Null Hypothesis Of Unit Root Research Articles

All Road User Casualties (Killed) in Great Britain from 1926. Linear and Nonlinear Trends with Persistent Data

This paper deals with the analysis of road casualties in Great Britain, using annual data since 1926. Based on the persistent nature of the data, fractional integration methods are used that include linear and non-linear (structural breaks) models. The results indicate that when the whole data set is employed the series is nonstationary I(1) implying permanency of shocks. However, considering data starting in 1964 we observe a significant negative time trend along with a lower degree of integration that implies transitory shocks. In order to avoid the abrupt change produced by the break, a nonlinear deterministic trend model based on Chebyshev polynomials in time is also considered with the whole sample, and though the order of integration is much lower than 1, the unit root null hypothesis cannot yet be rejected.

The Convergence Dynamics of Per Capita International Tourist Arrivals

ABSTRACT The study highlights the importance of comovements in tests of stochastic convergence in per capita international tourist arrivals for a large multi-country panel. LM unit root tests with allowance for comovements and structural breaks reveals a significant reduction in the number of rejections of the unit root null hypothesis when compared to LM unit root tests without comovements. Additional analysis allowing for Fourier gradual breaks confirms our findings of limited evidence of stochastic convergence. Upon further examination of convergence clubs, we identify four convergence clusters for per capita international tourist arrivals distinguished by whether a country is considered a small island economy.

전력 수요 시계열 분석과 장기예측

This study considers the time series characteristics in residential electricity demand function and forecasts long-run electricity demand in Korea. It is widely known that electricity demand and its determinants are unit root processes, so that estimating and forecasting the electricity demand function based on cointegration relationship are common in empirical analyses. We apply unit root tests on monthly time series data for the period 2006:01-2022:12. Korea has experienced the rapid development and social changes over this period, which provides convincing evidence of the possibility of structural changes. The unit root test of Dickey, Fuller (1979) tends to be biased in favor of non-rejection of the unit root null hypothesis if the process considered is trend-stationary with a slope change. What we found is that electricity demand and its determinants are trend-stationary processes allowing for a slope change, whereby there is no need to invoke either cointegration regression model or error-correction model under the unit root assumption. We apply a regression model with a structural change to estimate the residential electricity demand function and forecast the long-run electricity demand for the period 2023-2050.

Does the frequency of stochastic convergence in per capita ecological footprint matter?

Among the environmental economics research issues, the issue of convergence has received quite a lot of attention, which is also known as stationary analysis. In this research strand, whether shocks to the time series variable are permanent or temporary is tested via the unit root tests. In this study, based on the theory and empirical works of stochastic convergence, we evaluate the convergence for the BASIC member countries, including Brazil, South Africa, India, and China. We use a variety of methodologies to see whether the convergence of ecological footprint holds for these countries or not. We first use the wavelet decomposition technique to decompose the series into the short run, middle run, and long run, and then we run several unit root tests to confirm the stationarity property of the series. The methodologies implemented in this study allow us to apply econometric tests to the original series as well as to the decomposed series. The results of panel CIPS test demonstrate that the null hypothesis of unit root could be rejected for the short run but not for the middle and long run, implying that long-lasting impact might prevail due to any shocks to the ecological footprint in the middle and long run. The results for individual countries varied.

Gold and silver as safe havens: A fractional integration and cointegration analysis.

This paper investigates whether gold and silver can be considered safe havens by examining their long-run linkages with 13 stock price indices. More specifically, the stochastic properties of the differential between gold/silver prices and 13 stock indices are analysed applying fractional integration/cointegration methods to daily data, first for a sample from January 2010 until December 2019, then for one from January 2020 until June 2022 which includes the Covid-19 pandemic. The results can be summarised as follows. In the case of the pre-Covid-19 sample ending in December 2019, mean reversion is found for the gold price differential only vis-à-vis a single stock index (SP500). whilst in seven other cases, although the estimated value of d is below 1, the value 1 is inside the confidence interval and thus the unit root null hypothesis cannot be rejected. In the remaining cases the estimated values of d are significantly higher than 1. As for the silver differential, the upper bound is 1 only in two cases, whilst in the others mean reversion does not occur. Thus, the evidence is mixed on whether these precious metals can be seen as safe havens, though it appears that this property characterises gold in a slightly higher number of cases. By contrast, when using the sample starting in January 2020, the evidence in favour of gold and silver as possible safe havens is pretty conclusive since mean reversion is only found in a single case, namely that of the gold differential vis-à-vis the New Zealand stock index.

Stochastic structure of metal prices: Evidence from fractional integration non-linearities and breaks

This paper investigates the long memory properties of the prices series of two major precious metals (gold and silver) and six non-precious metals (aluminium, copper, lead, zinc, tin and nickel) by using a fractional integration modelling framework, while controlling for structural breaks and non-linearities. We use daily data in a range from November 01, 2007 to March 20, 2020. From the results, Copper and Tin exhibit a very small degree of mean reversion. However, if autocorrelation is permitted, the unit root null hypothesis cannot be rejected in any of the series. We also account for structural breaks and non-linearities. We observe that all the series under investigation are exposed to multiple breaks. Results obtained under white noise errors shows some evidence of mean reversion for silver aluminium, copper, tin and zinc in some of the subsamples. However, under the assumption of Bloomfield autocorrelated errors the confidence intervals are so wide that we cannot confirm this evidence in any single case.

Stock Market Efficiency in Asia: Evidence from the Narayan–Liu–Westerlund's GARCH‐based unit root test

AbstractStock market integration with efficiency is important in finance. This study therefore analyses the stock market efficiency in Vietnam and other Asian countries by using the recently developed Generalized Autoregressive Conditional Heteroscedasticity (GARCH)‐based unit root test of Narayan et al. to examine the stock market efficiency of Vietnam and other 18 Asian countries, using daily prices. Particularly, we examine weather stock market prices in these countries reflects all available information. The model flexibly accounts for heteroskedasticity and two structural breaks, the presence of which can lead to inaccurate results if neglected. Our results disclose the stock markets of 14 countries as inefficient following the rejection of the unit root null hypothesis. However, the stock markets of China, Hong Kong, Japan, and the Korea Republic are adjudged efficient. We further extend the model to accommodate a maximum of five breaks to check the robustness of our results to higher breaks. We observe that the results are largely consistent except for Lebanon and Singapore. For completeness, we compare the results with those of conventional GARCH models that do not account for structural breaks and discover differing results for some countries. Hence, the role of structural breaks is not negligible in assessing market efficiency. Future studies should also incorporate heteroskedasticity and structural breaks in their modelling framework to obtain accurate results.

Unit roots in lower-bounded series with outliers

This study examines a unit root process in lower-bounded time series with additive outliers. A standard unbounded unit root test may be unsuitable when applied to nonnegative or lower-bounded data; therefore, lower-bounded unit root tests that handle outliers are proposed. The results demonstrate that these tests reject less frequently the null hypothesis of unit root because of a nuisance parameter associated with the lower bound, either in homoskedastic or heteroskedastic settings. The empirical study of inflation and stock market volatility in South America reveals the presence of outliers related to the hyperinflation crisis and stock markets owing to multiple shocks, such as the recent COVID-19 pandemic. Moreover, these series cannot reject the unit root hypothesis if the lower bound is considered.

Testing for market efficiency in cryptocurrencies: evidence from a non-linear conditional quantile framework

ABSTRACT This study tests for the weak-form market efficiency of 15 cryptocurrency prices. The conventional unit root tests and stationary test results reveal that most cryptocurrency markets are efficient markets. However, the non-linear quantile unit root test proposed by Li and Park (2018) rejects the unit root null hypothesis over the whole quantile level. To derive more informative ideas, we split the whole quantile interval to several sub-intervals and find asymmetric behaviour of the market efficiency across the lower and upper sub-intervals in several cryptocurrency markets. Moreover, non-linear quantile unit root tests for Chainlink, Bitcoin Cash, Binance Coin, EOS, Tron, and Stellar indicate that markets for these cryptocurrencies are efficient at the upper sub-intervals.

Hysteresis and stochastic convergence in Eurozone unemployment rates: evidence from panel unit roots with smooth breaks and asymmetric dynamics

Research background: Studying the dynamic characteristics of unemployment rate is crucial for both economic theory and macroeconomic policies. Despite numerous research, the empirical evidence about stochastic behaviour of the unemployment rate remains disputable. It has been widely agreed that most economic variables, including unemployment rates, are characterized by both structural breaks and nonlinearities. However, a little work is done to examine both features simultaneously. Purpose of the article: In this paper, we analyse the stationarity properties of unemployment rates of Euro area member countries. Also, we aim to test stochastic convergence of unemployment rates among member countries. Our empirical procedures explicitly allow for simultaneous gradual breaks and nonlinearities in the series. Methods: This paper develops a new unit root test procedure for panel data, allowing for both gradual structural breaks and asymmetric adjustment towards equilibrium. We carry out Monte Carlo simulations to examine small sample performance of the proposed test procedure and compare it to the existing test procedures. We apply the newly proposed test to examine the stochastic properties of the unemployment rates of Euro-member countries as well as relative unemployment rates vis-?-vis the Eurozone unemployment rate. Findings & value added: We find that the newly developed test procedure outperforms existing tests in highly nonlinear settings. Also, these tests reject the null hypothesis of unit root in more cases when compared to the existing tests. We find stationarity in the series only after allowing for structural breaks in the data generating process. Allowing for nonlinear and asymmetric adjustment in addition to gradual breaks provides evidence of stationarity in more cases. Furthermore, our results suggest that relative unemployment rate series are stationary, providing evidence in favour of stochastic convergence in unemployment rates. Overall, our results imply a limited room for coordinated economic policy to fight unemployment in the Eurozone.

Purchasing Power Parity in Pakistan: Evidence from Fourier Unit Root Tests

ABSTRACT The paper empirically examines the validity of purchasing power parity (PPP) in Pakistan. For this purpose, unit root properties of real exchange rates (RERs) of Pakistan against its 21 major trading partners are examined using Fourier ADF (FADF) and Fourier KPSS (FKPSS) unit root tests for the period 1983Q1 to 2014Q4. Fourier unit root tests are used as they consider multiple temporary structural breaks and nonlinearity of the data. FADF test rejects the null hypothesis of unit root (non-stationary) in three RER series, while FKPSS test rejects the null hypothesis of stationary in nine RER series. Thus, FADF unit root test provide support for PPP hypothesis in three exchange rate series, while FKPSS test validates PPP theory in 12 exchange rate series. For robustness analysis, PPP equation is also estimated using regression analysis. The regression results show that PPP hypothesis is valid for nine exchange rate series. These findings suggest that PPP hypothesis partially holds in Pakistan.

Service Sector as an Engine of Growth: Empirical Analysis of Rwanda

This research was econometrically analyzing Service sector as an engine of growth: empirical analysis of Rwanda from 1995 to 2020. The data were collected from BNR and were analyzed using Eviews7. The study used different opinions of economists concerning the Philips curve, by constructing short-term and long-term Philips curves in Rwanda by making some conclusions about the results at the end. We pay special attention in our research to the study of Phillips curve made by some economists of the last period the findings of this study indicate the following results: *, ** and *** indicates rejection of the null hypothesis of unit root at 10, 5% and 1% significant level, respectively. The SERV, FDI, LR, GR series are not stationary at level, and then we should test the Stationarity at the first difference. (*), (**) & (***) represent respectively 10%, 5% and 1% level of significance.The results give an indication for the existence of long-run relationship between SERV and growth. The max and trace values statistic strongly reject the null hypothesis for “none “cointegration vector in favor of at least one cointegrating vectors at the 1 percent significance level. The cointegrating vector representing the long run relationship between service and growth. The above is endogenous because its probability of chi-square 0.000025 is less than 5% level of significance and it answers the second hypothesis of a Variable that can help national bank of Rwanda to control money supply in the short-run.The P- value of chi-square which is 0.0791 and this is greater than 0, 05 level of significant therefore, there is no short run causality between variables running from SERV, FDI, LR and GR at 5% level of significant. The results revealed out from the above table; LSERV, LFDI, LLR and LGR does Granger Cause LSERV at 10% level of significant due to their probability of 0.0284 which is less than 0.10 level of significance but LSERV does not Granger Cause LSERV, LFDI, LLR and LGR at 10% level of significant due to their probability of 0.1224 which is greater than 0.10 level of significance.

EMPIRICAL INVESTIGATION OF LONG RUN PPP HYPOTHESIS: THE CASE OF TEMPORARY STRUCTURAL BREAK AND ASYMMETRIC ADJUSTMENT

This study investigates the validity of the long-run PPP hypothesis for 60 economies using trade-weighted REER indices for the period 1994:01-2020:04. In addition to conventional tests, we also apply a battery of new unit root tests that allow for structural breaks and nonlinear adjustment. Our results suggest that test procedures that allow for both a structural break in the deterministic components of the series and nonlinearities in the adjustment towards equilibrium lead to a more frequent rejection of the unit root null hypothesis. In particular, after allowing for a temporary structural break in the series along with nonlinear adjustment towards the gradually changing equilibrium, we were able to reject the null hypothesis of unit root for all countries, thus providing some support for the PPP hypothesis.

Stochastic Pattern of Health Care Spending: Evidence from Nonlinear Panel Data Analysis

This paper analyses the stochastic pattern of health care spending for 188 countries around the world which are categorized into four groups based on the World Bank income categories. The main motivation of this article is to evaluate whether the stochastic features of total health care expenditure varies if decomposed into private and public health care consumption. To achieve this goal, in addition to conventional empirical methods, latterly developed panel stationarity approaches are employed for both linear and nonlinear regression processes. Our results demonstrate that allowing for cross-section dependency between series and nonlinearity in the estimation process may lead to more often rejection of the null hypothesis of unit root for all series in panel data set.

Are regional house prices stationary in Iran? New evidence using Fourier quantile unit root test

PurposeIn the Iranian economy, investing in the housing market has been very important and beneficial for investors and households, because of inflationary environment, low real interest rates, underdeveloped financial and tax systems and economic sanctions. Hence, prediction of house prices is the main concern of housing market agents in the economy. The purpose of this paper is to test the stationary properties of Iran's provinces to improve the prediction of future housing prices.Design/methodology/approachIn this paper, the authors have tested the stationary properties of 20 Iran’s province centers over the period from 1993 to 2017 using a novel Fourier quantile unit root test and conventional ordinary/generalized least squares (O/GLS) linear unit root/stationary tests.FindingsAccording to conventional O/GLS linear unit root/stationary tests, most of the house prices series exhibit random walk behavior, whereas by applying the Fourier quantile unit root test, the null hypothesis of unit root is rejected for 15 out of 20 series. Other results indicated that house prices of cities responded differently to positive and negative shocks.Originality/valuePrevious studies only addressed conventional OLS or GLS linear unit root or stationary tests, but novel Fourier quantile unit root test was not used. New results were obtained based on this unit root test, that, as a priori knowledge, will help benefiting from the positive effects, or avoiding being victimized by the negative effects.

Cryptocurrencies and stock market indices. Are they related?

In this paper, we investigate the stochastic properties of six major cryptocurrencies and their bilateral linkages with six stock market indices using fractional integration techniques. From the univariate analysis, we observe that for Bitcoin and Ethereum, the unit root null hypothesis cannot be rejected; for Litecoin, Ripple and Stellar, the order of integration is found to be significantly higher than 1; for Tether, however, we find evidence in favour of mean reversion. For the stock market indices, the results are more homogeneous and the unit root cannot be rejected in any of the series, with the exception of VIX where mean reversion is obtained. Concerning bivariate results within the cryptocurrencies and testing for cointegration, we provide evidence of no cointegration between the six cryptocurrencies. Along the same lines, testing for cointegration between the cryptocurrencies and the stock market indices, we find evidence of no cointegration, which implies that the cryptocurrencies are decoupled from the mainstream financial and economic assets. The findings in this paper indicate the significant role of cryptocurrencies in investor portfolios since they serve as a diversification option for investors, confirming that cryptocurrency is a new investment asset class.

A Simple Unit Root Test For Near Double-Integrated Time Series

We consider the problem of testing for unit root in time series where the error term of the series is near unit root. As the error term approaches unit root, existing tests no longer retain reasonable small sample properties. We introduce a test statistic that is well-behaved in small sample under such condition. Empirical applications reject the unit root null hypothesis for macroeconomic series, such as unemployment and consumer prices, where conventional unit root tests have been unable to do so.

Structural Breaks and Energy Consumption in the Gulf Cooperation Council Countries: Are Random Shocks Transitory or Permanent?

The impact of random shocks on the energy consumption of the Gulf Cooperation Council countries is essentially an empirical question which cannot be determined a priori without properly testing the integration properties of this variable. To this aim, we perform testing the unit root properties of this variable using both traditional unit root tests and the recently developed technique of the Fourier transformation function or simply known as the FADF test developed by Enders and Lee (2012), which not only takes into account for the existence of structural breaks but also that of non‐linearity in the energy consumption series of these countries. The results from the traditional unit root tests fail to reject the null hypothesis of non‐stationarity while that of the Fourier ADF unit root test which is more powerful has strongly rejected the null hypothesis of unit root for all the countries except Bahrain and Qatar. In sum, the results from this test indicate that the energy consumption variables of these countries are characterised by a stationary process and this has important policy implications. This suggests that these random shocks will have only a transitory effect on the energy consumption per capita of these countries.

Modeling calendar spread options

PurposeThe purpose of this paper is to derive a new option pricing model for options on futures calendar spreads. Calendar spread option volume has been low and a more precise model to price them could lead to lower bid-ask spreads as well as more accurate marking to market of open positions.Design/methodology/approachThe new option pricing model is a two-factor model with the futures price and the convenience yield as the two factors. The key assumption is that convenience follows arithmetic Brownian motion. The new model and alternative models are tested using corn futures prices. The testing considers both the accuracy of distributional assumptions and the accuracy of the models’ predictions of historical payoffs.FindingsPanel unit root tests fail to reject the unit root null hypothesis for historical calendar spreads and thus they support the assumption of convenience yield following arithmetic Brownian motion. Option payoffs are estimated with five different models and the relative performance of the models is determined using bias and root mean squared error. The new model outperforms the four other models; most of the other models overestimate actual payoffs.Research limitations/implicationsThe model is parameterized using historical data due to data limitations although future research could consider implied parameters. The model assumes that storage costs are constant and so it cannot separate between negative convenience yield and mismeasured storage costs.Practical implicationsThe over 30-year search for a calendar spread pricing model has not produced a satisfactory model. Current models that do not assume cointegration will overprice calendar spread options. The model used by the Chicago Mercantile Exchange for marking to market of open positions is shown to work poorly. The model proposed here could be used as a basis for automated trading on calendar spread options as well as marking to market of open positions.Originality/valueThe model is new. The empirical work supports both the model’s assumptions and its predictions as being more accurate than competing models.

The Efficient Market Hypothesis Re-Visited: New Evidence from 100 US Firms

In this paper, we test the efficient market hypothesis for 100 US firms listed on the New York Stock Exchange. To test the unit root null hypothesis, we develop a generalized autoregressive heteroskedasticity (GARCH) model that not only caters for the GARCH errors but also allows for two endogenous structural breaks in the data series. We study the size and power properties of the proposed GARCH structural break unit root test and find that it statistically performs well in finite samples. We find that only 22% of firms have a stationary stock price series.