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Estimation for nearly unit root processes with GARCH errors 被引量:4
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作者 YUAN Yu-ze ZHANG Rong-mao Department of Mathematics, Zhejiang University, Hangzhou 310027, China 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2010年第3期297-306,共10页
In this paper the limiting distribution of the least square estimate for the autoregressive coefficient of a nearly unit root model with GARCH errors is derived. Since the limiting distribution depends on the unknown ... In this paper the limiting distribution of the least square estimate for the autoregressive coefficient of a nearly unit root model with GARCH errors is derived. Since the limiting distribution depends on the unknown variance of the errors, an empirical likelihood ratio statistic is proposed from which confidence intervals can be constructed for the nearly unit root model without knowing the variance. To gain an intuitive sense for the empirical likelihood ratio, a small simulation for the asymptotic distribution is given. 展开更多
关键词 Nearly unit root GARCH error least square estimation Ornstein-Uhlenbeck process empirical likelihood.
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A note on self-normalized Dickey-Fuller test for unit root in autoregressive time series with GARCH errors 被引量:1
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作者 YANG Xiao-rong ZHANG Li-xin 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2008年第2期197-201,共5页
In this article, the unit root test for AR(p) model with GARCH errors is considered. The Dickey-Fuller test statistics are rewritten in the form of self-normalized sums, and the asymptotic distribution of the test s... In this article, the unit root test for AR(p) model with GARCH errors is considered. The Dickey-Fuller test statistics are rewritten in the form of self-normalized sums, and the asymptotic distribution of the test statistics is derived under the weak conditions. 展开更多
关键词 unit root AR (p)-GARCH (1 1) SELF-NORMALIZED Dickey-Fuller test statistic.
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Characterizing the Urban Temperature Trend Using Seasonal Unit Root Analysis:Hong Kong from 1970 to 2015
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作者 Wai-Ming TO Tat-Wai YU 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 2016年第12期1376-1385,共10页
This paper explores urban temperature in Hong Kong using long-term time series. In particular, the characterization of the urban temperature trend was investigated using the seasonal unit root analysis of monthly mean... This paper explores urban temperature in Hong Kong using long-term time series. In particular, the characterization of the urban temperature trend was investigated using the seasonal unit root analysis of monthly mean air temperature data over the period January 1970 to December 2013. The seasonal unit root test makes it possible to determine the stochastic trend of monthly temperatures using an autoregressive model. The test results showed that mean air temperature has increased by 0.169~ C (10 yr) - 1 over the past four decades. The model of monthly temperature obtained from the seasonal unit root analysis was able to explain 95.9% of the variance in the measured monthly data -- much higher than the variance explained by the ordinary least-squares model using annual mean air temperature data and other studies alike. The model accurately predicted monthly mean air temperatures between January 2014 and December 2015 with a root-mean-square percentage error of 4.2%. The correlation between the predicted and the measured monthly mean air temperatures was 0.989. By analyzing the monthly air temperatures recorded at an urban site and a rural site, it was found that the urban heat island effect led to the urban site being on average 0.865~C warmer than the rural site over the past two decades. Besides, the results of correlation analysis showed that the increase in annual mean air temperature was significantly associated with the increase in population, gross domestic product, urban land use, and energy use, with the R2 values ranging from 0.37 to 0.43. 展开更多
关键词 urban temperature trend urban heat island effect seasonal unit root tests long-term time series
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Is There Hysteresis in Unemployment in OECD Countries? Evidence From Panel Unit Root Test With Structural Breaks
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作者 Meliha Ener Feyza Ariea 《Chinese Business Review》 2011年第4期294-304,共11页
This study tests the hysteresis hypothesis of unemployment in fifteen OECD countries by using panel unit root tests which allow for structural breaks. We apply annual unemployment rates covering 1985-2008 periods. We ... This study tests the hysteresis hypothesis of unemployment in fifteen OECD countries by using panel unit root tests which allow for structural breaks. We apply annual unemployment rates covering 1985-2008 periods. We test whether unemployment rates are stationary by using second generation tests which allow cross section dependency among series and panel unit root test based on structural break advanced by Carrion-i-Silvestre, Barrio-Castro and Lopez-Bazo (2005). We find series as a stationary process with structural breaks according to Carrion-i Silvestre et al. (2005) test, while we find series as unit root process with second generation panel unit root test. According to the Carrion-i Silvestre et al. (2005) test, we find the evidence of absence of hysteresis in analyzed countries. As a result, temporary shocks have temporary effects on unemployment instead of permanent effect. Structural factors can affect the natural rate of unemployment and, therefore, unemployment would be stationary around a process that is subject to structural breaks. So, there still exists a unique natural rate of unemployment to which the economy eventually will converge. 展开更多
关键词 structural break UNEMPLOYMENT cross-section dependence panel unit root tests
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Unit Root Analysis of Traffic Time Series in Toll Highways
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作者 Antonio Sanchez Solino Antonio L. Lara Galera 《Journal of Civil Engineering and Architecture》 2012年第12期1641-1647,共7页
Concession contracts in highways often include some kind of clauses (for example, a minimum traffic guarantee) that allow for better management of the business risks. The value of these clauses may be important and ... Concession contracts in highways often include some kind of clauses (for example, a minimum traffic guarantee) that allow for better management of the business risks. The value of these clauses may be important and should be added to the total value of the concession. However, in these cases, traditional valuation techniques, like the NPV (net present value) of the project, are insufficient. An alternative methodology for the valuation of highway concession is one based on the real options approach. This methodology is generally built on the assumption of the evolution of traffic volume as a GBM (geometric Brownian motion), which is the hypothesis analyzed in this paper. First, a description of the methodology used for the analysis of the existence of unit roots (i.e., the hypothesis of non-stationarity) is provided. The Dickey-Fuller approach has been used, which is the most common test for this kind of analysis. Then this methodology is applied to perform a statistical analysis of traffic series in Spanish toll highways. For this purpose, data on the AADT (annual average daily traffic) on a set of highways have been used. The period of analysis is around thirty years in most cases. The main outcome of the research is that the hypothesis that traffic volume follows a GBM process in Spanish toll highways cannot be rejected. This result is robust, and therefore it can be used as a starting point for the application of the real options theory to assess toll highway concessions. 展开更多
关键词 Real options unit root analysis INVESTMENT highway concession traffic.
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Assessing the Convergence of Cropland Ecological Balance:A Panel Data Analysis of 13 Major Agricultural Countries
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作者 Orhan Simsek İlkay Güler +2 位作者 Sefa Ozbek Mustafa Naimoglu Zafer Adali 《Journal of Environmental & Earth Sciences》 2025年第7期16-34,共19页
This study investigates the convergence hypothesis and stochastic dynamics of agricultural land use and ecological balance across 13 major agricultural countries from 1992 to 2022.The study's concentrated samples ... This study investigates the convergence hypothesis and stochastic dynamics of agricultural land use and ecological balance across 13 major agricultural countries from 1992 to 2022.The study's concentrated samples are Russia,the United States,the Netherlands,Brazil,Germany,China,France,Spain,Italy,Canada,Belgium,Indonesia,and India.The research uncovers notable variations in ecological balance by utilizing a comprehensive set of advanced panel unit root tests(Panel CIPS,CADF,Panel-LM,Panel-KPSS,and Bahmani-Oskooee et al.’s Panel KPSS Unit Root Test).The findings highlight significant improvements in Canada,contrasting with declines in the Netherlands,France,Germany,and the United States.The results indicate convergence in ecological balance among these countries,suggesting that agricultural practices are progressively aligning with sustainability objectives.The considered countries can determine and enact joint and collective policy actions addressing cropland sustainability.However,the univariate outcome also shows that the cropland ecological balance of Germany,China,France,Indonesia,and India does contain a unit root and stationary which means the presence of the constant-mean.The univariate actions from the mentioned governments will not promote persistent impact.Therefore,joint actions determined by the countries considered are recommended for the mentioned countries.However,the rest of the countries also enact local policies.The insights gained are critical for informing global sustainability strategies and aiding policymakers in developing effective measures to enhance agricultural practices and mitigate environmental impacts.This research provides a data-driven foundation for optimizing agricultural sustainability and supports international efforts to achieve long-term ecological stability. 展开更多
关键词 Agricultural Land Use Ecological Balance Convergence Hypothesis Stochastic Dynamics Panel unit Root Tests Sustainable Development
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Robust tests of stock return predictability under heavy-tailed innovations
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作者 WONG Hsin-Chieh CHUNG Meng-Hua +1 位作者 FUH Cheng-Der PANG Tian-xiao 《Applied Mathematics(A Journal of Chinese Universities)》 2025年第1期149-168,共20页
This paper provides a robust test of predictability under the predictive regression model with possible heavy-tailed innovations assumption,in which the predictive variable is persistent and its innovations are highly... This paper provides a robust test of predictability under the predictive regression model with possible heavy-tailed innovations assumption,in which the predictive variable is persistent and its innovations are highly correlated with returns.To this end,we propose a robust test which can capture empirical phenomena such as heavy tails,stationary,and local to unity.Moreover,we develop related asymptotic results without the second-moment assumption between the predictive variable and returns.To make the proposed test reasonable,we propose a generalized correlation and provide theoretical support.To illustrate the applicability of the test,we perform a simulation study for the impact of heavy-tailed innovations on predictability,as well as direct and/or indirect implementation of heavy-tailed innovations to predictability via the unit root phenomenon.Finally,we provide an empirical study for further illustration,to which the proposed test is applied to a U.S.equity data set. 展开更多
关键词 domain of attraction of the normal law heavy-tailed least squares estimator predictive regres-sion unit root robust test
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Examination of Causal Relationship Among Consumer Goods Price Index, Bovine, and Water Buffalo Milk Price in Turkey With Vector Error Correction Model
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作者 Senol celik 《Economics World》 2016年第2期82-90,共9页
In this study, causalities among consumer goods price index (CPI), cattle milk price, and buffalo milk price are researched for Turkey using data covering the period from January 2005 to December 2014. The cointegra... In this study, causalities among consumer goods price index (CPI), cattle milk price, and buffalo milk price are researched for Turkey using data covering the period from January 2005 to December 2014. The cointegration analysis and vector error correction model (VECM) are used the casualty relationship among CPI, cattle milk piece, and buffalo milk piece in estimating. According to unit root test, results indicate that each of series is not stationary, when the variables are defined in levels; but that each of series is stationary, when the variables are defined in first differences. Johansen's cointegration test results show that there exists a long-run equilibrium relationship among CPI, cattle milk piece, and buffalo milk piece. It is concluded that there are three cointegration vectors in the data. Since the series are found to be cointegrated, it used VECM model to test the existence of causality. According to the VECM, there has been no long-term relationship among the variables. In the results of cointegration analysis, its relation between cattle milk piece and CPI is found to be negative. However, a positive relationship has been found between cattle milk price and buffalo milk piece. 展开更多
关键词 unit roots stationary lag number long-run changes short-run changes milk price
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The impact of bank lending on Palestine economic growth:an econometric analysis of time series data
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作者 Ibrahim M.Awad Mohammed S.Al Karaki 《Financial Innovation》 2019年第1期219-239,共21页
Banking is an essential sector of Palestine’s economy.More credits provided by banks are considered to have a positive impact on economic growth so that the overall objective of this study is to examine the impact of... Banking is an essential sector of Palestine’s economy.More credits provided by banks are considered to have a positive impact on economic growth so that the overall objective of this study is to examine the impact of bank lending on economic growth in Palestine.The study employs the Augmented Dickey-Fuller to test for stationarity in the time series,The Johansen co-integration,Vector Autoregressive Model and Vector Error Correction Model are employed to identify the long-run and short-run dynamics among the variables,and Granger causality test in order to determine the direction of causality.The study finds that a long run relationship exists among the variables and insignificant short run relationship.Also,the study findings show that there is unidirectional causality and runs from GDP to bank lending.The insignificant contribution of bank lending to GDP is attributed to the fact that banks are not highly interested in lending to the production sector of the economy due to the high level of risk.However,the primary empirical evidence reveals that bank lending doesn’t cause economic growth,but economic growth causes bank lending. 展开更多
关键词 Economic growth Error correction model Bank lending Granger causality test Palestine unit root tests Solow growth model
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The ASEAN experience of the purchasing power parity theory
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作者 S.M.Woahid Murad Mohammad Amzad Hossain 《Financial Innovation》 2018年第1期333-343,共11页
We used panel data analysis to evaluate the relative purchasing power parity(PPP)hypothesis of the ten ASEAN member countries between 1973 and 2015.We incorporated the cross-sectionally augmented panel unit root test ... We used panel data analysis to evaluate the relative purchasing power parity(PPP)hypothesis of the ten ASEAN member countries between 1973 and 2015.We incorporated the cross-sectionally augmented panel unit root test as proposed by Pesaran(J Appl Econ 22:265-312,2007).For panel cointegration analysis,we employed the four error-correction-based Westerlund(Oxf Bull Econ Stat 69:709-748,2007)panel cointegration tests.The Westerlund(Oxf Bull Econ Stat 69:709-748,2007)tests are general enough to permit a large degree of heterogeneity,both in the long-run cointegrating relationship and in the short-run dynamics,and dependence within as well as across the cross-sectional units.To check the robustness of the results,we further estimated the cointegration test excluding Indonesia and Brunei.The findings support our initial results.Further,all the results overwhelmingly support the relative PPP hypothesis.Consequently,the monetary authority would be able to implement a self-regulating monetary policy.It would also be able to control the exchange rates. 展开更多
关键词 Purchasing power parity Panel unit root test Panel cointegration test ASEAN countries
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Impact of Inflation, Dollar Exchange Rate and Interest Rate on Red Meat Production in Turkey: Vector Autoregressive (VAR) Analysis
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作者 Senol Celik 《Chinese Business Review》 2015年第8期367-381,共15页
In this study, impact of inflation (WPI--Wholesale Price Index), exchange rate, and interest rate on the production of red meat in Turkey was examined using the vector autoregressive (VAR) model. The model consist... In this study, impact of inflation (WPI--Wholesale Price Index), exchange rate, and interest rate on the production of red meat in Turkey was examined using the vector autoregressive (VAR) model. The model consisting of variables of dollar exchange rate, inflation rate, interest rate, beef, buffalo meat, mutton, and goat meat production amounts has been estimated for the period from 1981 to 2014. It has been detected that there is a tie among the dollar exchange rate, inflation rate, interest rate, and the amount of red meat production in Turkey. In order to determine the direction of this relation, Granger causality test was conducted. A one-way causal relation has been observed between: the goat meat production and dollar exchange rate; the buffalo meat production and the mutton production; and the beef production and the mutton production. To interpret VAR model, the impulse response function and variance decomposition analysis was used. As a result of variance decomposition, it has been detected that explanatory power of changes in the variance of dollar exchange rate, inflation rate, and interest rate in goat meat production amount is more than explanatory power of changes in the variances of mutton, beef, and buffalo meat variables. 展开更多
关键词 vector autoregressive (VAR) model impulse response analysis variance decomposition unit root test CAUSALITY red meat
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Effect of Macro Factor Volatility on the Returns of Financial Sector in Southeast Asian Stock Markets
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作者 Siriwun Wongsrida Prasert Chaitip 《Chinese Business Review》 2014年第1期28-33,共6页
The emphasis of this study is on the practice of the Pooled Mean Group (PMG) estimators to investigate the magnitude of macroeconomic performances: Real Gross Domestic Product (RGDP), Foreign Exchange Rate (EX)... The emphasis of this study is on the practice of the Pooled Mean Group (PMG) estimators to investigate the magnitude of macroeconomic performances: Real Gross Domestic Product (RGDP), Foreign Exchange Rate (EX), and Deposit Interest Rate (DINT) affecting on the rate of financial sector returns in Southeast Asian Stock Markets including Stock Exchange Of Thailand (SET) index (Thailand), the Kuala Lumpur Composite Index (KLSE) index (Malaysia), Financial Times Share Index (FTSI) (Singapore), Philippine Stock Exchange (PSE), and the Jakarta Composite Index (JKSE) (Indonesia). The Panel Autoregressive Distributed Lag (Panel ARDL) is applied to model the relations. The study applies the Levin, Lin, and Chu (LLC) test (2002) and Im, Pesaran, and Shin (IPS) test (2003) to investigates a set of time series data to examine whether the determinants and the rate of financial sector returns contain a unit root, the next step is investigated the cointegration and causality relationship of the determinants of financial sector influencing on long-run rate of returns of financial sector in Southeast Asian Stock Markets. 展开更多
关键词 rate of returns financial sector Southeast Asian Stock Markets panel unit root Panel AutoregressiveDistributed Lag (Panel ARDL)
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Problems Existed in Applications of Cointegration Theory in China
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作者 WANG Rui-ze 《Chinese Business Review》 2007年第2期43-46,共4页
Although the Cointegration Theory was founded by the C.W.J Granger and other economists in the 1980s, it was not widely used in China until C.W.J Granger was awarded with Nobel Prize in 2003. Since then, a lot of econ... Although the Cointegration Theory was founded by the C.W.J Granger and other economists in the 1980s, it was not widely used in China until C.W.J Granger was awarded with Nobel Prize in 2003. Since then, a lot of economic papers introducing or applying Cointegration Theory have emerged, but the phenomenon of misuse of this theory possibly arose at the same time. Based on some of these papers obtained from web site (www.cnki.net), this paper explores the applications of Cointegration Theory in China and draws some initial conclusions. Most of these applications are reasonable, but some of them are a bit blindfold or even contradictory in conclusions, which indicates that the overall application quality has a large room to get improved and should be paid more attention by academe. 展开更多
关键词 COINTEGRATION non-stationary time series unit root testing
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The weak form market efficiency investigation of American, European and Asian stock markets
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作者 Nuray Ergul 《Chinese Business Review》 2010年第10期1-11,共11页
This paper investigates the empirical validity of the Weak Form Efficient Market Hypothesis for American, European and Asian stock markets. Random Walk Hypothesis is used to prove weak form efficiency in American, Eur... This paper investigates the empirical validity of the Weak Form Efficient Market Hypothesis for American, European and Asian stock markets. Random Walk Hypothesis is used to prove weak form efficiency in American, European and Asian stock indices. ADF and PP Unit Root Tests have been used to test unit root in time series of daily data of American, European and Asian stock indices. Results show that sample of stock markets are weak-form efficient in terms of the Random Walk Hypothesis. 展开更多
关键词 weak form efficiency Random Walk Hypothesis unit root tests
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The Random Walk and Trend Stationary Models with an Analysis of the US Real GDP: Can We Distinguish between the Two Models?
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作者 Kazumitsu Nawata 《Open Journal of Statistics》 2021年第1期213-229,共17页
The unit root can lead to major problems in economic time series analyses. I obtain the asymptotic distributions of the ordinary least squares (OLS) estimator when the true model is trend stationary for the following ... The unit root can lead to major problems in economic time series analyses. I obtain the asymptotic distributions of the ordinary least squares (OLS) estimator when the true model is trend stationary for the following three cases: 1) the null model is a random walk without drift, and the auxiliary regression model does not contain a constant;2) the null model is a random walk with drift, and the auxiliary regression model contains a constant;and 3) the null model is a random walk with drift, and the auxiliary regression model contains both a constant and a time trend. In the third case, the asymptotic distribution of the OLS estimator is determined by the first order of the autocorrelation, and we can distinguish between the random walk and trend stationary models, unlike in previous studies. Based on these results, the real US gross domestic product is analyzed. A time trend model with autoregressive error terms is chosen. The results suggest that the impacts of a shock can become larger than the original shock in some periods and then gradually decline. However, the impacts continue for a long period, and policy makers should account for this to design better economic policies. 展开更多
关键词 Dickey-Fuller Test unit Root Random Walk Trend Stationary US GDP
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Relationship between the price of green tea and black tea of the world’s major tea countries
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作者 XU Yong-mei 《Ecological Economy》 2020年第2期82-89,共8页
Black tea and green tea are the most important tea in the world.In this paper we analyze the relationship of the world green price and black tea price.The results show that:in the world tea markets,the world black tea... Black tea and green tea are the most important tea in the world.In this paper we analyze the relationship of the world green price and black tea price.The results show that:in the world tea markets,the world black tea price and the world green tea price have no co-integration,independent of the curve segmentation.In the major green tea countries,there are co-integration relationships between China and Japan,China and Brazil,Japan and Brazil,while Vietnam has a first-order stationary sequence.In the major black tea countries,Sri Lanka and India have no co-integration,Sri Lanka and Indonesia no co-integration,India and Indonesia no co-integration,Sri Lanka and Kenya have co-integration,India and Kenya have co-integration,Kenya and Indonesia have co-integration. 展开更多
关键词 tea price green tea black tea unit root test Granger causality test co-integration test
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The Classification to Stationary Process of Tidal Motion Observed at the Time of Kuroshio’s Meandering
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作者 Kenta Kirimoto 《International Journal of Modern Nonlinear Theory and Application》 2023年第1期30-54,共25页
The tide level displays information about the state of the sea current and the tidal motion. The tide level of the southern coast of Japan Island is affected strongly by Kuroshio Current flowing in the western part of... The tide level displays information about the state of the sea current and the tidal motion. The tide level of the southern coast of Japan Island is affected strongly by Kuroshio Current flowing in the western part of North Pacific Ocean. When Kuroshio takes the straight path and flow along the Japan Islands, the tide level increases, and it is calculated from two tide level data observed at Kushimoto and Uragami in the southern part of Kii Peninsula. In contrast, the tide level decreases at the time when Kuroshio leaves from the Japan Islands. In this paper, the hourly tidal data are analyzed using the Autocorrelation Function (ACF) and the Mutual Information (MI) and the phase trajectories at first. We classify the results into 5 types of tidal motion. Each categorized type is investigated and characterized precisely using the mean tide level and the unit root test (ADF test) next. The frequency of the type having unstable tidal motion increases when the Kuroshio Current is non-meandering or in a transition state or the tide level is high, and the type shows a non-stationary process. On the other hand, when the Kuroshio Current meanders, the tidal motion tends to take a periodical and stable state and the motion is a stationary process. Though it is not frequent, we also discover a type of stationary and irregular tidal motion. 展开更多
关键词 Kuroshio Current Tide Level Autocorrelation Function Mutual Information unit Root Test Phase Trajectories Stationary Process
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