly virus engulfed China and some neighboring countries, which claimed thousands of lives in February 2020. The proposed hybrid methodology involves the application of discreet wavelet decomposition to the dataset of deaths due to COVID-19, which splits the input data into component series and then applying an appropriate econometric model to each of the component series for making predictions of death cases in future. ARIMA models are well known econometric forecasting models capable of generating accurate forecasts when applied on wavelet decomposed time series. The input dataset consists of daily death cases from most affected five countries by COVID-19, which is given to the hybrid model for validation and to make one month ahead prediction of death cases. These predictions are compared with that obtained from an ARIMA model to estimate the performance of prediction. The predictions indicate a sharp rise in death cases despite various precautionary measures taken by governments of these countries.

Development of New Hybrid Model of Discrete Wavelet Decomposition and Autoregressive Integrated Moving Average (ARIMA) Models in Application to One Month Forecast the Casualties Cases of COVID-19.

Recurrent neural networks based modelling of industrial grinding operation

This paper proposes a time series model based on wavelet transform and long short-term memory (LSTM) network to forecast vehicle emission. It implements the semi-supervised collaborative training regression to compensate missing emissions data. The accumulated carbon monoxide (CO), hydrocarbons (HC), and nitric oxide (NO) concentrations emitted by vehicles in different lanes per hour were taken to quantitatively characterize the vehicle emissions. The original time series of vehicle emission data, which may be highly variable, is decomposed into several lowly variable sub-series by wavelet transform. For each sub-series, an LSTM time series model is proposed to forecast vehicle emissions. More specifically, the inputs of that LSTM model are the weather variables, the driving variables of the concerned vehicle and historical emissions records while its output is the predicted accumulated concentrations of CO, HC, and NO. The three types of predicted concentrations of all sub-series are summed up, respectively, and produce the desired prediction of the total emission of each type. The proposed model is verified through real data which was collected between May 2017 and December 2017 at the multi-lane monitoring station of Baimiao South Road, Daxing District, Beijing, China. It confirms that our model based on wavelet transform and LSTM can efficiently improve the correlation coefficient (R) and the index of agreement (IA) against conventional models, such as ARIMA and wavelet-ARIMA model.

Vehicle Emission Forecasting Based on Wavelet Transform and Long Short-Term Memory Network

Integral Equations, Origin, and Basic Tools Modeling of Problems as Integral Equations Volterra Integral Equations The Green's Function Fredholm Integral Equations Existence of the Solutions: Basic Fixed Point Theorems Higher Quadrature Rules for the Numerical Solutions Appendices Answers to Exercises References Index.

Introduction to integral equations with applications, by Abdul J. Jerri. Pp 254. $47·50. 1985. ISBN 0-8247-7293-8 (Marcel Dekker)

In recent years, air pollution has been a major concern for its implications on human health. Specifically, ozone (
 $$\mathrm{O}_{3}$$
 ) pollution is causing common respiratory diseases. In this paper, we illustrate the process of modeling and prediction hourly $$\mathrm{O}_ {3}$$
 pollution measurements using wavelet transforms. We split the time series of $$\mathrm{O}_{3}$$
 in daily intervals and estimate scale and wavelet coefficients for each interval by the discrete wavelet transform (DWT) with Haar filter. Subsequently we apply cumulated autoregressive integrated moving average (ARIMA) to estimate the coefficients and forecast their evolution in future intervals. Then the inverse discrete wavelet transform is implemented for the reconstruction of the time series and the forecast in the near future. In order to assess the performance of the proposed methodology, we compare the predictions obtained by the DWT–ARIMA with those obtained by the ARIMA model. Several theoretical results are shown through a simulation study.

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Predicting hourly ozone concentrations using wavelets and ARIMA models

The research contained in this paper belongs to the qualitative theory of dynamic equations on time scales. Via the detailed analysis of solutions of the associated Riccati equation and an advanced averaging technique, we provide the description of domain of nonoscillation of very general equations. The results are formulated and proved for half-linear equations (i.e., equations connected to PDEs with one dimensional p-Laplacian) on time scales. Nevertheless, we obtain new results also for linear difference equations. Moreover, the combination of the presented results with previous ones shows that many useful equations are conditionally oscillatory. Such equations are ideal as testing and comparison equations in real-world models which are beyond capabilities of known oscillation and nonoscillation criteria often.

Nonoscillation of half‐linear dynamic equations on time scales

The interest rates (or nominal yields) can be negative, this is an unavoidable fact which has already been visible during the Great Depression (1929-39). Nowadays we can find negative rates easily by e.g. auditing. Several theoretical and practical ideas how to model and eventually overcome empirical negative rates can be suggested, however, they are far beyond a simple practical realization. In this paper we discuss the dynamical reasons why negative interest rates can happen in the second order differential dynamics and how they can influence the variance and expectation of the interest rate process. Such issues are highly practical, involving e.g. banking sector and pension securities.

Negative interest rates: why and how?

We discuss the following problem: Given a set of information criteria for optimal designs, the numerical and computational complexity may drastically differ from one criterion to another. A general...

Jozef Kiselak

Papers

Predicting hourly ozone concentrations using wavelets and ARIMA models

Nonoscillation of half‐linear dynamic equations on time scales

Negative interest rates: why and how?

Fredholm integral relation between compound estimation and prediction (FIRCEP)

Negative interest rates: why and how?