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Theoretical and Empirical Comparisons of Cointegration Tests

Thesis Info

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Author

Khan, Asad Ul Islam

Program

PhD

Institute

International Islamic University

City

Islamabad

Province

Islamabad.

Country

Pakistan

Thesis Completing Year

2018

Thesis Completion Status

Completed

Subject

Economics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/11631/1/Asad%20ul%20Islam%20Khan_Econometrics_2018_IIU_PRR.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676725143782

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During the last three decades, a variety of cointegration tests has been developed to investigate the long-run relationship between two data series. All these tests are based on different characteristics/structures of original time series. These tests were assessed for their performance on basis of their size and power properties using Monte Carlo simulations in a number of studies like, Banerjee, Dolado et al. (1986), Kremers, Ericsson et al. (1992), Haug (1996), Mariel (1996), Österholm (2003), Gabriel (2003), Pesavento (2004) and many more. However, these studies did not give a decisive conclusion that which test is performing better than rest. This is due to variant features of underlying series and every test has its domain of weaknesses and strengths. As it is the basic principle of comparison that tests can be compared on basis of their power properties only when all of tests have same size or stable size around nominal size. However, all of these comparisons were carried out using asymptotic critical values and their sizes were not same and stable. As almost all of comparisons were based on Monte Carlo simulations and the design of Monte Carlo supports the assumptions of model and in real data one doesn’t know whether the assumptions of model hold or not, so there was a gap in literature that these tests may be compared on basis of their size and power properties in a universal set of alternatives using Monte Carlo methods and also these tests may be compared on basis of some real economic data. To fill this gap, this study was carried out in which 24 cointegration tests were assessed for their performance. Out of these 24 tests, 16 tests belonged to the class with null hypothesis of no cointegration and 8 tests belonged to the class with null hypothesis ii of cointegration. These tests were evaluated on basis of stringency criterion (Zaman 1996) using Monte Carlo methods and on basis of Empirical Size and Power properties using real data of income and consumption of 100 countries from 1970 to 2014. First tests were assessed for their size stability using asymptotic critical values and then size of these tests was stabilized using simulated critical values. All of 24 tests were assessed on basis of stringency criterion using simulated critical values by considering two assumptions, one that the nature of deterministic part was known a priori and second that the nature of deterministic part was unknown, so an automatic selection procedure of deterministic part (Elder and Kennedy 2001) was followed. As it is strongly recommended by economic theory that income and consumption of same country are cointegrated and income and consumption of two different countries are not cointegrated, so on basis of this economic theory all of 24 tests were evaluated for their performance on basis of Empirical Size and Power. The study revealed that almost all of tests i.e. 21 out 24 had unstable size when asymptotic critical values were used and all of tests had stable size when simulated critical values were used. From tests with null hypothesis of no cointegration, Phillips and Ouliaris ˆ P m test was the leading performer as it was the most stringent test at all specifications of deterministic part. In addition to this test Choi Durbin-Hausman test, Phillips and Ouliaris’ ˆt Z test, Phillips and Ouliaris’ ˆ Z a test and the t-test of cointegration in a single equation Error Correction Model also performed overall better than rest of tests. Three tests i.e. Johansen Trace, Johansen Maximum Eigen Value and Phillips and Ouliaris ˆz P performed overall poor. In same manner from tests with null hypothesis of cointegration LM test based on KPSS statistic was the leading performer as it was the iii most stringent test for all of three specifications of deterministic part. Shin’s C test was the second overall better performing test and three tests i.e. Xiao Fluctuation, Hansen’s cL and Hausman H1 overall performed poorly. It was also revealed that on basis of real data comparison tests with null hypothesis of no cointegration performed way well as compared to tests with null hypothesis of cointegration. On basis of real data, from tests with null hypothesis of no cointegration five tests i.e. the t-test of cointegration in a single equation Error Correction Model, Boswijk Wald test, Phillips and Ouliaris ˆ P m test, Phillips and Ouliaris’ ˆ Z a test and Choi Durbin-Hausman test were the leading performers both in terms of Empirical Size and Power. However, on basis of real data, from test with null hypothesis of cointegration not a single test had performance that is worth to mention. It is recommended in light of our study that use of asymptotic critical values may be eluded and instead simulated critical values may be used. It is also recommended that tests with null hypothesis of no cointegration may be given preference over tests with null hypothesis of cointegration for a specific real economic problem and if tests with null hypothesis of cointegration are used then, they may only be used for confirmatory purposes. Five tests with null hypothesis of no cointegration are recommended and these are Phillips and Ouliaris ˆ P m test, the t-test of cointegration in a single equation Error Correction Model, Boswijk Wald test, Phillips and Ouliaris’ ˆ Z a test and Choi Durbin-Hausman test. Similarly, from tests with null hypothesis of cointegration only one test i.e. LM test based on KPSS statistic may be used for confirmatory purpose.
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پاپائے رومہ بنڈکٹ پانزدہم

پاپائے رومہ ، بنڈکٹ پانز دہم

            آغاز سال رواں میں پاپائے رومہ، بنڈکٹ پانز دہم نے انتقال فرمایا، ان سطروں کے شائع ہونے تک ان کے جانشین کا بھی انتخاب ہوچکا ہوگا، جس وقت سے پاپائیت کا باضابطہ عہدہ قائم ہوا ہے، صدہا افراد اس منصب پر مامور رہ چکے ہیں، بلکہ اگر ابتدائی عیسوی صدیوں کے بشپ صاحبوں کو بھی اس فہرست میں شامل سمجھا جائے تو شاید شمار سیکڑوں سے متجاور ہوجائے، سوال صرف اس قدر ہے کہ اس طویل و عظیم فہرست میں کسی غیر یورپی شخص کا بھی نام تلاش کرنے سے مل سکتا ہے؟ مسیحیت کے حدود تو ماشاء اﷲ ایشیاء، افریقہ کے گوشہ گوشہ تک وسیع ہوچکے ہیں اور ان ممالک میں کروڑوں باشندہ ’’ابن اﷲ‘‘ کے کلمہ گو موجود ہیں، پھر کیا اب تک ان بے شمار نفوس میں ایک شخص بھی یورپی مسیحیوں کی ہم سطح وہم پلہ نہیں پیدا ہوسکا ہے؟

(سید سليمان ندوی، فروری ۱۹۲۲ء)

 

مشكلات التمويل بالمرابحة من وجهة نظر العملاء (دراسة ميدانية على عينة من عملاء المصارف المتمولين بالمرابحة بمدينة الأبيض)

هدفت الدراسة إلى التعرف على المشكلات التي تواجه عملاء المصارف عند طلب التمويل بالمرابحة، واقتراح الحلول اللازمة لمعالجة هذه المشكلات حتى تتحقق الاستفادة الكاملة من فرص التمويل بالمرابحة، وقد أظهرت نتائج الدراسة أن من المشكلات التي تواجه العملاء عند طلب التمويل بالمرابحة تتمثل في: تحديد البنك المركزي لمجالات محددة للتمويل بالمرابحة وعدم السماح لبعض المجالات الأمر الذي يؤدي إلى حرمان بعض العملاء من الاستفادة من هذا التمويل، وأن السقوفات التي يضعها البنك المركزي للتمويل بالمرابحة ولا يسمح بتجاوزها لا تتناسب والطموحات الاستثمارية لبعض العملاء، وأوصت الدراسة بضرورة سماح البنك المركزي للمصارف بالتوسع في مجالات التمويل بالمرابحة، والسماح بزيادة سقوفات التمويل بالمرابحة حتى تتحقق الاستفادة الكاملة من هذا التمويل. الكلمات المفتاحية: المرابحة، مشكلات التمويل بالمرابحة. المصارف

Automation of Software Modeling and Verification

Formal methods help in quantifying the functional and nonfunctional requirements that are later used in the verification process for safety assurance in real-time systems. System formalism is a crucial step in terms of exploring system’s behavior and listing the non-functional requirements. In the context of real-time systems, the non-functional requirements refer to the verification properties of the system. Formalism in software development life cycle refines every process, starting from the formalization of system''s requirements, analysis of system''s behavior and exploring its properties, implementation of the problem''s solution under consideration and verification of safety critical properties. Rule-based Expert System helps in inferring unknown on the basis of some known input, that is, knowledge and rule-set. Knowledge comprises of something known by an individual called as an expert of that domain. It requires an expert skill set (that is, syntax and notations of the Model Checker and Verifier) in order to model and verify some system in Model Checkers like UPPAAL. This research consists of three parts. Firstly, it explores the variations (two case studies) of traffic light systems, models the systems in UPPAAL model checker and later verifies the safety critical properties of the generated systems like safety, live-ness, fairness, reachability and deadlock freeness. Experimental results are recorded for both systems with variety of search options to check the time efficiency. Second part of the research deals with the computational conversion via translation rules for transforming C++ code into UPPAAL’s automata and then cross-checked the validity of transformation rule set. This part focuses on providing the rule-based expert system for inferring timed automata (input of UPPAAL Model Checker) on the basis of fact cum input, that is, C++ code. Structural facts are used along with the transformation rule set to get the timed automata that verifies safety properties of selected case studies – multiple variations of Traffic Light System. Last part of the research is related to the reverse engineering of the verification artifact back to the implemented code. Experimental results of the first contribution show that verification time used by the UPPAAL model checker is worth mentioning for safety and deadlock freeness properties. Kernel responded all properties in no time, but the deadlock property took 0.01seconds. Elapsed time is the one that responds uniquely for all of the verified properties. Safety property took maximum elapsed time i.e., 0.02 seconds and with fractional change deadlock freeness property has 0.018 seconds of elapsed time used. Outcome of the second part that is, translation from C++ code to UPPAAL model is verified successfully. In the proposed methodology, the correctness of the transformation is crosschecked twice. Firstly, the informally mentioned behavior of C++ program is presented in the transformed automata and secondly the interaction among the functions via function call is preserved in UPPAAL’s automata via synchronization of channels. Third part is successfully reverse engineered from UPPAAL’s automata to C++ code.