Comovements Between Diffusion Processes

1997 ◽  
Vol 13 (5) ◽  
pp. 646-666 ◽  
Author(s):  
Valentina Corradi
Keyword(s):  
Hypothesis Testing ◽  
Error Correction ◽  
Linear Combination ◽  
Diffusion Processes ◽  
Sampling Schemes ◽  
Long Run ◽  
Linear Diffusions

The aim of this paper is to characterize and analyze long-run comovements among diffusion processes. Broadly speaking, if X = (X1,,X2,;t ≥ 0) is a nonergodic diffusion in R2, but there exists a linear combination, say, γ′X, that is instead ergodic in R, then we say there exists a linear stochastic comovement between the components of X. Linear diffusions exhibiting stochastic comovements admit an error correction representation. Estimation of γ and hypothesis testing, under different sampling schemes, are considered.

Hypothesis testing with error correction models

2021 ◽  
pp. 1-9
Author(s):  
Patrick W. Kraft ◽  
Ellen M. Key ◽  
Matthew J. Lebo
Keyword(s):  
Hypothesis Testing ◽  
Error Correction ◽  
Null Hypothesis ◽  
Alternative Hypothesis ◽  
Correction Coefficient ◽  
Correction Model ◽  
Long Run ◽  
Independent Variable ◽  
The Right ◽  
General Error

Abstract Grant and Lebo (2016) and Keele et al. (2016) clarify the conditions under which the popular general error correction model (GECM) can be used and interpreted easily: In a bivariate GECM the data must be integrated in order to rely on the error correction coefficient, $\alpha _1^\ast$ , to test cointegration and measure the rate of error correction between a single exogenous x and a dependent variable, y. Here we demonstrate that even if the data are all integrated, the test on $\alpha _1^\ast$ is misunderstood when there is more than a single independent variable. The null hypothesis is that there is no cointegration between y and any x but the correct alternative hypothesis is that y is cointegrated with at least one—but not necessarily more than one—of the x's. A significant $\alpha _1^\ast$ can occur when some I(1) regressors are not cointegrated and the equation is not balanced. Thus, the correct limiting distributions of the right-hand-side long-run coefficients may be unknown. We use simulations to demonstrate the problem and then discuss implications for applied examples.

scholarly journals Semantically Secure Symmetric Encryption with Error Correction for Distributed Storage

2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
Juha Partala
Keyword(s):  
Error Correction ◽  
Network Coding ◽  
Linear Combination ◽  
Distributed Storage ◽  
Homomorphic Encryption ◽  
Error Correcting Codes ◽  
Symmetric Encryption ◽  
Goppa Codes ◽  
Linear Network ◽  
Linear Network Coding

A distributed storage system (DSS) is a fundamental building block in many distributed applications. It applies linear network coding to achieve an optimal tradeoff between storage and repair bandwidth when node failures occur. Additively homomorphic encryption is compatible with linear network coding. The homomorphic property ensures that a linear combination of ciphertext messages decrypts to the same linear combination of the corresponding plaintext messages. In this paper, we construct a linearly homomorphic symmetric encryption scheme that is designed for a DSS. Our proposal provides simultaneous encryption and error correction by applying linear error correcting codes. We show its IND-CPA security for a limited number of messages based on binary Goppa codes and the following assumption: when dividing a scrambled generator matrix G^ into two parts G1^ and G2^, it is infeasible to distinguish G2^ from random and to find a statistical connection between G1^ and G2^. Our infeasibility assumptions are closely related to those underlying the McEliece public key cryptosystem but are considerably weaker. We believe that the proposed problem has independent cryptographic interest.

The Methodology of Cointegration

1992 ◽  
Vol 4 ◽  
pp. 237-247 ◽  
Author(s):  
Nathaniel Beck
Keyword(s):  
Error Correction ◽  
Political Attitudes ◽  
Error Correction Model ◽  
Correction Model ◽  
Long Run ◽  
Economic Circumstance ◽  
Economics Department ◽  
Technical Area

It is hardly surprising that I applaud the fine work of both Durr and Ostrom and Smith. I am on record in favor of the utility of the error correction model (e.g., Beck 1985) and it is impossible to obtain a visa to visit the economics department at UCSD without swearing an oath of loyalty to the methodology of cointegration. The two works here are notable for their methodological sophistication, their exposition of a relatively unknown and highly technical area, and, most important, their substantive contributions. Both articles show that political attitudes (approval and policy mood) adjust, in the long run, to changes in objective and subjective economic circumstance. Both articles are good examples of the synergy of methods and theory, since it is the methodology of cointegration that leads to this type of theorizing, and this type of theorizing can most easily be tested in the context of cointegration or error correction.

scholarly journals Cointegration and error correction modelling of agricultural commodity trade: The case of ASEAN agricultural exports to the EU

2003 ◽  
Vol 12 (Supplement) ◽  
Author(s):  
J. NIEMI
Keyword(s):  
Error Correction ◽  
Agricultural Commodity ◽  
Commodity Trade ◽  
Price Changes ◽  
Agricultural Exports ◽  
Long Run ◽  
Export Supply ◽  
Asean Countries ◽  
The Eu ◽  
Modelling Approach

The objecti e of this study is to increase our understanding of the specification and estimation of agricultural commodity trade models as well as to provide instruments for trade policy analysis. More specifically,the aim is to build a set of dynamic,theory-based econometric models which are able to capture both short-run and long-run effects of income and price changes,and which can be used for prediction and policy simulation under alternati e assumed conditions.A relati ely unrestricted,data determined,econometric modelling approach based on the error correction mechanism is used,in order to emphasise the importance of dynamics of trade functions.Econometric models are constructed for se en agricultural commodities –cassa a,cocoa,coconut oil,palm oil,pepper, rubber,and tea –exported from the Association of Southeast Asian Nations (ASEAN)to the European Union (EU).With the aim of providing broad commodity co erage,the intent is to explore whether the chosen modelling approach is able to catch the essentials of the behavioural relationships underlying the specialised nature of each commodity market. The import demand analysis of the study examines two key features:(1)the response of EU ’s agricultural commodity imports to income and price changes,and (2)the length of time required for this response to occur.The estimations of the export demand relationships provide tests whether the exporters ’ market shares are influenced by the le el of relati e export price,and whether exports are affected by ariations in the rate of growth of imports.The export supply analysis examines the relati e influence of real price and some non-price factors in stimulating the supply of exports.The lag distribution (the shape and length of the lag)is found to be ery critical in export supply relationships,since the effects of price changes usually take a long time to work themselves through and since the transmission of the price effects can be complex.The set of dynamic econometric models estimated in the study are then used to simulate the effects different types of trade policies.More specifically,attempts are made to quantify the effects of a unilateral tariff remo al by the EU,an imposition of export subsidies and taxes by the ASEAN countries as well as exchange rate adjustments on ASEAN agricultural exports to the EU. The results suggest that concepts such as cointegration and error correction specification are well suited for the study of agricultural trade flows,which are typically non-stationary time series.The error correction specification is found to provide a good representation of the data-generating process for agricultural commodity flows from ASEAN countries to the EU.Furthermore,the study shows the importance of inspection of the time series properties and the examination of both short-and long-run adjustment when studying trade functions.The different dynamic responses are often critical to the outcomes of the types of trade policies considered.;

scholarly journals Empirical evidence of a long-run relationship between agriculture and manufacturing industry output in Nigeria

2019 ◽  
Author(s):  
Eze Osuagwu
Keyword(s):  
Error Correction ◽  
Empirical Evidence ◽  
Manufacturing Industry ◽  
Policy Implications ◽  
Necessary Condition ◽  
Macroeconomic Factors ◽  
Vector Error Correction ◽  
Vector Error ◽  
Long Run ◽  
Industry Output

<p>This study investigates a relationship between agriculture and manufacturing industry output in Nigeria from 1982-2015, using the Granger causality, co-integration and error correction techniques. Empirical evidence reveals a bidirectional relationship between the sectors. Although, a positive and significant relationship exists in the short and long-run estimates, a long-run divergence from the vector error correction model suggest that changes in agricultural productivity are not restored to equilibrium, given that macroeconomic factors distort the linkage. Policy implications indicate that macroeconomic stability is a necessary condition for agricultural and manufacturing sectors to foster economic growth.</p>

scholarly journals An application of the error correction model in analyzing the long run equilibrium between Ghana’s exports and imports

2015 ◽  
Vol 9 (3) ◽  
pp. 57-62
Author(s):  
Henry de-Graft Acquah ◽  
Joyce De-Graft Acquah
Keyword(s):  
Error Correction ◽  
Trade Deficit ◽  
Error Correction Model ◽  
Correction Coefficient ◽  
Equilibrium Relation ◽  
Macroeconomic Policies ◽  
Correction Model ◽  
Long Run ◽  
Step Procedure ◽  
Long Run Equilibrium

This study investigates the long-run relationship between Ghana’s exports and imports for the period of 1948 to 2012. Using the Engle Granger two-step procedure we find that Ghana’s exports and imports are cointegrated. However, the slope coefficients from the cointegration equations were not statistically equal to 1. Furthermore, application of the error correction model reveals that 1% increase in the imports will significantly result in 0.56% increase in exports, suggesting that the exports’ responsiveness to imports is low. The estimated error correction coefficient suggests that 32% of the deviation from the long run equilibrium relation is eliminated, leaving 68% to persist into the next period. These results suggest persistence in the trade deficit and an option of curbing the deficit is to re-order the relationship between imports and exports with a view to reducing imports demand. These results imply that though Ghana’s past macroeconomic policies have been effective in bringing its imports and exports into a long run equilibrium, it is yet to satisfy the sufficient condition for sustainability of foreign deficit.

scholarly journals Causality Analysis of Google Trends and Dengue Incidence in Bandung, Indonesia With Linkage of Digital Data Modeling: Longitudinal Observational Study

10.2196/17633 ◽  
2020 ◽  
Vol 22 (7) ◽  
pp. e17633 ◽  
Author(s):  
Muhammad Syamsuddin ◽  
Muhammad Fakhruddin ◽  
Jane Theresa Marlen Sahetapy-Engel ◽  
Edy Soewono
Keyword(s):  
Linear Combination ◽  
Stationary Process ◽  
Impulse Response Function ◽  
Google Trends ◽  
Digital Data ◽  
Causality Analysis ◽  
Long Term Effects ◽  
Long Run ◽  
Dengue Outbreaks ◽  
Long Run Equilibrium

Background The popularity of dengue can be inferred from Google Trends that summarizes Google searches of related topics. Both the disease and its Google Trends have a similar source of causation in the dengue virus, leading us to hypothesize that dengue incidence and Google Trends results have a long-run equilibrium. Objective This research aimed to investigate the properties of this long-run equilibrium in the hope of using the information derived from Google Trends for the early detection of upcoming dengue outbreaks. Methods This research used the cointegration method to assess a long-run equilibrium between dengue incidence and Google Trends results. The long-run equilibrium was characterized by their linear combination that generated a stationary process. The Dickey-Fuller test was adopted to check the stationarity of the processes. An error correction model (ECM) was then adopted to measure deviations from the long-run equilibrium to examine the short-term and long-term effects. The resulting models were used to determine the Granger causality between the two processes. Additional information about the two processes was obtained by examining the impulse response function and variance decomposition. Results The Dickey-Fuller test supported an implicit null hypothesis that the dengue incidence and Google Trends results are nonstationary processes (P=.01). A further test showed that the processes were cointegrated (P=.01), indicating that their particular linear combination is a stationary process. These results permitted us to construct ECMs. The model showed the direction of causality of the two processes, indicating that Google Trends results will Granger-cause dengue incidence (not in the reverse order). Conclusions Various hypothesis testing results in this research concluded that Google Trends results can be used as an initial indicator of upcoming dengue outbreaks.

scholarly journals The dynamic effect of exchange-rate volatility on Turkish exports: Parsimonious error-correction model approach

2015 ◽  
Vol 62 (4) ◽  
pp. 429-451 ◽  
Author(s):  
Erdal Demirhan ◽  
Banu Demirhan
Keyword(s):  
Exchange Rate ◽  
Error Correction ◽  
Exchange Rate Volatility ◽  
Dynamic Effect ◽  
Error Correction Model ◽  
Impulse Response Functions ◽  
Correction Model ◽  
Long Run ◽  
Export Volume ◽  
Short Run

This paper aims to investigate the effect of exchange-rate stability on real export volume in Turkey, using monthly data for the period February 2001 to January 2010. The Johansen multivariate cointegration method and the parsimonious error-correction model are applied to determine long-run and short-run relationships between real export volume and its determinants. In this study, the conditional variance of the GARCH (1, 1) model is taken as a proxy for exchange-rate stability, and generalized impulse-response functions and variance-decomposition analyses are applied to analyze the dynamic effects of variables on real export volume. The empirical findings suggest that exchangerate stability has a significant positive effect on real export volume, both in the short and the long run.

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