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系統識別號 U0002-1701200610380800
中文論文名稱 風險衡量與預測-以原油商品為例
英文論文名稱 Risk Measuring and Forecasting-The Case of Crude Oil
校院名稱 淡江大學
系所名稱(中) 財務金融學系博士班
系所名稱(英) Department of Banking and Finance
學年度 94
學期 1
出版年 95
研究生中文姓名 鄭婉秀
研究生英文姓名 Wan-Hsiu Cheng
學號 890490013
學位類別 博士
語文別 英文
口試日期 2005-12-24
論文頁數 75頁
口試委員 指導教授-邱建良
指導教授-李命志
委員-梁發進
委員-俞海琴
委員-葉銀華
委員-莊武仁
委員-謝文良
委員-李命志
中文關鍵字 原油  風險值  拔靴法  跳躍  預測包含力 
英文關鍵字 Crude oil  Vaule-at-Risk  Bootstrapping  Jump  Forecast encompassing 
學科別分類 學科別社會科學商學
中文摘要 風險之衡量與預測為財務上重要的課題,但多數文獻皆集中探討金融商品上之風險與預測,對於能源商品之探討相對較為缺乏。然而受到供需不均、國際石油輸出組織政策及政治面干涉等因素影響,原油市場的價格波動極大,油價持續向上攀升,不僅對原油市場的交易造成影響,金融市場亦間接受到不小衝擊。有鑑於原油市場價格之高度波動性,因此探討原油商品的風險亦為重要的課題。本文除修正傳統方法在衡量與預測上之不足,更進一步研究與分析西德州(West Texas Intermediate, WTI)原油商品之風險值、跳躍波動以及在預測上所面臨的問題。
第一個主題探討風險值。風險值是財務上最為廣泛用來估計風險的指標,本文採用RiskMetrics及AR-GARCH兩模型估計原油之風險值,結合移動視窗(rolling window)與拔靴法(bootstrapping)的方法進行估計。拔靴法解決了蒙地卡羅模擬法需要設定分配的假設及使用歷史模擬法恐有樣本資料不足的情形,因此晚近研究均以拔靴法取代財務上過去常用之蒙地卡羅模擬法與歷史模擬法。拔靴法的結果顯示在「估計期間外一天的預測 (one-day-ahead forecast)」風險值預測表現較佳,但「估計期間外十天的預測(ten-days-ahead forecast)」表現則不盡理想。另外,使用RiskMetrics或是AR-GARCH模型估計之預測績效差異不大。
第二個主題探討加入跳躍值來衡量原油與汽油之波動性。傳統模型多建立在連續且平穩的擴散過程上,一旦有異常事件發生,價格產生劇烈波動,估計結果將產生偏誤。因此,當面臨波灣戰爭之重大事件時,考量具間斷特性的跳躍模型有其必要性,藉以正確估計波動性。本文依據Chan (2003)所提出之雙變量跳躍GARCH模型估計原油與汽油間之波動性與相關性,並進一步探討兩次波灣戰爭期間,在價格上所造成之衝擊。實證結果發現,原油與汽油之跳躍點幾乎相同,但波動共移性的程度卻逐漸下降,共變異數在第二次波灣戰爭時明顯低於第一次波灣戰爭;而在波灣戰爭期間,原油之波動性高且較為敏感。再者,因戰爭所引起之大幅度波動皆未持續很長一段時間,符合跳躍模型之特性,因此,以此模型來估計原油商品的波動性是較為恰當的。
第三個主題探討樣本內估計期間長短對樣本外預測正確性所產生之影響,截至目前為止,少有文章將重心放在此研究主題上。本文同時採用預測包含力檢定(forecast encompassing)與預測誤差檢驗(mean square forecast errors, MSE)為模型選取的準則。一般而言,在適切的模型下,估計樣本期間越長,資訊漸趨完整,估計與預測結果將越正確;過短的估計期間將產生估計與預測偏誤的結果。針對此主題,本文針對一有結構性轉變之時間序列資料建立兩個實證模型,一包含結構性轉變,代表模型設定正確;另一則無結構性轉變,代表模型設定錯誤。此外,本文採用移動視窗與遞迴(recursive)的預測方式進行估計與預測,以檢驗樣本內估計期間長短對預測結果之影響。實證結果發現,正確模型的預測誤差隨著估計期間的增加而較低。當樣本估計期間較短時,將導致接受錯誤決策的結果。最後,本文將此結論應用於避險績效上,亦有一致性的結果,即避險績效在遞迴預測方式下最佳。
英文摘要 Risk measuring and forecasting are important issues in finance, however most literature focuses on the financial assets, and fewer papers discuss energy assets. The Petroleum market is characterized as highly volatile, the imbalance of supply and demand, the strategies adopted by the Organization of Petroleum Exporting Countries (OPEC), the interference of politics and so on have all stimulated prices. The oil prices have climbed up steadily recently, and it has not only shocked the petroleum market traders, but also influenced the financial market as well, owing to the high volatility of the crude oil. Thus the investigation of the crude oil risk is an important issue. This thesis analyzes the value-at-risk, the jump volatilities, and the forecast problems in crude oil of West Texas Intermediate (WTI), which modifies the shortcomings of traditional models in measurements and forecasts.
The first topic is discussing the Value-at-Risk (VaR). VaR is the most popular and attractive method of risk measuring. We estimate the VaR of the return on crude oil via RiskMetrics and the AR-GARCH model using the rolling bootstrapping methods. We adopt the bootstrapping method rather than using the Monte Carlo simulation or the historical simulation method because traditionally they are methods to estimate VaR. Even though they are traditional methods but they actually have the two severe problems of distribution assumption, Monte Carlo simulation, and a short observation period, historical simulation. The empirical results demonstrate that the bootstrapping method outperforms the no-bootstrapping method in the one-day-ahead VaR forecast but not in the ten-days-ahead forecasts. Furthermore, the performances of VaR forecasts are statistically indifferent in both the RiskMetrics and the AR-GARCH models.
The second topic is estimating the volatility of crude oil and gasoline while considering jumps. Previous studies in the literature almost all assumed that time series data follows a smooth and continuous volatility process. However, the presence of abnormal events induce serious violate in price, and the diffusion models are misspecified statistically. Therefore, considering the jump model with discrete characteristics is necessary while facing the abnormal events like two Gulf Wars. We further employ a correlated bivariate Poisson GARCH model suggested by Chan (2003) to investigate the relationship between the volatility of crude oil and gasoline; especially during the period of the Gulf War. We find that greater jumps occurring in crude oil returns will appear in gasoline returns at the same time, but the magnitude of the co-movements in volatility falls. The covariance is relatively smaller in the Second Gulf War compared to the first conflict. The volatility of crude oil is more sensitive than gasoline during the periods of wars. Furthermore, the jump that occurred by the war did not lead both spot prices to a high persistent level for a long period, which fits the feature of the jump models.
The third topic investigates an essential problem of how to determine the estimation period in forecasting. Until now, less attention has been given to the problem of determining the appropriate estimation periods. Using the forecast encompassing and accuracy test, this investigation discusses the importance of considering the overall useful information in the in-sample period. An excessively short sample period will increase the variance of the parameter estimation and bias the out-of-sample forecasts. This study further constructs a nested linear regression model, either with or without the structural change, depending on the existence of a break, and comparing the performance of the two versions of the model for each estimation period and forecast scheme. The empirical results demonstrate that forecasts under the correct model reduces both measurement loss and the mean square forecast as we increase the in-sample estimation period. For the forecast accuracy and encompassing tests, the use of fewer observations in making an estimate could easily lead to wrong decisions and the acceptance of the wrong model. Finally, these results are also consistent with the hedge effectiveness, namely that the effectiveness is better under the recursive scheme in terms of considering all useful information.
論文目次 TABLE OF CONTENTS
Page
ACKNOWLEDGEMENT i
ABSTRACT IN CHINESE ii
ABSTRACT IN ENGLISH iv
LIST OF TABLES xi
LIST OF FIGURES xii

PART I
Modeling Value-at-Risk for Oil Prices Using a Bootstrapping Approach
ABSTRACT 2
CHAPTER
1. Introduction 3
1.1 Motivations and Objectives 3
1.2 Flow Chart 5
2. Literature Review 6
2.1 Value-at-Risk in Crude Oil 6
2.2 Calculating the VaR 6
2.3 Observation Periods and Out-of-Sample Forecast 9
3. Measurement of Value-at-Risk 11
3.1 Definition of VaR 11
3.2 Statistical Tests 11
3.3 Estimate Methodology: Bootstrapping 12
3.4 Empirical Models 13
3.5 Observation Periods and Out-of-Sample Forecast in Rolling Window 15
4. Empirical Results 16
4.1 Data 16
4.2 Estimated Results of the RiskMetrics Method: Mean of the Decay Factor
16
4.3 Estimated Results and the Adaptation of the AR(1)-GARCH(1,1) Method
17
4.4 Failure Rates and the Performance of VaR Models 19
5. Conclusions 23
Bibliography 24

PART II
Correlated Jumps in Crude Oil and Gasoline during the Gulf War
ABSTRACT 28
CHAPTER
1. Introduction 29
1.1 Motivations and Objectives 29
1.2 Flow Chart 32
2. Literature Review 33
2.1 The Jump Model 33
2.2 The Bivariate Jump Model 34
3. Correlated Bivariate Poisson GARCH Model (CBP-GARCH) 36
3.1 Definition 36
3.2 The Probability Function of Jump and the Jump Intensity 37
3.3 GARCH Function 38
4. Empirical Results 40
4.1 Data 40
4.2 The Empirical Results of the CBP-GARCH Model 41
4.3 The Effects of Wars and Politics 45
4.4 The Covariance between Crude Oil and Gasoline 48
5. Conclusions 50
Bibliography 51

PART III
Enhancing the Forecast Accuracy by Using Long Estimation Periods
ABSTRACT 55
CHAPTER
1. Introduction 56
1.1 Motivations and Objectives 56
1.2 Flow Chart 58
2. Literature Review 59
2.1 Sample Period Length 59
2.2 Rolling Scheme vs. Recursive Scheme 59
2.3 Constructing Model with Structural Break 60
2.4 Out-of-Sample Forecast Error Tests 61
3. Methodology 63
3.1 The Model-Setting and Forecast Scheme 63
3.2 Forecast Accuracy and Forecast Encompassing Tests 63
4. Empirical Results 65
4.1 Data and the Empirical Model 65
4.2 The Empirical Results 66
4.2.1 Under the Rolling Scheme 66
4.2.2 Under the Recursive Scheme 68
4.3 Application in Hedge Effectiveness 69
5. Conclusions 72
Bibliography 73
LIST OF TABLE Page
PART I
Table 1. The mean of λ with the RiskMetrics method 16
Table 2. RESET test 17
Table 3. The empirical results of the AR(1)-GARCH(1,1) model 18
Table 4. The number of failure and the failure rates 20
Table 5. Failure rate test 21

PART II
Table 1. Descriptive statistics 40
Table 2. Empirical results of CBP model 42
Table 3. The covariance of crude oil and gasoline price in different periods 49

PART III
Table 1. Empirical results under the rolling scheme 67
Table 2. Empirical results under the recursive scheme 69
Table 3. Hedge effectiveness 71


LIST OF FIGURES
Page
PART I
Figure 1. The time series plot of crude oil prices from 1994/1/1 to 2004/7/31 3
Figure 2. The definition of observation periods and holding period 15
Figure 3. Crude oil returns and VaR with one-day-ahead forecast and 500-days
observation periods 21
Figure 4. Crude oil returns and VaR with ten-days-ahead forecast and 500-days
observation periods 22

PART II
Figure 1. The time series plot of the spot price of crude oil and gasoline 30
Figure 2. Returns of crude oil and gasoline 41
Figure 3. Time varying jump intensities in crude oil and gasoline 44
Figure 4. Correlated jump intensities and jump counter correlations 44
Figure 5. Jump variance in crude oil and gasoline 45
Figure 6. Jump covariance in crude oil and gasoline 45
Figure 7. The jump conditional variances and covariance during Gulf War I 48
Figure 8. The jump conditional variances and covariance during Gulf War II 48
參考文獻 part I
Basle Committee on Banking Supervision, 1995, An Internal Model-Based Approach to Market Risk Capital Requirements, Basle, Switzerland.
Bartolomei, S. M., and A. L. Sweet, 1989, A Note on a Comparison of Exponential Smoothing Methods for Forecasting Seasonal Series, International Journal of Forecasting, 5, 111-116.
Beltratti, A. and C. Morana, 1999, Computing Value at Risk with High Frequency Data, Journal of Empirical Finance, 6, 431-455.
Billo, M. and L. Pelizzon, 2000, Value-at-Risk: A Multivariate Switching Regime Approach, Journal of Empirical Finance, 7, 531-554.
Bollerslev, T., 1986, Generalized Autoregressive Conditional Heteroskedasticity, Journal of Economics, 31, 307-327.
Brooks, C., A. D. Clare and G. Persand, 2000, A Word of Caution on Calculating Market-Based Minimum Capital Risk Requirements, Journal of Banking and Finance, 14, 1557-1574.
Brooks, C., A. D. Clare and G. Persand, 2002, A Note on Estimating Market-Based Minimum Capital Risk Requirements: A Multivariate GARCH Approach, The Manchester School, 70, 666-681.
Cabedo, J. D. and I. Moya, 2003, Estimating Oil Price ‘Value at Risk’ Using the Historical Simulation Approach, Energy Economics, 25, 239-253.
Callen, J. L., C. C. Y. Kwan, P. C. Y. Yip and Y. Yuan, 1996, Netural Network Forecasting of Quarterly Accounting Earnings, International Journal of Forecasting 12, 1996, pp. 475-482.
Cassidy, C. and M. Gizycki, 1997, Measuring Trading Market Risk: Value-at-Risk and Backtesting Techniques, Reserve Bank of Australia, Research Discussion Paper.
Christoffersen, P. F. and F. X. Diebold, 2000, How Relevant is Volatility Forecasting for Financial Risk Management, Review of Economics and Statistics, 82, 12-22.
Christoffersen, P., J. Hahn and A. Inoue, 2001, Testing and Comparing Value-at-Risk Measures, Journal of Empirical Finance, 8, 325-342.
Dowd, K., 1998, Beyond Value-at-Risk, Wiley.
Engle, R., 1982, Autoregressive Conditional Heteroskedasticity with Estimates of Variance of United Kingdom Inflation, Econometrics, 50, 987-1007.
Giot, P. and S. Laurent, 2003, Market Risk in Commodity Markets: A VaR Approach, Energy Economics, 25, 435-457.
Giot, P. and S. Laurent, 2004, Modelling Daily Value-at-Risk Using Realized Volatility and ARCH Type Models, Journal of Empirical Finance, 11, 379-398.
Hendricks, D., 1996, Evaluation of Value-at-Risk Models Using Historical Data, Federal Reserve Bank of New York Economic Policy Review, April, 39-69.
Hsieh, D. A., 1993, Implications of Nonlinear Dynamics for Financial Risk Management, Journal of Financial and Quantitative Analysis, 28, 41-64.
J. P. Morgan / Reuters, 1996, RiskMetrics – Technical Document (4th edition), New York.
Jorion, P., 2002, Value-at-Risk: The New Benchmark for Controlling Market Risk (2d edition), New York McGraw-Hill.
Kupiec, P., 1995, Techniques for Varying the Accuracy of Risk Measurement Models, Journal of Derivatives, 2, 173-184.
Lacoursiere, C., 1997, VAR Comes to Energy Risk Management, Derivatives Strategy, March, 48-49.
Moosa, I. A. and B. Bollen, 2002, A Benchmark for Measuring Bias in Estimated Daily Value at Risk, International Review of Financial Analysis, 11, 85-100.
Pan, P. N. and W. H. Starbucks, 1990, Innocents in the Forest: Forecasting and Research Methods, Journal of Management, 16, 433-460.
Sadorsky, P., 1999, Oil Price Shocks and Stock Market Activity, Energy Economics, 21, 449-469.
Sarma, M., S. Thomas and A. Shah, 2003, Selecting of Value-at-Risk Models, Journal of Forecasting, 22, 337-358.
Siegl, T. and A. West, 2001, Statistical Bootstrapping Methods in VaR Calculation, Applied Mathematical Finance, 8, 167-181.
Swanson, N. R. and H. White, 1997, Forecasting Economic Time Series Using Flexible Versus Fixed Specification and Linear versus Nonlinear Econometric Models, International Journal of Forecasting, 13, 439-461.
part II
Ahn, D. H., R. Dittmar, and A. R. Gallant, 2002, Quadratic Term Structure Models: Theory and Evidence, The Review of Financial Studies, 15, 243-288.
Andersen, T. G., 1996, Return Volatility and Trading Volume: An Information Flow Interpretation to Stochastic Volatility, Journal of Finance, 51, 169-204.
Bahmani-Oskooee, M. and F. Brown, 2004, Kalman Filter Approach to Estimate the Demand for International Reserves, Applied Economics, 36, 1655-1668.
Bai, J. and P. Perron, 2003, Computation and Analysis of Multiple Structural Change Models, Journal of Applied Economics, 18, 1-22.
Baillie, R. T. and R. J. Myers, 1991, Bivariate GARCH Estimation of the Optimal Commodity Futures Hedge, Journal of Applied Economics, 6, 109-124.
Bjørnland, H. C., 2001, Identifying Domestic and Imported Core Inflation, Applied Economics, 33, 1819-1831.
Bollerslev, T., 1986, Generalized Autoregressive Conditional Heteroskedasticity, Journal of Economics, 31, 307-327.
Campbell, J. T., 1934, The Poisson Correlation Function, Proceedings of the Edinburgh Mathematical Society, Series 2, 18-26.
Chan, W. H. and J. M. Maheu, 2002, Conditional Jump Dynamics in Stock Market Returns, Journal of Business & Economic Statistics, 20, 377-389.
Chan, W. H., 2003, A Correlated Bivariate Poisson Jump Model for Foreign Exchange, Empirical Economics, 28, 669-685.
Chan, W. H., 2004, Conditional Correlated Jump Dynamics in Foreign Exchange, Economics Letters, 83, 23-28.
Chang, K. H. and M. J. Kim, 2001, Jumps and Time-varying Correlations in Daily Foreign Exchange Rates, Journal of International Money and Finance, 20, 611-637.
Chaudhuri, K., 2001, Long-run Prices of Primary Commodities and Oil Prices, Applied Economics, 33, 531-538.
Das, S. R., 2001, The Surprise Element: Jumps in Interest Rates, Journal of Econometrics, 106, 27-65.
Engle, R., 1982, Autoregressive Conditional Heteroskedasticity with Estimates of Variance of United Kingdom Inflation, Econometrics, 50, 987-1007.
Eraker, B., M. Johannes, and N. Polson, 2003, The Impact of Jumps in Volatility and Returns, Journal of Finance, 63, 1269-1300.
Ewing, B. T., F. Malik, and O. Ozfidan, 2002, Volatility Transmission in the Oil and Natural Gas Markets, Energy Economics, 24, 525-538.
Hammoudeh, S., H. Li and B. Jeon, 2003, Causality and Volatility Spillovers among Petroleum Prices of WTI, Gasoline and Heating Oil in Different Locations, North American Journal of Economics and Finance, 14, 89-114.
Jiménez-Rodríguez, R., and M. Sánchez, 2005, Oil Price Shocks and Real GDP Growth: Empirical Evidence for Some OECD Countries, Applied Economics, 37, 201-228.
Johannes, M., 2003, The Statistical and Economic Role of Jumps in Continuous-time Interest Rate Models, Journal of Finance, 59, 227-260.
Jorion, P., 1988, On Jump Processes in the Foreign Exchange and Stock Markets, Review of Financial Studies, 1, 427-445.
M’Kendrick, A. G., 1926, Applications of Mathematics to Medical Problems, Proceedings of the Edinburgh Mathematical Society, 44, 98-130.
Maheu, J. M. and T. H. McCurdy, 2004, News Arrival, Jump Dynamics and Volatility Components for Individual Stock Returns, Journal of Finance, 59, 755-793.
Pan, J., 2002, The Jump-risk Premia Implicit in Options: Evidence from an Integrated Time-series Study”, Journal of Financial Economics, 63, 3-50.
Ross, S. A., 1989, Information and Volatility: The No-Arbitrage Martingale Approach to Timing and Resolution Irrelevancy, Journal of Finance, 44, 1-17.
Sadorsky, P., 1999, Oil Price Shocks and Stock Market Activity, Energy Economics, 21, 449-469.
Taylor, S. J., 1986, Modeling financial time series, Wiley, Chichester.
part III
Bai, J. and P. Perron, 1998, Estimating and Testing Linear Models with Multiple Structural Changes, Econometrica, 66, 47-78.
Bai, J. and P. Perron, 2003, Computation and Analysis of Multiple Structural Change Models, Journal of Applied Econometrics, 18, 1-22.
Chauvet, M and S. Potter, 2002, Predicting a Recession: Evidence from the Yield Curve in the Presence of Structural Breaks, Economic letters, 77, 245-253.
Chong, Y. Y. and D. F. Hendry, 1986, Econometric Evaluation of Linear Macroeconomic Models, Review of Economic Studies, 53, 671-690.
Clark, T. E. and M. W. McCracken, 2001, Tests of Equal Forecast Accuracy and Encompassing for the Nested Models, Journal of Econometrics, 105, 85-110.
Clark, T. E. and M. W. McCracken, 2004, Improving Forecast Accuracy by Combining Recursive and Rolling Forecasts, Working Paper, Federal Reserve Bank of Kansas City and University of Missouri-Columbia.
Clements, M. P. and D. F. Hendry, 1993, On the Limitations of Comparing Mean Squared Forecast Errors: Comment, Journal of Forecasting, 12, 617-637.
Clements, M. P. and D. F. Hendry, 1998, Forecasting Economic Processes, International Journal of Forecasting, 14, 111-131.
Clements, M. P. and D. F. Hendry, 1999, Forecasting Non-stationary Economic Time Series, Cambridge, MA: MIT Press.
Diebold, F. X. and R. S. Mariano, 1995, Comparing Predictive Accuracy, Journal of Business and Economic Statistics, 13, 253-263.
Gabriel, A., S. Lopes and L. C. Nunes, 2003, Instability in Conintegration Regressions: A Brief Review with an Application to Money Demand in Portugal, Applied Economics, 35, 893-900.
Giacomini, R. and H. White, 2005, Test of Conditional Predictive Ability, Working Paper, University of California, San Diego.
Hamilton, J. D., 2001, A Parametric Approach to Flexible Non-linear Inference, Econometrica, 69, 537-573.
Harris, R. D. F. and J. Shen, 2003, Robust Estimation of the Optimal Hedge Ratio, Journal of Futures Markets, 23, 799-816.
Harvey, D. I., S. J. Leybourne and P. Newbold, 1998, Tests for Forecast Encompassing, Journal of Business and Economic Statistics, 16, 254-259.
Inoue, A. and L. Kilian, 2002, In-sample or Out-of-sample Tests of Predictability? Which One Should We Use? Working Paper, No. 195, European Central Bank.
Jardet, C., 2004, Why Did the Term Structure of Interest Rates Lose Its Predictive Power? Economic Modelling, 21, 509-524.
Koop, G. and S. Potter, 2000, Non-linearity, Structural Breaks, or Outliers in Economic Time Series, Chapter 4 in Non-linear Econometrics Modeling in Time Series Analysis, W. A. Barnett, D. F. Hendry, S. Hylleberg, T. Terasvirta, D. Tjostheim and A. Wurtz (Eds.), Cambridge University Press, 61-78.
Krolzig, H., 2001, Business Cycle Measurement in the Presence of Structural Change: International Evidence, International Journal of Forecasting, 17, 349-368.
McCracken, M. W., 2004, Asymptotics for Out of Sample Tests of Granger Causality, Working Paper, University of Missouri, Columbia.
Ng, H. G. and M. McAleer, 2004, Recursive Modelling of Symmetric and Asymmetric Volatility in the Presence of Extreme Observations, International Journal of Forecasting, 20, 115-129.
Pesaran, M. H. and A. Timmermann, 2004, How Costly Is It to Ignore Breaks When Forecasting the Direction of a Time Series? International Journal of Forecasting, 20, 411-425.
Rapach, D. and C. E. Weber, 2004, Financial Variables and the Simulated Out-of-sample Forecast Ability of U.S. Output Growth Since 1985: An Encompassing Approach, Economic Inquiry, 42, 717-738.
Shaffer, S., 2003, Using Prior Bias to Improve Forecast Accuracy, Applied Economic Letters, 10, 459-461.
Stock, J. H. and M. W. Watson, 2003, Forecasting Output and Inflation: The Role of Asset Prices, Journal of Economic Literature, 41, 788-829.
Swanson, N. R. and H. White, 1997, Forecasting Economic Time Series Using Flexible verses Fixed Specification and Linear versus Nonlinear Econometric Models, International Journal of Forecasting, 13, 439-461.
Wang, Z. and D. A. Bessler, 2004, Forecasting Performance of Multivariate Time Series Models with Full and Reduced Rank: An Empirical Examination, International Journal of Forecasting, 20, 683-695.
West, K. D., 1996, Asymptotic Inference about Predictive Ability, Econometrica, 64, 1067-1084.
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