Estimation for nearly unit root processes with GARCH errors

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.

A note on self-normalized Dickey-Fuller test for unit root in autoregressive time series with GARCH errors

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.

Characterizing the Urban Temperature Trend Using Seasonal Unit Root Analysis:Hong Kong from 1970 to 2015

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.

The Classification to Stationary Process of Tidal Motion Observed at the Time of Kuroshio’s Meandering

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.

The impact of bank lending on Palestine economic growth:an econometric analysis of time series data

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.

The ASEAN experience of the purchasing power parity theory

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.

The Random Walk and Trend Stationary Models with an Analysis of the US Real GDP: Can We Distinguish between the Two Models?

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.

Relationship between the price of green tea and black tea of the world’s major tea countries

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.

A Unit Root Test for an AR(1)Process with AR Errors by Using Random Weighted Bootstrap

A great deal of economic problems are related to detecting the stability of time series data,where the main interest is in the unit root test.In this paper,we consider the unit root testing problem with errors being long-memory processes with the LARCH structure.A new test statistic is developed by using the random weighted bootstrap method.It turns out that the proposed statistic has a chisquared distribution asymptotically regardless of the process being stationary or nonst at ionary,and with or without an intercept term.The simulation results show that the statistic has a desired finite sample performance in terms of both size and power.A real data application is also given relying on the inflation rate data of 17 countries.

Fiscal Sustainability:Public Revenue-Expenditure Nexus in a Few Asymmetric Countries in the Globe

This article examines the public revenue and expenditure patterns and its nexus of a few countries.This paper employs panel unit root,panel cointegration and Vector Error Correction Model to analyze the inter-temporal association among the variables of government revenues,expenditures and the growth of GDP through the panel data of ten divergent nations over the period 2001 to 2017.The study exercised three cointegration tests and these estimates find the evidence of long run association among articulated three variables.To know the cross-section status of different nations this paper diverted Phillips-Peron test with bandwidth statistics and it asserted that,all ten countries secured the long run association among the variables.The study uncovered that,growth of GDP has escalated in 0.78%by one percentage increase in revenue expenditure;meanwhile,1.41%lessening in GDP growth by one percentage increase in revenue income.The specified model is supported by a few diagnostic tests.

Research on Prediction of the Scale of OTC Drug Market in China Based on Quantitative Analysis

Objective To analyze the scale of domestic OTC drug market and its influencing factors,so as to predict its future market and provide a scientific basis for pharmaceutical enterprises to grasp the opportunities in the market.Methods The scale of OTC drug market from 1999 to 2018 in China and its influencing factors were analyzed by unit root test,Granger causality test and co-integration test.Results and Conclusion From the perspective of the global pharmaceutical market,OTC drug market has broad prospects and great development potential.Since the influence of GDP and the number of elderly populations on the scale of OTC drug market is positive,the predicted growth rate of OTC market in the next three years is 5.82%,5.86%and 5.90%,respectively.