Forecasts can either be short term, medium term or long term. In this work we considered short term forecast because of the problem of limited data or time series data that is often encounter in time series analysis. ...Forecasts can either be short term, medium term or long term. In this work we considered short term forecast because of the problem of limited data or time series data that is often encounter in time series analysis. This simulation study considered the performances of the classical VAR and Sims-Zha Bayesian VAR for short term series at different levels of collinearity and correlated error terms. The results from 10,000 iteration revealed that the BVAR models are excellent for time series length of T=8 for all levels of collinearity while the classical VAR is effective for time series length of T=16 for all collinearity levels except when ρ = -0.9 and ρ = -0.95. We therefore recommended that for effective short term forecasting, the time series length, forecasting horizon and the collinearity level should be considered.展开更多
In 1956, Tong established an asymptotic formula for the mean square of the error term of the summatory function of the Piltz divisor function d3（n）. The aim of this paper is to generalize Tong＇s method to a class o...In 1956, Tong established an asymptotic formula for the mean square of the error term of the summatory function of the Piltz divisor function d3（n）. The aim of this paper is to generalize Tong＇s method to a class of Dirichlet series L（s） which satisfies a functional equation. Let a（n） be an arithmetical function related f t to a Dirichlet series L（s）, and let E（x） be the error term of ∑＇n≤x a（n）. In this paper, after introducing a class of Diriclet series with a general functional equation （which contains the well-known Selberg class）, we establish a Tong-type identity and a Tong-type truncated formula for the error term of the Riesz mean of the coefficients of this Dirichlet series L（s）. This kind of Tong-type truncated formula could be used to study the mean square of E（x） under a certain assumption. In other words, we reduce the mean square of E（x） to the problem of finding a suitable constant σ＊ which is related to the mean square estimate of L（s）. We shall represent some results of functions in the Selberg class of degrees 2 -4.展开更多
Let Zm be the additive group of residue classes modulo m.Let s(m,n)denote the number of subgroups of the group Z_(m)×Z_(n),where m and n are arbitrary positive integers.For any x≥1,we consider the asymptotic beh...Let Zm be the additive group of residue classes modulo m.Let s(m,n)denote the number of subgroups of the group Z_(m)×Z_(n),where m and n are arbitrary positive integers.For any x≥1,we consider the asymptotic behavior of D_(s)(x):=∑m^(2)+n^(2)≤xS(M,n)and obtain an asymptotic formula by using the elementary method.展开更多
An upper bound is given for the error termS(r, |a j |,f) in Nevanlinna’s inequality. For given positive increasing functions p and $ with ∫ 1 ∞ dr/p(r) = ∫ 1 ∞ dr/r ?(r) = ∞, setP(r) = ∫ 1 r dt/p,Ψ(r) = ∫ 1 r...An upper bound is given for the error termS(r, |a j |,f) in Nevanlinna’s inequality. For given positive increasing functions p and $ with ∫ 1 ∞ dr/p(r) = ∫ 1 ∞ dr/r ?(r) = ∞, setP(r) = ∫ 1 r dt/p,Ψ(r) = ∫ 1 r dt/t ?(t) We prove that $$S(r, \left\{ {a_j } \right\}, f) \leqslant \log \frac{{T(r, f)\phi (T(r, f))}}{{p(r)}} + O(1)$$ holds, with a small exceptional set of r, for any finite set of points |a j | in the extended plane and any meromorphic function f such thatΨ(T(r, f)) =O(P(r)). This improves the known results of A. Hinkkanen and Y. F. Wang. The sharpness of the estimate is also considered.展开更多
In this paper we study the mean square of the error term in the Weyl's law of an irrational (2l + 1)-dimensional Heisenberg manifold. An asymptotic formula is established.
Standard automatic dependent surveillance broadcast (ADS-B) reception algorithms offer considerable performance at high signal-to-noise ratios (SNRs). However, the performance of ADS-B algorithms in applications can b...Standard automatic dependent surveillance broadcast (ADS-B) reception algorithms offer considerable performance at high signal-to-noise ratios (SNRs). However, the performance of ADS-B algorithms in applications can be problematic at low SNRs and in high interference situations, as detecting and decoding techniques may not perform correctly in such circumstances. In addition, conventional error correction algorithms have limitations in their ability to correct errors in ADS-B messages, as the bit and confidence values may be declared inaccurately in the event of low SNRs and high interference. The principal goal of this paper is to deploy a Long Short-Term Memory (LSTM) recurrent neural network model for error correction in conjunction with a conventional algorithm. The data of various flights are collected and cleaned in an initial stage. The clean data is divided randomly into training and test sets. Next, the LSTM model is trained based on the training dataset, and then the model is evaluated based on the test dataset. The proposed model not only improves the ADS-B In packet error correction rate (PECR), but it also enhances the ADS-B In terms of sensitivity. The performance evaluation results reveal that the proposed scheme is achievable and efficient for the avionics industry. It is worth noting that the proposed algorithm is not dependent on conventional algorithms’ prerequisites.展开更多
文摘Forecasts can either be short term, medium term or long term. In this work we considered short term forecast because of the problem of limited data or time series data that is often encounter in time series analysis. This simulation study considered the performances of the classical VAR and Sims-Zha Bayesian VAR for short term series at different levels of collinearity and correlated error terms. The results from 10,000 iteration revealed that the BVAR models are excellent for time series length of T=8 for all levels of collinearity while the classical VAR is effective for time series length of T=16 for all collinearity levels except when ρ = -0.9 and ρ = -0.95. We therefore recommended that for effective short term forecasting, the time series length, forecasting horizon and the collinearity level should be considered.
基金supported by National Key Basic Research Program of China (Grant No. 2013CB834201)National Natural Science Foundation of China (Grant No. 11171344)+1 种基金Natural Science Foundation of Beijing (Grant No. 1112010)the Fundamental Research Funds for the Central Universities in China (Grant No. 2012YS01)
文摘In 1956, Tong established an asymptotic formula for the mean square of the error term of the summatory function of the Piltz divisor function d3（n）. The aim of this paper is to generalize Tong＇s method to a class of Dirichlet series L（s） which satisfies a functional equation. Let a（n） be an arithmetical function related f t to a Dirichlet series L（s）, and let E（x） be the error term of ∑＇n≤x a（n）. In this paper, after introducing a class of Diriclet series with a general functional equation （which contains the well-known Selberg class）, we establish a Tong-type identity and a Tong-type truncated formula for the error term of the Riesz mean of the coefficients of this Dirichlet series L（s）. This kind of Tong-type truncated formula could be used to study the mean square of E（x） under a certain assumption. In other words, we reduce the mean square of E（x） to the problem of finding a suitable constant σ＊ which is related to the mean square estimate of L（s）. We shall represent some results of functions in the Selberg class of degrees 2 -4.
基金This work was supported by the National Natural Science Foundation of China(Grant No.11971476)。
文摘Let Zm be the additive group of residue classes modulo m.Let s(m,n)denote the number of subgroups of the group Z_(m)×Z_(n),where m and n are arbitrary positive integers.For any x≥1,we consider the asymptotic behavior of D_(s)(x):=∑m^(2)+n^(2)≤xS(M,n)and obtain an asymptotic formula by using the elementary method.
文摘An upper bound is given for the error termS(r, |a j |,f) in Nevanlinna’s inequality. For given positive increasing functions p and $ with ∫ 1 ∞ dr/p(r) = ∫ 1 ∞ dr/r ?(r) = ∞, setP(r) = ∫ 1 r dt/p,Ψ(r) = ∫ 1 r dt/t ?(t) We prove that $$S(r, \left\{ {a_j } \right\}, f) \leqslant \log \frac{{T(r, f)\phi (T(r, f))}}{{p(r)}} + O(1)$$ holds, with a small exceptional set of r, for any finite set of points |a j | in the extended plane and any meromorphic function f such thatΨ(T(r, f)) =O(P(r)). This improves the known results of A. Hinkkanen and Y. F. Wang. The sharpness of the estimate is also considered.
基金supported by National Natural Science Foundation of China (Grant No. 10771127)
文摘In this paper we study the mean square of the error term in the Weyl's law of an irrational (2l + 1)-dimensional Heisenberg manifold. An asymptotic formula is established.
文摘Standard automatic dependent surveillance broadcast (ADS-B) reception algorithms offer considerable performance at high signal-to-noise ratios (SNRs). However, the performance of ADS-B algorithms in applications can be problematic at low SNRs and in high interference situations, as detecting and decoding techniques may not perform correctly in such circumstances. In addition, conventional error correction algorithms have limitations in their ability to correct errors in ADS-B messages, as the bit and confidence values may be declared inaccurately in the event of low SNRs and high interference. The principal goal of this paper is to deploy a Long Short-Term Memory (LSTM) recurrent neural network model for error correction in conjunction with a conventional algorithm. The data of various flights are collected and cleaned in an initial stage. The clean data is divided randomly into training and test sets. Next, the LSTM model is trained based on the training dataset, and then the model is evaluated based on the test dataset. The proposed model not only improves the ADS-B In packet error correction rate (PECR), but it also enhances the ADS-B In terms of sensitivity. The performance evaluation results reveal that the proposed scheme is achievable and efficient for the avionics industry. It is worth noting that the proposed algorithm is not dependent on conventional algorithms’ prerequisites.
