scholarly journals Entropy Ratio and Entropy Concentration Coefficient, with Application to the COVID-19 Pandemic

Entropy ◽  
2020 ◽  
Vol 22 (11) ◽  
pp. 1315
Author(s):  
Christoph Bandt
Keyword(s):  
Time Series ◽  
Markov Chain ◽  
Population Density ◽  
Gross Domestic Product ◽  
Homogeneous Distribution ◽  
Concentration Coefficient ◽  
Self Similar ◽  
Product Application ◽  
Product Measures ◽  
Different Levels

In order to study the spread of an epidemic over a region as a function of time, we introduce an entropy ratio U describing the uniformity of infections over various states and their districts, and an entropy concentration coefficient C=1−U. The latter is a multiplicative version of the Kullback-Leibler distance, with values between 0 and 1. For product measures and self-similar phenomena, it does not depend on the measurement level. Hence, C is an alternative to Gini’s concentration coefficient for measures with variation on different levels. Simple examples concern population density and gross domestic product. Application to time series patterns is indicated with a Markov chain. For the Covid-19 pandemic, entropy ratios indicate a homogeneous distribution of infections and the potential of local action when compared to measures for a whole region.

An improved grey Markov chain model with ANN error correction and its application in gross domestic product forecasting

2021 ◽  
pp. 1-11
Author(s):  
Yuan Zou ◽  
Daoli Yang ◽  
Yuchen Pan
Keyword(s):  
Neural Network ◽  
Markov Chain ◽  
Gross Domestic Product ◽  
Error Correction ◽  
Historical Data ◽  
Markov Chain Model ◽  
Back Propagation ◽  
The United States ◽  
Domestic Product ◽  
Chain Model

Gross domestic product (GDP) is the most widely-used tool for measuring the overall situation of a country’s economic activity within a specified period of time. A more accurate forecasting of GDP based on standardized procedures with known samples available is conducive to guide decision making of government, enterprises and individuals. This study devotes to enhance the accuracy regarding GDP forecasting with given sample of historical data. To achieve this purpose, the study incorporates artificial neural network (ANN) into grey Markov chain model to modify the residual error, thus develops a novel hybrid model called grey Markov chain with ANN error correction (abbreviated as GMCM_ANN), which assembles the advantages of three components to fit nonlinear forecasting with limited sample sizes. The new model has been tested by adopting the historical data, which includes the original GDP data of the United States, Japan, China and India from 2000 to 2019, and also provides predications on four countries’ GDP up to 2022. Four models including autoregressive integrated moving average model, back-propagation neural network, the traditional GM(1,1) and grey Markov chain model are as benchmarks for comparison of the predicted accuracy and application scope. The obtained results are satisfactory and indicate superior forecasting performance of the proposed approach in terms of accuracy and universality.

scholarly journals Towards a novel design perspective for system vulnerability using a Markov chain

2018 ◽  
Author(s):  
A C Habben Jansen ◽  
E A E Duchateau ◽  
A A Kana
Keyword(s):  
Markov Chain ◽  
Distributed Systems ◽  
Early Stage ◽  
Test Case ◽  
Damage Scenarios ◽  
System Vulnerability ◽  
Residual Capacity ◽  
Design Perspective ◽  
Novel Design ◽  
Different Levels

In order to investigate to which extent naval ships can execute their operational scenario after damage, an early stage assessment of the vulnerability of distributed systems needs to be carried out. Such assessments are currently mostly done by evaluating the performance of predefined concepts. However, such an approach does not necessarily lead to the most desirable solution, since solutions outside the scope of the designer’s preconceived ideas or experience are inherently hard to investigate. This paper therefore proposes several steps towards an approach that enables a vulnerability assessment that is independent of predefined concepts. This is done by incorporating several additions to an existing system vulnerability approach developed by the authors, using a Markov chain. With this approach there is no longer a need for modelling individual hits or damage scenarios. Whereas the approach has previously been shown in concept, this paper introduces three improvements that contribute to the applicability of the approach: 1)it is scaled up in order to model a larger number of compartments and distributed systems, 2) the hit probabilities for different compartments can be adjusted, and 3) it is shown how the availability of main ship functions can be derived from the availability of individual connections. A test case that compares two powering concepts (conventional and full electric powering) of a notional Oceangoing Patrol Vessel (OPV) is provided to illustrate the principles behind the improvements. From the results the two main contributions of this paper can be obtained: 1)the possibility to assess the system vulnerability for different levels of required residual capacity at different impact levels, and 2) and the quantitative nature of the results, aiding ship designers and naval staff with understanding the consequences of various concepts on the system vulnerability. 

scholarly journals VECTOR AUTOREGRESSIVE APPROACH AFTER FIRST DIFFERENCING: A TIME SERIES ANALYSIS OF INFLATION AND ITS DETERMINANTS IN TANZANIA

2021 ◽  
pp. 43-56
Author(s):  
Rachel R. Cheti ◽  
Bahati Ilembo
Keyword(s):  
Time Series ◽  
Exchange Rate ◽  
Gross Domestic Product ◽  
Money Supply ◽  
Inflation Rate ◽  
Negative Impact ◽  
Causal Effect ◽  
Domestic Product ◽  
Series Data ◽  
Vector Autoregressive

The objective of the study was to examine the trend of inflation and its key determinants in Tanzania. We used secondary time series data observed annually from January 1970 to 2020 which are inflation rate, GDP, Exchange rate and money supply. The vector autoregressive (VAR) model was employed for modeling. Augmented Dickey-Fuller test (ADF) found that inflation rate, Gross Domestic Product (GDP), exchange rate and Money supply (M3) were initially non-stationary but they became stationary after first differencing so as to proceed with the analysis. Preliminary tests before obtaining vector auto regressive model were carried out before determining the relationship between the variables. Diagnostic test such as serial correlation, heteroscedasticity, stability and normality were also important to evaluate the model assumptions and investigate whether or not there are observations with a large, undue influence on the analysis. We used Granger causality test (GCT) to determine causal- effect relationship between the variables. The results show that, there is a long run relationship between the variables, also the results showed that exchange rate and money supply (M3) both have a positive impact on inflation rate while gross domestic product (GDP) revealed a negative impact on inflation rate. Finally, the forecast of inflation rate for 15 years ahead was performed. The study recommends that the government should pursue both contractionary monetary policy and fiscal policy in order to control inflation in the country.

scholarly journals Faktor-Faktor yang Mempengaruhi Alih Fungsi Lahan Sawah di Kabupaten Aceh Besar

2018 ◽  
Vol 3 (4) ◽  
pp. 525-533
Author(s):  
Raudhatul Husna ◽  
Azhar Azhar ◽  
Edy Marsudi
Keyword(s):  
Time Series ◽  
Population Density ◽  
Rice Field ◽  
Time Series Data ◽  
Statistical Tests ◽  
Secondary Data ◽  
Series Data ◽  
Factors Affecting ◽  
Rice Productivity ◽  
Negative Impacts

Abstrak. Alih fungsi lahan atau lazimnya disebut sebagai konversi lahan adalah  perubahan fungsi sebagian atau seluruh kawasan lahan dari fungsinya semula (seperti yang direncanakan) menjadi fungsi lain yang membawa dampak negatif terhadap lingkungan dan potensi lahan itu sendiri. Penelitian ini bertujuan untuk mengetahui apakah harga lahan, kepadatan penduduk, produktivitas padi dan jumlah PDRB dapat mempengaruhi alih fungsi lahan sawah di Kabupaten Aceh Besar. Data yang digunakan dalam penelitian ini adalah data sekunder. Data yang dikumpulkan adalah data time series dengan range tahun 2002 sampai 2016. Penelitian ini menggunakan metode analisis  regresi linier berganda. hasil penelitian dan pembahasan serta pengujian SPSS menunjukkan bahwa harga lahan, kepadatan penduduk, dan produktivitas padi berpengaruh nyata terhadap alih fungsi lahan sawah di Kabupaten Aceh Besar. sedangkan jumlah PDRB tidak berpengaruh terhadap alih fungsi lahan sawah. Hal ini ditunjukkan oleh koefisien regresi untuk variabel jumlah PDRB sebesar 0,00015. Hasil pengujian statistik menunjukkan nilai t hitung untuk jumlah PDRB sebesar 1,315 dengan nilai signifikan sebesar 0,218. Sedangkan nilai t tabel sebesar 1,782 yang berarti nilai t hitung t tabel (1,315 1,782).  Factors Affecting The Conversion Of Paddy Fields In Kabupaten Aceh Besar Abstract. Land use change or commonly referred to as land conversion is a change in the function of part or all of the land area from its original function (as planned) into other functions that bring negative impacts to the environment and the potential of the land itself. This study aims to find out whether the price of land, population density, rice productivity and the amount of GRDP can affect the conversion of rice field functions in Aceh Besar District. The data used in this research is secondary data. The data collected is time series data with range of year 2002 until 2016. This research use multiple linier regression analysis method. the results of research and discussion and testing of SPSS showed that land price, population density, and rice productivity significantly affected the conversion of wetland in Aceh Besar district. while the number of GDP does not affect the conversion of wetland. This is indicated by the regression coefficient for the GRDP variable of 0.00015. The results of statistical tests show the value of t arithmetic for the amount of GRDP by 1.315 with a significant value of 0.218. While the value of t table of 1.782 which means the value of t arithmetic t table (1,315 1.782).

scholarly journals An analysis of the relationship of inflation and unemployment to the gross domestic product (gdp) in zimbabwe

2014 ◽  
Vol 1 (3) ◽  
pp. 156-162
Author(s):  
Tendai Makoni
Keyword(s):  
Time Series ◽  
Gross Domestic Product ◽  
Cointegration Test ◽  
Domestic Product ◽  
Long Run ◽  
Causality Tests ◽  
Granger Causality Tests ◽  
Relationship Of ◽  
The Relationship ◽  
Yearly Data

The time series yearly data for Gross Domestic Product (GDP), inflation and unemployment from 1980 to 2012 was used in the study. First difference of the logged data became stationary as suggested by the time series plots. Johansen Maximum Likelihood Cointegration test indicated a long-run relationship among the variables. Granger Causality tests suggested unidirectional causality between inflation and GDP, implying that GDP is Granger caused by inflation in Zimbabwe. Another unidirectional causality was noted between unemployment and inflation. The causality between unemployment and inflation imply that unemployment do affect GDP indirectly since unemployment influences inflation which in turn positively affect GDP.

Time Series Association State Analysis Method for Attacks on the Smart Internet of Electric Vehicle Charging Network

2019 ◽  
Vol 2673 (4) ◽  
pp. 217-228 ◽  
Author(s):  
Qianmu Li ◽  
Yinhai Wang ◽  
Ziyuan Pu ◽  
Shuo Wang ◽  
Weibin Zhang
Keyword(s):  
Time Series ◽  
Markov Chain ◽  
Electric Vehicle ◽  
The State ◽  
Analysis Method ◽  
Security Risks ◽  
Electric Vehicle Charging ◽  
Vehicle Charging ◽  
Association State ◽  
State Analysis

A robust, integrated and flexible charging network is essential for the growth and deployment of electric vehicles (EVs). The State Grid of China has developed a Smart Internet of Electric Vehicle Charging Network (SIEN). At present, there are three main ways to attack SIEN maliciously: distributed data tampering; distributed denial of service (DDoS); and forged command attacks. Network attacks are random and continuous, closely related to time. By contrast, when analyzing the alarm in malicious attacks, the traditional Markov chain based model ignores the association relationship in the time series between states of alarm, so that the analysis and prediction of alarms are not suitable for real situations. This paper analyzes the characteristics of the three types of attack and proposes an association state analysis method on the time series. This method firstly analyzes alarm logs at different locations, different levels, and different types, and then establishes the temporal association of scattered and isolated alarm information. Secondly, it tracks the transition trend of abnormal events in the SIEN’s main station layer, the channel layer, and the sub-station layer. It also identifies the real attack behavior. This method not only provides a prediction of security risks, but, more importantly, it can also accurately analyze the trend of SIEN security risks. Compared with the ordinary Markov chain model, this method can better smooth the fluctuation of processing values, with higher real-time performance, stronger robustness, and higher precision. This method has been applied to the State Grid of China.

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