An Essay on Cointegration and Error Correction Models

1992 ◽  
Vol 4 ◽  
pp. 185-228 ◽  
Author(s):  
Robert H. Durr
Keyword(s):  
Time Series ◽  
Error Correction ◽  
Empirical Models ◽  
Nonstationary Time Series ◽  
Longitudinal Analyses ◽  
Correlated Errors ◽  
Error Correction Models ◽  
Selective Perception ◽  
Post Hoc

For political scientists who engage in longitudinal analyses, the question of how best to deal with nonstationary time-series is anything but settled. While many believe that little is lost when the focus of empirical models shifts from the nonstationary levels to the stationary changes of a series, others argue that such an approach erases any evidence of a long-term relationship among the variables of interest. But the pitfalls of working directly with integrated series are well known, and post-hoc corrections for serially correlated errors often seem inadequate. Compounding (or perhaps alleviating, if one believes in the power of selective perception) the difficult question of whether to difference a time-series is the fact that analysts have been forced to rely on subjective diagnoses of the stationarity of their data. Thus, even if one felt strongly about the superiority of one modeling approach over another, the procedure for determining whether that approach is even applicable can be frustrating.

Auxiliary Modeling Procedures

2019 ◽  
pp. 136-153
Author(s):  
David McDowall ◽  
Richard McCleary ◽  
Bradley J. Bartos
Keyword(s):  
Time Series ◽  
Error Correction ◽  
Unit Root ◽  
Model Building ◽  
Causal Effect ◽  
Information Criteria ◽  
Unit Root Tests ◽  
Error Correction Models ◽  
Control Time ◽  
Model Building Strategy

Chapter 5 describes three sets of auxiliary methods that have emerged as add-on supplements to the traditional ARIMA model-building strategy. First, Bayesian information criteria (BIC) can be used to inform incremental modeling decisions. BICs are also the basis for the Bayesian hypothesis tests introduced in Chapter 6. Second, unit root tests can be used to inform differencing decisions. Used appropriately, unit root tests guard against over-differencing. Finally, co-integration and error correction models have become a popular way of representing the behavior of two time series that follow a shared path. We use the principle of co-integration to define the ideal control time series. Put simply, a time series and its ideal counterfactual control time series are co-integrated up the time of the intervention. At that point, if the two time series diverge, the magnitude of their divergence is taken as the causal effect of the intervention.

scholarly journals Novel FTLRNN with Gamma Memory for Short-Term and Long-Term Predictions of Chaotic Time Series

2009 ◽  
Vol 2009 ◽  
pp. 1-21
Author(s):  
Sanjay L. Badjate ◽  
Sanjay V. Dudul
Keyword(s):  
Neural Network ◽  
Time Series ◽  
Mean Squared Error ◽  
Chaotic Time Series ◽  
Nonstationary Time Series ◽  
Medium Term ◽  
Short Term ◽  
Squared Error ◽  
Wide Range

Multistep ahead prediction of a chaotic time series is a difficult task that has attracted increasing interest in the recent years. The interest in this work is the development of nonlinear neural network models for the purpose of building multistep chaotic time series prediction. In the literature there is a wide range of different approaches but their success depends on the predicting performance of the individual methods. Also the most popular neural models are based on the statistical and traditional feed forward neural networks. But it is seen that this kind of neural model may present some disadvantages when long-term prediction is required. In this paper focused time-lagged recurrent neural network (FTLRNN) model with gamma memory is developed for different prediction horizons. It is observed that this predictor performs remarkably well for short-term predictions as well as medium-term predictions. For coupled partial differential equations generated chaotic time series such as Mackey Glass and Duffing, FTLRNN-based predictor performs consistently well for different depths of predictions ranging from short term to long term, with only slight deterioration after k is increased beyond 50. For real-world highly complex and nonstationary time series like Sunspots and Laser, though the proposed predictor does perform reasonably for short term and medium-term predictions, its prediction ability drops for long term ahead prediction. However, still this is the best possible prediction results considering the facts that these are nonstationary time series. As a matter of fact, no other NN configuration can match the performance of FTLRNN model. The authors experimented the performance of this FTLRNN model on predicting the dynamic behavior of typical Chaotic Mackey-Glass time series, Duffing time series, and two real-time chaotic time series such as monthly sunspots and laser. Static multi layer perceptron (MLP) model is also attempted and compared against the proposed model on the performance measures like mean squared error (MSE), Normalized mean squared error (NMSE), and Correlation Coefficient (r). The standard back-propagation algorithm with momentum term has been used for both the models.

scholarly journals EFFECTS OF POLYNOMIAL TRENDS ON DETRENDING MOVING AVERAGE ANALYSIS

Fractals ◽  
2015 ◽  
Vol 23 (03) ◽  
pp. 1550034 ◽  
Author(s):  
YING-HUI SHAO ◽  
GAO-FENG GU ◽  
ZHI-QIANG JIANG ◽  
WEI-XING ZHOU
Keyword(s):  
Time Series ◽  
Numerical Experiments ◽  
Moving Average ◽  
Nonstationary Time Series ◽  
Hurst Index ◽  
Forward Algorithm ◽  
Average Analysis ◽  
Polynomial Trends ◽  
Linear Trends

The detrending moving average (DMA) algorithm is one of the best performing methods to quantify the long-term correlations in nonstationary time series. As many long-term correlated time series in real systems contain various trends, we investigate the effects of polynomial trends on the scaling behaviors and the performances of three widely used DMA methods including backward algorithm (BDMA), centered algorithm (CDMA) and forward algorithm (FDMA). We derive a general framework for polynomial trends and obtain analytical results for constant shifts and linear trends. We find that the behavior of the CDMA method is not influenced by constant shifts. In contrast, linear trends cause a crossover in the CDMA fluctuation functions. We also find that constant shifts and linear trends cause crossovers in the fluctuation functions obtained from the BDMA and FDMA methods. When a crossover exists, the scaling behavior at small scales comes from the intrinsic time series while that at large scales is dominated by the constant shifts or linear trends. We also derive analytically the expressions of crossover scales and show that the crossover scale depends on the strength of the polynomial trends, the Hurst index, and in some cases (linear trends for BDMA and FDMA) the length of the time series. In all cases, the BDMA and the FDMA behave almost the same under the influence of constant shifts or linear trends. Extensive numerical experiments confirm excellently the analytical derivations. We conclude that the CDMA method outperforms the BDMA and FDMA methods in the presence of polynomial trends.

scholarly journals Credit Risk Determinants in Indonesia

2018 ◽  
Vol 1 (2) ◽  
pp. 106-115
Author(s):  
Amin Yusuf Efendi
Keyword(s):  
Time Series ◽  
Interest Rate ◽  
Credit Risk ◽  
Error Correction ◽  
Error Correction Model ◽  
Series Data ◽  
Short Term ◽  
Correction Model ◽  
Spurious Regression

Credit is the main business of the banking industry, therefore, in running the business, the bank is always overshadowed by the credit risk the which can be determined by the ratio of non-performing loans (NPL). The development of technology, finance digital brings the outside could impact on the financial industry both positive and negative. The purpose of this study was to analyze the interest rate, inflation, exchange rates, gross domestic product (GDP), a dummy finance digitalization policies in the long term and the short term of the non-performing loan (NPL) of conventional commercial banks in Indonesia The analytical method used in this research is-EG Error Correction Model (ECM), The Data used in this research is secondary quarterly time series data from the 2008 quarter 1-2017 4. The time series of data are not stationar Often that can cause spurious regression results, the exact models used is-EG Error Correction Model (ECM), This models may explain the behavior of short-term and long-term. The results Showed in the short-term variable interest rates significanly to non-performing loans, while in the long-term variable interest rate, exchange rate, and GDP Significantly, non-performing loans. Kredit merupakan bisnis utama dari industri perbankan, oleh karena itu dalam menjalankan bisnisnya, bank selalu dibayangi oleh risiko kredit yang dapat diketahui melalui rasio non-performing loans (NPL). Perkembangan teknologi, menghadirkan digital finance yang membawa dampak luar bisa terhadap industri keuangan baik positif dan negatif. Tujuan dari penelitian ini adalah untuk menganalisis suku bunga, inflasi, kurs, produk domestik bruto (PDB) dummy kebijakan digitalisasi keuangan dalam jangka panjang dan jangka pendek terhadap non-performing loan (NPL) bank umum konvensional di Indonesia  Metode analisis yang digunakan dalam penelitian ini adalah Error Correction Model-EG (ECM). Data yang digunakan dalam penelitian ini adalah data sekunder runtut waktu kuartalan dari 2008 kuartal 1 – 2017 kuartal 4. Data runtun waktu sering tidak stationar sehingga bisa menyebabkan hasil regresi palsu (spurious regression), Model yang tepat digunakan adalah Error Correction Model-EG (ECM), model ini dapat menjelaskan perilaku jangka pendek dan jangka panjang. Hasil penelitian menunjukkan dalam jangka pendek variabel suku bunga berpengaruh secara signifikan terhadap non performing loan, sedangkan dalam jangka panjang variabel suku bunga, kurs, dan PDB berpengaruh secara signifikan terhadap non perfoming loan.

Market and Price Linkage for Dual-Listings

2013 ◽  
pp. 155-205
Keyword(s):  
Hong Kong ◽  
Error Correction ◽  
Information Flow ◽  
Quantitative Methods ◽  
Complex Environment ◽  
Chinese Firms ◽  
Error Correction Models ◽  
Price Changes ◽  
Arbitrage Opportunity

Chinese firms that cross-list in the China A-share market, China B-share market, Hong Kong, and other international locations operate in a complex environment. Theoretically, when one firm is trading on multiple exchanges, the shares across exchanges are expected to be perfect substitutes, and when they are not, an arbitrage opportunity exists. Using quantitative methods, this chapter explores whether there are price and volatility disparities. The Froot and Dabora (1999) approach is used to investigate which of the markets is dominant. Engle and Granger (1987) evaluates whether there is a long-term relationship between these markets, and error correction models are used to check for the speed at which prices are restored in equilibrium. Although the majority of cross-listed Chinese securities become cointegrated in the long term, the information flow exhibits a uni-directional feature and demonstrates that overseas markets have influential power over price changes.

Constructing Congressional Activity: Uncertainty and the Dynamics of Legislative Attention

2015 ◽  
Vol 6 (2) ◽  
pp. 299-321 ◽  
Author(s):  
Josh M. Ryan
Keyword(s):  
Error Correction ◽  
Policy Area ◽  
Error Correction Models ◽  
Electoral Incentives ◽  
Public Demand

Members and parties have electoral incentives to address issues on the congressional agenda to satisfy public demand. When determining which issues to address, majorities seek to minimize their uncertainty about the costs and electoral benefits of legislating by revisiting policy areas previously addressed. This theory is tested using error-correction models that demonstrate that policy activity within each chamber is in a long-term equilibrium and that the passage of legislation, even important bills, promotes future policymaking in the same policy area. This relationship is stronger when the majority has less information about the costs of lawmaking—specifically, when it faces a chamber controlled by the opposite party and when it is a new majority.

Continuous Dynamical Combination of Short and Long-Term Forecasts for Nonstationary Time Series

2014 ◽  
Vol 25 (1) ◽  
pp. 241-246 ◽  
Author(s):  
Domingos Savio Pereira Salazar ◽  
Paulo Jorge Leitao Adeodato ◽  
Adrian Lucena Arnaud
Keyword(s):  
Time Series ◽  
Nonstationary Time Series ◽  
Short And Long Term
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