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Testing the order of integration of each individual series with the test of Robinson (1994) 

Testing the order of integration of each individual series with the test of Robinson (1994) 

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This paper examines the relationships between the CAC40 index, the Dow Jones index and the Euro/USD exchange rate using daily data over the period 1999-2008. We find that these variables are I(1) nonstationary series, but they are fractionally cointegrated: equilibrium errors exhibit slow mean reversion, responding slowly to shocks. Therefore, with...

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Citations

... Aloy et al. (2010) used fractional integration and co-integration in stock prices and exchange rates. They found that these variables are integrating order one nonstationary Sinha (2014) combined ANN and ARIMA model for time series forecasting. ...
Thesis
Agricultural datasets are mostly nonlinear, nonstationary and leptokurtic in nature. These properties of dataset pose a variety of problems in forecasting. Precise forecasting helps both farming community and policy makers to undertake informed decisions. Literature suggests that each of the forecasting models has their own limitations. A single forecasting model is not able to handle problems like nonstationary and nonlinearity simultaneously. Accordingly, the present study proposes three different hybrid models i.e. empirical mode decomposition based support vector regression (EMD-SVR), time-delay neural network with error correction term (TDNN-ECT) and multivariate adaptive regression splines based artificial neural network (MARS-ANN) models. The novelty of these models lies in the fact that they can handle both nonstationary and nonlinear features of dataset simultaneously. In EMD-SVR model, the nonstationary and nonlinear dataset is decomposed into different intrinsic mode functions and final residue through EMD method. Then the decomposed components are forecasted using SVR model and finally, all forecasted values are summed up to produce the final forecast. In the second model, TDNN-ECT uses the error correction term from the two co-integrated series as auxiliary variable. The auxiliary information in the form of ECT improves the forecasting accuracy. Further, selection of important input variables is a crucial step in determining the accuracy of any forecasting model. Hence, MARS-ANN hybrid model was developed in which the MARS algorithms was employed to extract important factors determining crop yield and the extracted factors were used for yield prediction using ANN methodology. The performance of proposed hybrid models is evaluated with individual forecasting models using three different agricultural datasets. The performance measures like RMSE, MAD, MAPE and ME are used to evaluate the model. The results indicated that the performance of the proposed hybrid models are substantially superior as compared to the individual forecasting model. Key words: Co-integration, Nonlinearity, Nonstationary, EMD, SVR, TDNN, and MARS.
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