CUSUM Of Squares Test Research Articles

Manufactured exports, disaggregated imports and economic growth: the case of Kuwait

This study investigates whether manufactured exports contribute to economic growth and whether imports can augment the role of exports in fostering export diversification. In the case of the latter, the study also examines which categories of imports are most likely to facilitate economic growth in the long run. In particular, the study focuses on the case of Kuwait over the period 1970–2019 and utilizes a Cobb–Douglas production function augmented with manufactured exports and primary and manufactured imports. The long-run relationships between the model variables are explored using two cointegration tests, namely the Johansen test and the dynamic ordinary least squares. The short-run causality is investigated utilizing the multivariate Granger approach in a vector autoregressive model, the parameters of which are assessed for stability using the CUSUM of squares test and recursive residuals plots. To examine the causal relationships in the long run, the Toda and Yamamoto test is applied. The cointegration tests show that the variables are cointegrated, while the Granger causality test shows that manufactured exports and disaggregated imports, together with the inputs of production, cause economic growth in the short run, which, in turn, leads to import growth. In the long run, the expansion of both primary and manufactured imports drives export diversification, whereas manufactured exports do not contribute to economic growth. These findings are very important for Kuwait’s policymakers to consider in their plans to implement Kuwait Vision 2035 as overseas demand for oil wanes.

Financial Innovation and Demand for Money in Nigeria

This study examined the impact of financial innovation on money demand in Nigeria, using quarterly time series for the period 2009-2019. The dependent variable was money demand, represented by broad money, while the independent variable was financial innovation represented by modern payment channels such as volume of Automated Teller Machines (ATMs) transactions, volume of Point of Sales (POS) transactions, volume of Internet banking transactions, and volume of Mobile banking transactions. The study employed the ordinary least squares (OLS) regression technique as the estimation method within the cointegration, granger causality, and error correction modelling. The result obtained showed that financial innovation has mixed impact on money demand in Nigeria during the period of analysis. For instance, financial innovation has positive impact on money demand through volume of ATM transactions in the current period, two periods lagged of volume of mobile banking transactions, current period and one period lagged of volume of internet banking transactions, and current period’s volume of Point of Sales (POS) transactions in Nigeria. On the other hand, financial innovation has negative impact on money demand through one period lagged of volume of point of sales in Nigeria. On the stability of the demand for money function, the result of the stability tests based on the CUSUM test and CUSUM of squares test showed that the demand for money function was stable during the evaluation period. The study recommended that monetary policy strategy of the central bank of Nigeria (CBN) should be fine-tuned to ensure it is well suited to deal with the challenges posed by financial innovation by way of proliferation of sophisticated payment channels.

Recent progress in parameter change test for integer-valued time series models

In this study, we review a recent progress regarding the change point test for integer-valued time series models, specifically concentrating on the CUSUM test for integer-valued autoregressive (INAR) and generalized autoregressive conditional heteroscedastic (INGARCH) models. Because time series often experience changes in underlying models, the change point test has been a fundamental issue in time series analysis during the past decades. We first introduce the CUSUM test in a general set-up and then construct estimate-, score vector- and residual-based CUSUM tests in INAR and INGARCH models and state their limiting null distributions. Finally, the residual-based CUSUM of squares test and the robust change point test based on the density power divergence are addressed.

Long-run and short-run responses of agricultural sector growth to its determinants in Nigeria

The study examined the long-run and short-run responses of agricultural sector growth to its determinants in Nigeria using time series data (1981 2015). Dynamic Ordinary Least Square (DOLS) method was employed in the analysis of the data. Jarque-Bera Normality Test, Breusch-Godfrey serial correlation LM test, Engle Granger 2-Step Test for Co-Integration and CUSUM of Squares Test were used to test for normality, serial correlation and structural dynamic stability of the data. The trend of agricultural sector growth revealed that sustained growth of the sector has been experienced since 2001 up till 2015. The results revealed that agricultural sector growth was positively and significantly influenced by capital expenditure in the sector, which was proxy by Total Government Agricultural Expenditure (TGAE), in the long-run; while in the short-run, the sector growth was positively and significantly influenced by labour employment. It is therefore recommended that for sustained agricultural sector growth and development in the country, increased capital expenditure in the sector should be pursued with sustained vigour. Since agriculture sector shows immediate and significant response to employment, it should be made attractive to youth employment by provision of incentive. This would ensure dual gain of tackling unemployment problem in the country and ensure agricultural sector growth.

Randomised Pseudolikelihood Ratio Change Point Estimator in Garch Models

In this paper, a randomised pseudolikelihood ratio change point estimator for GARCH model is presented. Derivation of a randomised change point estimator for the GARCH model and its consistency are given. Simulation results that support the validity of the estimator are also presented. It was observed that the randomised estimator outperforms the ordinary CUSUM of squares test, and it is optimal with large variance change ratios.

Financial Innovation and Demand for Money in Nigeria

This study examined the impact of financial innovation on money demand in Nigeria, using quarterly time series for the period 2009-2019. The dependent variable was money demand, represented by broad money, while the independent variable was financial innovation represented by modern payment channels such as volume of Automated Teller Machines (ATMs) transactions, volume of Point of Sales (POS) transactions, volume of Internet banking transactions, and volume of Mobile banking transactions. The study employed the ordinary least squares (OLS) regression technique as the estimation method within the cointegration, granger causality, and error correction modeling. The result obtained showed that financial innovation has mixed impact on money demand in Nigeria during the period of analysis. For instance, financial innovation has positive impact on money demand through volume of ATM transactions in the current period, two periods lagged of volume of mobile banking transactions, current period and one period lagged of volume of internet banking transactions, and current period’s volume of Point of Sales (POS) transactions in Nigeria. On the other hand, financial innovation has negative impact on money demand through one period lagged of volume of point of sales in Nigeria. On the stability of the demand for money function, the result of the stability tests based on the CUSUM test and CUSUM of squares test showed that the demand for money function was stable during the evaluation period. The study recommended that monetary policy strategy of the central bank of Nigeria (CBN) should be fine-tuned to ensure it is well suited to deal with the challenges posed by financial innovation by way of proliferation of sophisticated payment channels.

A bootstrap bias correction of long run fourth order moment estimation in the CUSUM of squares test

ABSTRACTThe aim of this paper is to propose a bias correction of the estimation of the long run fourth order moment in the CUSUM of squares test proposed in Sansó et al. [Testing for change in the unconditional variance of financial time series. Rev Econ Financ. 2004;4(1):32–53] for the detection of structural breaks in financial data. The correction is made by using the stationary bootstrap. The choice of this resampling technique is justified by the stationarity and weak dependence of the time series under the assumptions which ensure the existence of the limiting distribution of the test statistic, under the null hypothesis. Monte Carlo experiments have been implemented to evaluate the effect of the proposed bias correction considering two particular data generating processes, the GARCH(1,1) and the log-Normal Stochastic Volatility. The effectiveness of the bias correction has been evaluated also on real data sets.

Residual-based CUSUM of squares test for Poisson integer-valued GARCH models

ABSTRACTThis study considers the problem of testing for a parameter change in integer-valued time series models in which the conditional density of current observations is assumed to follow a Poisson distribution. As a test, we consider the CUSUM of the squares test based on the residuals from INGARCH models and find that the test converges weakly to the supremum of a Brownian bridge. A simulation study demonstrates its superiority to the residual and standardized residual-based CUSUM tests of Kang and Lee [Parameter change test for Poisson autoregressive models. Scand J Statist. 2014;41:1136–1152] and Lee and Lee [CUSUM tests for general nonlinear inter-valued GARCH models: comparison study. Ann Inst Stat Math. 2019;71:1033–1057.] as well as the CUSUM of squares test based on standardized residuals.

Crude oil market and global financial crisis - structural break and market volatility analysis

This research paper aims to analyse the impact of the recent global financial crisis on the volatility of crude spot market in India. The data has been collected for the period 2005 to 2014 from Multi Commodity Exchange, India. This paper first uses Ramsay RESET test to check the linearity of the relationship between spot and futures natural log returns. For structural break analysis, tests like Chow test, Chow forecast test, recursive estimates of CUSUM test and CUSUM of squares test have been performed on the monthly data of spot and futures price return series. No evidence of structural break was found in any test except CUSUM of squares test. Using EGARCH model with a dummy, we found that there was no effect of the global financial crisis on the volatility of crude spot market. The possible reason for the volatility of crude in 2008 could be financialisation of commodity exchanges and excessive speculation in crude oil futures.

Wachstum ohne Beschäftigung – empirische Evidenz aus Nahost und Nordafrika

In this study, we use Okun’s Law to examine whether growth has been jobless in seventeen MENA countries. The methods used are the ARDL approach for the individual country and the panel data analysis for the entire sample. The period considered in this study is from 1980 to 2013. To test for results robustness, we estimate the dynamic difference and three gap models based on three de-trending techniques: the HP filter, the BK filter, and the quadratic trend. Our findings can be summarized as follows: First, the estimation results suggest that Okun’s Law is valid, and hence job creation is associated with growth in only six of the seventeen countries, namely Algeria, Egypt, Iran, Jordan, Lebanon, and Turkey. Second, our results reveal that the valid estimates are, in general, bigger in Arab than non-Arab countries in the sample. Third, the CUSUM of squares test confirms that Okun’s Law is stable in Algeria, Egypt, and Iran, unstable in Jordan, and ambiguous in Lebanon and Turkey. Fourth, our panel data analyses suggest that Okun’s Law is valid for the entire MENA sample; however, our estimations reveal that the impact of GDP growth is weak on job creation in the region. Finally, our individual and panel estimations are not robust as they are sensitive to the choice of the estimation model and to the de-trending method.

CHANGE POINT TEST FOR DISPERSION PARAMETER BASED ON DISCRETELY OBSERVED SAMPLE FROM SDE MODELS

In this paper, we consider the cusum of squares test for the dispersion parameter in stochastic differential equation models. It is shown that the test has a limiting distribution of the sup of a Brownian bridge, unaffected by the drift parameter estimation. A simulation result is provided for illustration.

Subsampling tests for variance changes in the presence of autoregressive parameter shifts

In this paper, we consider the problem of testing for variance changes in the linear autoregressive processes including AR( p ) processes when there are autoregressive parameter shifts. In performing a test, we employ the conventional residual CUSUM of squares test (RCUSQ) statistic. The RCUSQ test is based on the subsampling method introduced by Jach and Kokoszka (2004) [16] to eliminate the influence caused by autoregressive parameter shifts. It is shown that under regularity conditions, the test statistic behaves asymptotically the function of a standard Brownian bridge. We establish the asymptotic validity of this method and assess its performance both theoretically and numerically.

Modified tests for variance changes in autoregressive regression

In this paper, we consider the problem of testing for variance changes in the linear autoregressive processes including AR( p) processes meanwhile autoregressive parameters shifts occur. In performing a test, we employ the conventional residual CUSUM of squares test (RCUSQ) statistic. The RCUSQ test is based on the bootstrap method introduced to eliminate the influence caused by the autoregressive parameters shifts. It is shown that under regularity conditions, the test statistic behaves asymptotically the function of a standard Brownian bridge. Simulation results as to AR(1) processes and an example of real data analysis are provided for illustration.

Estimation Mean Change-Point in ARCH Models with Heavy-Tailed Innovations

The quest of the mean change-point in ARCH models with innovations in the domain of attraction of a κ-stable law appears to still be ongoing. We derive the asymptotic distribution of the residuals CUSUM of squares test (RCUSQ) statistic and find it depends on the stable index κ which is often typically unknown and difficult to estimate. Therefore, the subsampling method is proposed to detect changes without estimating κ. The tests are easy to use and are found to perform well in a Monte Carlo experiment.

Bootstrap tests for structural change with infinite variance observations

The quest of structural change with infinite variance observations appears to be relatively common. Conventional residual CUSUM of squares test (RCUSQ) are unreliable in the presence of such behavior, having nonpivotal asymptotic null distributions. In this paper we propose a residual-based bootstrap approach to RCUSQ testing that is valid against a range of infinite variance processes. Our proposed method does not require the practitioners to specify knowledge for tailed index. Consistency and the rate of convergence for the estimated change point are also obtained. We also show via simulations that our asymptotic results provide good approximations in finite samples. In addition, we apply our results to investigate the original returns for NO.1 SDS using a historical data set that covers the period 1999–2002.

Subsampling tests for the mean change point with heavy-tailed innovations

The quest of the mean change point with innovations in the domain of attraction of a κ -stable law appears to still be ongoing. We adopt the residual CUSUM of squares test (RCUSQ) and derive its null asymptotic distribution, which is dependent on stable index κ . Then a residual-based subsampling is proposed to approximate the null distribution when stable index κ is unknown. Consistency and the rate of convergence for the estimated change point are also obtained. We establish the asymptotic validity of this method and assess its performance both theoretically and numerically.

Schwarz information criterion based tests for a change-point in regression models

Standard Schwarz information criterion for testing a change-point in regression models is considered and two new test procedures are evolved. The case of small sample size is investigated. Numerical approximations to the power against various alternatives are given and compared with powers of tests based on r-ahead recursive residuals and of the CUSUM of squares test. Application of these procedures to some real data is also provided.

The CUSUM of squares test for the stability of regression models with non-stationary regressors

In this paper, we propose a modified CUSUM of squares test in time series regression models with a non-stationary regressor and show that the limiting distribution of this test is the sup of the absolute value of a Brownian bridge.

A non-local perspective on the power properties of the CUSUM and CUSUM of squares tests for structural change

Abstract We consider the power properties of the CUSUM and CUSUM of squares (CUSQ) tests in the presence of a one-time change in the parameters of a linear regression model. A result due to Ploberger and Kramer [1990. The local power of the cusum and cusum of squares tests. Econometric Theory 6, 335–347.] is that the CUSQ test has only trivial asymptotic local power in this case, while the CUSUM test has non-trivial local asymptotic power unless the change is orthogonal to the mean regressor. The main theme of the paper is that such conclusions obtained from a local asymptotic framework are not reliable guides to what happens in finite samples. The approach we take is to derive expansions of the test statistics that retain terms related to the magnitude of the change under the alternative hypothesis. This enables us to analyze what happens for non-local to zero breaks. Our theoretical results are able to explain how the power function of the tests can be drastically different depending on whether one deals with a static regression with uncorrelated errors, a static regression with correlated errors, a dynamic regression with lagged dependent variables, or whether a correction for non-normality is applied in the case of the CUSQ. We discuss in which cases the tests are subject to a non-monotonic power function that goes to zero as the magnitude of the change increases, and uncover some curious properties. All theoretical results are verified to yield good guides to the finite sample power through simulation experiments. We finally highlight the practical importance of our results.

On the cusum of squares test for variance change in nonstationary and nonparametric time series models

In this paper we consider the problem of testing for a variance change in nonstationary and nonparametric time series models. The models under consideration are the unstable AR(q) model and the fixed design nonparametric regression model with a strong mixing error process. In order to perform a test, we employ the cusum of squares test introduced by Inclan and Tiao (1994,J. Amer. Statist. Assoc.,89, 913–923). It is shown that the limiting distribution of the test statistic is the sup of a standard Brownian bridge as seen in iid random samples. Simulation results are provided for illustration.