CUSUM Test Research Articles

Takeoff Monitoring Algorithm with Prediction

A takeoff-monitoring algorithm is proposed that allows predicting the rate of an aircraft takeoff run and recognizing emergency situations that require reject the takeoff. The algorithm is based on combined use of a polynomial approximation of the dependence of the takeoff speed on time and the CUSUM test to detect abrupt changes in the dynamics of the aircraft. Mathematical modeling of the algorithm is presented using a model of a lightweight aircraft.

The Relationship between Electric Power Consumption, Foreign Direct Investment and Economic Growth in Sri Lanka

Purpose: This paper investigates the long run relationship between electricity consumption, foreign direct investment and economic growth in Sri Lanka.
 Design/Methodology/Approach: The annual time series data over the period 1970–2017 is considered to this study. Augmented Dickey–Fuller (ADF) unit root analysis is employed for examining the stationary properties of the variables. Consequently, Autoregressive Distributed Lag (ARDL) analysis is employed to examining the short- run and long-run relationship between electricity consumption, foreign direct investment and economic growth in Sri Lanka. Further, this study used the diagnostic tests such as the residual normality test, heteroskedasticity and serial autocorrelation tests for misspecification to validate the parameter estimation outcomes achieved by the estimated model. CUSUM test is applied to test the stability of the model. Collected data were analyzed using STATA version 15.
 Findings: The findings of the bound test confirm that the variables are cointegrated. Further the results reveal that there is a statistically positive significant relationship between electricity consumption, foreign direct investment and economic growth in Sri Lanka in the long run and short term. The empirical finding reveals that one percent increase in electricity consumption and foreign direct investment increases the GDP by 1.5 percent and 12.9 percent in the long run respectively.

Military Expenditure Economic Growth Nexus in Jordan: An Application of ARDL Bound Test Analysis in the Presence of Breaks

ABSTRACT The Hashemite Kingdom of Jordan is a nation that has persisted through turbulent times. The country’s leaders have long attempted to balance the allocation of resources between a strong military and a developing economy in their quest for stability, peace and prosperity. This paper examines and sheds further light on the relationship between Jordan’s military expenditure and its economic growth during the period 1970–2015. Using the Gregory -Hansen cointegration technique allowing for structural breaks, and the ARDL methodology this paper tests the short – and long–run equilibrium relationship between military expenditure and economic growth in Jordan. Furthermore, with the error correction model (ECM) and the CUSUM and CUSUMSQ tests, we examine the stability of the above relationship. The results reveal positive short – and long–run relationships between military expenditure and economic growth in Jordan, during the period under study. This finding has important policy implications for the Jordanian state, as it justifies the transfer of resources to the military, showing that it has not had a negative impact on economic growth.

Cusum tests for changes in the Hurst exponent and volatility of fractional Brownian motion

In this letter, we construct cusum change-point tests for the Hurst exponent and the volatility of a discretely observed fractional Brownian motion. As a statistical application of the functional Breuer–Major theorems by Bégyn (2007) and Nourdin and Nualart (2019), we show under infill asymptotics consistency of the tests and weak convergence to the Kolmogorov–Smirnov law under the no-change hypothesis. The test is feasible and pivotal in the sense that it is based on a statistic and critical values which do not require knowledge of any parameter values. Consistent estimation of the break date under the alternative hypothesis is established. We demonstrate the finite-sample properties in simulations and a data example.

Looking back over the past two decades on the nexus between air pollution, energy consumption, and agricultural productivity in China: a qualitative analysis based on the ARDL bounds testing model.

Increasing population and food demand has led to steadily declining resources as a result of over-exploitation and fossil fuel consumption that cause air contamination and reduce soil fertility. Therefore, this study aimed to investigate the correlation between air pollution, energy consumption, and the contribution of agriculture to national GDP. Secondary study data covering two decades were collected from different sources, and an autoregressive distributed lag (ARDL) bounds testing model was employed to determine long-run and short-run correlations. First, the unit root test was used to determine the stationarity of variables, and results showed that variables were integrated at level, ARDL co-integration equation estimation, which rejected the null hypothesis at less than 5% significance level. Further, based on the results of the ARDL bounds testing model, F-statistic values exceeded the upper bound value. This entire model was adjusted at a speed of -2.364 towards long-run equilibrium. In addition, CUSUM test and CUSUMSQ test results confirmed the goodness of fit of this model. In light of the resulting policy implications, the Chinese government may consider measures to improve the agricultural industry to meet the food demand for the fast-growing population while maintaining a healthy environment and safeguarding the available limited resources for future generations.

Numerical investigation on the power of parametric and nonparametric tests for trend detection in annual maximum series

Abstract. The need to fit time series characterized by the presence of a trend or change points has generated increased interest in the investigation of nonstationary probability distributions in recent years. Considering that the available hydrological time series can be recognized as the observable part of a stochastic process with a definite probability distribution, two main topics can be tackled in this context: the first is related to the definition of an objective criterion for choosing whether the stationary hypothesis can be adopted, whereas the second regards the effects of nonstationarity on the estimation of distribution parameters and quantiles for an assigned return period and flood risk evaluation. Although the time series trend or change points are usually detected using nonparametric tests available in the literature (e.g., Mann–Kendall or CUSUM test), the correct selection of the stationary or nonstationary probability distribution is still required for design purposes. In this light, the focus is shifted toward model selection criteria; this implies the use of parametric methods, including all of the issues related to parameter estimation. The aim of this study is to compare the performance of parametric and nonparametric methods for trend detection, analyzing their power and focusing on the use of traditional model selection tools (e.g., the Akaike information criterion and the likelihood ratio test) within this context. The power and efficiency of parameter estimation, including the trend coefficient, were investigated via Monte Carlo simulations using the generalized extreme value distribution as the parent with selected parameter sets.

Monitoring parameter changes in models with a trend

We develop a CUSUM-type monitoring procedure based on the ordinary least squares residuals for detecting structural changes in models with a trend. A proper boundary function is designed to control the size. We derive the limiting null distribution and the consistency of the procedure under the alternative. In addition, we derive the asymptotic distribution of the delay time for the CUSUM procedure as well as the fluctuation procedure proposed by Qi etal. (2016). The simulation and empirical results indicate that although neither procedure is uniformly superior to the other, the CUSUM test is more suitable for an early break.

Forecast for the Cameroon’s Residential Electricity Demand Based on the Multilinear Regression Model

The electricity needs of populations in Cameroon are increasing and are still very inadequate. Companies, public buildings and households are facing frequent blackout which constrain development and social well-being. Therefore, the present work tried to forecast the electricity demand in the residential sector in Cameroon, in order to contribute significantly to the mastery of electricity consumption and highlight decision-makers in this sector. Six macroeconomics parameters covering the period 1994-2014 are used for these issues. Stationarity tests within gross domestic product, gross domestic product per capita, electricity consumption, population and numbers of subscribers and households respectively; reveal that all the series are I(1). Thus, the VAR (Vector Autoregressive) model has been retained to forecast the electricity demand until 2020. The cusum test and the cusum of squared test attest the stability of that model with a margin of error of 0.02%. Previsions are then more reliable and show that the electric request will skip from 1721 GWh in 2014 to more than 2481 GWh in 2020 approximatively, following a growing yearly rate of 5.36%. In order to reach its emergence, Cameroon ought to speed up its production in the domain of hydroelectric and thermal grid in order to meet the requirements in electric power in short and long term.

Long-Run Money Demand in Ghana: In Search of Stability

In this study, we employed annual time series data of Ghana from 1982 to 2019 to examine the long-run money demand function and its stability. Through the methods of co-integration, Vector Error Correction Model, Auto-regressive Distributed Lag bounds test, CUSUM test (cumulative sum of the recursive residuals) and CUSUM sq test (cumulative sum squared of the recursive residuals) we established total stability and long-run relationship between money demand function and its determining factors. Accordingly, our key recommendation is for monetary policymakers to improve on their supervision and monitoring role in the financial market and institutions to avert failures within the sector such as what happened beginning 2014 with the proliferation of several Ponzi-schemes. Monitoring and supervision are key to the maintenance of confidence and stability in the monetary system.

Evaluation of the Analytical Performance of Lifotronic H9 Glycated Hemoglobin Analyzer and its Effect on Clinical Decision Making

We aimed to analyze the analytical performance of Lifotronic H9 glycated hemoglobin analyzer (Lifotronic H9) with Arkray Adams HA-8160 glycated hemoglobin analyzer (Arkray HA8160), which is currently used for measurement of HbA1c test in our laboratory. The verification studies of the Lifotronic H9 were performed by comparison with the Arkray HA8160, which has been verified and is already used in our laboratory, and in accordance with the CLSI EP5-A3 and CLSI 15-A3 guidelines. The method comparison study was performed with 316 subjects. Both instruments demonstrated perfect repeatability (within-run) CVs (0.8% - 1.6%), between-run CVs (0.2% - 1.0%), within-day CVs (0.8% - 1.7%), between-day CVs (0.3% - 0.6%), and within laboratory (total im-precision) CVs (0.8% - 1.8%) with two levels of quality control materials. Very good linearity was observed in the method-comparison studies based on Passing-Bablok regression analysis (y = -0.03 + 1.02 x, CUSUM test p = 0.07). Intraclass correlation coefficient (ICC = 0.995) for results and Kappa value (κ = 0.86) for classification of results according to the American Diabetes Association recommendations showed almost perfect agreement. The Lifotronic H9 analyzer shows good precision with lower than recommended total CV 2% and linearity with Arkray HA8160. The Lifotronic H9 is a suitable analyzer for the diagnosis of diabetes and monitoring diabetic control.

The stability of money demand in India in the post reform period: an empirical analysis

This paper provides an empirical analysis of the stability of demand for money in India using ARDL cointegration framework. The study of stability of money demand plays an important role in deciding the appropriate instruments of monetary policy. The present study examines the demand for money by using annual data over the period 1991-2015. The ARDL model bound test procedure has confirmed that a stable, long relationship exists between M1 and its determinants such as income, interest rates, exchange rates and inflation. Through results we conclude that income elasticity coefficient is positive and significant while the coefficient of inflation and interest rate is negative. Based on the Bahmoni-Oskooee and Pourhedrian (1990) argument, exchange rates negatively affect the demand for money. This study also examines the cointegration in the presence of structural break by using Gregory-Hansen single structural break approach. The study does not find any cointegration in presence of single structural break. Our result also reveals that M1 is stable between the sample period when we incorporated the CUSUM and CUSUMSQ tests.

The stability of money demand in India in the post reform period: an empirical analysis

This paper provides an empirical analysis of the stability of demand for money in India using ARDL cointegration framework. The study of stability of money demand plays an important role in deciding the appropriate instruments of monetary policy. The present study examines the demand for money by using annual data over the period 1991-2015. The ARDL model bound test procedure has confirmed that a stable, long relationship exists between M1 and its determinants such as income, interest rates, exchange rates and inflation. Through results we conclude that income elasticity coefficient is positive and significant while the coefficient of inflation and interest rate is negative. Based on the Bahmoni-Oskooee and Pourhedrian (1990) argument, exchange rates negatively affect the demand for money. This study also examines the cointegration in the presence of structural break by using Gregory-Hansen single structural break approach. The study does not find any cointegration in presence of single structural break. Our result also reveals that M1 is stable between the sample period when we incorporated the CUSUM and CUSUMSQ tests.

Do Google Trends and Shariah Compliant Stocks Co-Integrated? An Evidence from India

The objective of the study is to understand the dynamic relationship between Shariah-compliant stocks and the Google search value index (GSVI). The search strength is identified by the search volume of Shariah-compliant stocks on Google. The sample for the study consists of Shariah-compliant stocks commonly available in all the three Shariah indices in India, sample stock data has been extracted on a weekly basis from Sept 2014 to Sept 2019. The results of the study are based on the diagnostic analysis suggests that there is no serial correlation as demonstrated by LM residual test, CUSUM test shows stability in data, coefficient Wald test is showing there is no short-run causality running between selected Shariah-compliant stocks and GSVI. The outcome suggests that there is a long-run equilibrium relationship existing between Shariah-compliant stocks and the Google search value index. Trace statistics has five co-integration equations and Max-Eigen statistics has one co-integration. The vector error correction model (VECM) suggests the acceptability of the model. There are many potential investment opportunities for investors in the Islamic stock market of India. The motive of Shariah is to provide an avenue for ethical and viable investment to the investors. This study will not only be advantageous for the Muslim investors but also the other investors, industrialist, Shariah-compliant advisor as well.

Exploring the Climate Change Impact on Major Food Crops of Bangladesh - A Time Series Analysis

This paper tries to explore the dynamic relationship between the yield of major crops in Bangladesh (aus, amas, boro, wheat and potato) and climate change (average rainfall, average maximum temperature and average minimum temperature). Graphical visualization shows that, there is increasing trend in average annual minimum temperature and average annual minimum rainfall, while there is decreasing trend of average annual maximum temperature. We applied autoregressive distributive lag (ARDL) cointegration method in order to study the dynamic relationship. The paper finds long run dynamic link between yield of aus rice and average rainfall and average minimum temperature. We have found short run dynamic relationship for yield of aman rice, boro rice and potato. However, we do not find any dynamic relationship has been found for yield of wheat with the variables of climate change. After estimation the dynamic relationship, we ensure there is no serial correlation among residuals using Breusch-Godfrey test and models are normally distributed using histogram and Jarque-Bera test. Finally, we ensure the stability of the models applying CUSUM test.

Block bootstrapping for a panel mean break test

We consider block bootstrappings for panel mean change test of the squared CUSUM test of Horvath and Huskova (J Time Ser Anal 33:631–648, 2012): the circular block bootstrapping and stationary bootstrapping. First order asymptotic null validity of the test is proved under serial and/or cross-sectional correlation. Consistency of the test under an alternative hypothesis is also proved. A Monte-Carlo experiment reveals that the existing tests of Horvath and Huskova (2012) and others have severe size distortions for serially and/or cross-sectionally correlated panels, and the block bootstrappings remedy this size distortion problem. A real data analysis illustrates the proposed method.

Public debt, foreign direct investment and economic growth dynamics

Purpose The purpose of this paper is to examine the dynamic and long-run relationships among public debt, FDI and output growth in five individual Caribbean countries over the period 1975–2015. Design/methodology/approach Zivot and Andrews (1992) unit root test with structural break is used to examine the stationarity of the variables and then the autoregressive distributed lag bounds testing procedure is used to ascertain existence of cointegration among them. Finally, order-invariant generalized forecast error variance decomposition (GFEVD) is used to establish the strength of the causal relationship between the examined variables. Findings The results confirm that the examined variables are cointegrated. FDI, domestic investment, trade openness, human capital (HC) and institutional quality were found to have significantly positive effects on economic growth, while higher public debt and inflation rates hampered growth. GFEVD revealed unidirectional Granger causality running from FDI to economic growth in two countries; unidirectional causality from growth to FDI in two other countries; and bidirectional causality between growth and FDI in one other country. The results also indicate one-way causality from output growth to public debt in three countries and bidirectional causality between these two variables in two other countries. Practical implications The implication is that the Caribbean Governments may need to adopt effective debt management as a major policy and intensify efforts at utilizing loans obtained judiciously for human and capital projects that have direct positive net present value but, to secure strong and inclusive growth, these strategies must be linked to policies that enhance macroeconomic stability and the quality of their institutions, encourage capital inflows and domestic investments vis-à-vis domestic savings, and increase HC and trade earnings. Originality/value In contrast to extant studies of the public debt–FDI–output growth nexus, this study controls for the possibility of structural breaks in unit root tests along with performing bounds test for cointegration, variance decomposition analysis, Granger causality tests, and CUSUM and CUSUMSQ tests for the stability of the dynamic output growth model. This is a unique contribution to the existing literature, and highlights the originality value of this paper.

On partial-sum processes of ARMAX residuals

We establish general and versatile results regarding the limit behavior of the partial-sum process of ARMAX residuals. Illustrations include ARMA with seasonal dummies, misspecified ARMAX models with autocorrelated errors, nonlinear ARMAX models, ARMA with a structural break, a wide range of ARMAX models with infinite-variance errors, weak GARCH models and the consistency of kernel estimation of the density of ARMAX errors. Our results identify the limit distributions, and provide a general algorithm to obtain pivot statistics for CUSUM tests.

Learning curve in open inguinal hernia repair: a quality improvement multicentre study about Lichtenstein technique.

Inguinal hernia repair is one of the most performed procedure all over the world with more than 20 million procedures performed each year. Due to the lack of data in literature about the learning curve of the Lichtenstein procedure, we decided to reproduce a research on learning curves with the same methodology proposed in our previous study about laparoscopic hernia repair. The aim of this multicentre study was to analyse how many cases are required to achieve the learning curve for a Lichtenstein procedure. We performed a retrospective analysis of the first 100 Lichtenstein procedures performed by 4 trainees from three different institutions and compared them with the same number of procedures performed by 3 senior surgeons from the same institutions. The data about the achieving of learning curve were evaluated with CUSUM and KPSS test. No differences about biometrical features were found between the seven groups of patients. CUSUM analysis showed that the trainees achieve the learning curve after 37-42 procedures, reaching an operative time similar to that one of the senior surgeons. In conclusion, we have shown that the number of procedures required to reach the learning curve from the beginning of surgical residency is around 40 hernia repairs. This number, produced in a controlled environment under strict supervision, could be the minimum requirement to start the procedure of accreditation and specialization in hernia surgery and is higher and steeper than previously reported.

Comparison between bone alkaline phosphatase immunoassay and electrophoresis technique in hemodialysis patients.

Problem of the variability between the different methods using for bone alkaline phosphatase (bALP) determination greately influences the clinical significance of bALP as direct marker of bone metabolism. The aim of this study was to compare immunoassay with electrophoresis technique for bALP determination. We measured bALP in 71 patients on hemo - dialysis with agar gel electrophoresis (ISO-PAL, SEBIA) and immunoassay (OSTASE, Beckman Coulter). The analyzed methods showed significant correlation (Spearman's rho: 0.776, P < 0.01), but we found statistically significant (P < 0.01) positive bias (27%) for the results measured by immunoassay. In support of this, using electrophoresis technique we have detected presence of the intestinal isoenzymes of alkaline phosphatase in 55% of patients with median value of 30% of the total alkaline phoshatase and presence of liver-2 alkaline phosphatase isoform in 42% of patients with median value of 16.6%. The Kendall's W of 0.787 (P<0.0001) revealed significant concordance between two analysed methods. Cusum test showed no significant deviation from linearity (P=0.850). Despite good agreement between immuno - assay methods and electrophoresis technique for bALP determination, interchangeability between these two methods is questionable. Although immunoassays are increasingly used, as fully automated methods, in a large number of laboratories and become routine methods for bALP determination, it should be beared in mind, besides various interferences, also the heterogeneity of the bALP itself, especially in patients on hemodialysis.

Fixed-bandwidth CUSUM tests under long memory

A family of self-normalized CUSUM tests for structural change under long memory is proposed. The test statistics apply non-parametric kernel-based long-run variance estimators and have well-defined limiting distributions that only depend on the long-memory parameter. A Monte Carlo simulation shows that these tests provide finite sample size control while outperforming competing procedures in terms of power.