Non linear model predictability of vietnam stock market price

NATIONAL ECONOMICS UNIVERSITY INSTITUTE OF SOCIAL STUDIES HANOI THE HAGUE VIETNAM – NETHERLANDS CENTER FOR DEVELOPMENT ECONOMICS AND PUBLIC POLICY Non-linear model predictability of Vietnam stock market price A thesis presented by DINH VAN TUAN– MDE15 In partial fulfillment of the requirements for the obtaining the Degree of ên uy Ch MASTER OF ARTS IN DEVELOPMENT ECONOMICS đề Supervisor Ph.D NGUYEN VIET HUNG c ự th p tậ Tố HANOI - 2012 p iệ gh tn CERTIFICATION "I certify that the substance of this dissertation has not already been submitted for any degree and is not being currently submitted for any other degree I certify that to the best of my knowledge any help received in preparing this dissertation, and all sources used, have been acknowledged in this dissertation" Dinh Van Tuan November, 2011 ên uy Ch đề c ự th p tậ p iệ gh tn Tố LIST OF CONTENTS ACKNOWLEDGEMENTS ABBREVIATION LIST OF TABLES .5 LIST OF FIGURES CHAPTER 1: INTRODUCTION .7 1.1 Problem Statement 1.2 Reseach Objective .8 1.3 Research questions 1.4 Literature review .8 1.5 Thesis Methodology 11 1.6 Thesis Structure .11 CHAPTER 2: ANALYTICAL FRAMWORK 12 2.1 Concept and Definition 12 2.2 Models for predicting stock market price 13 CHAPTER 3: PERFORMANCE OF VIETNAM STOCK MARKET .19 Ch 3.1 Overview of Vietnam Stock Market .19 ên uy 3.2 Performance of five Blue Chips in therecent time 27 CHAPTER 4: MODEL SPECIPICATION AND DATA ANALYSIS 32 đề 4.1 Description of data 32 ự th 4.2 Estimated results 32 CHAPTER 5: CONCLUSIONS 46 c p tậ REFERENCE .47 APPENDIX 50 p iệ gh tn Tố ACKNOWLEDGEMENTS I would like to express my special thanks Ph.D Nguyen Viet Hung, at National Economic University in Hanoi for his valuable instructions, comments, criticism, and correction during the development of this thesis My deepest gratitude goes to the Vietnam - Netherlands Project for MA Program in Development Economics where I have learned and been able to write this thesis I would like to thank all lecturers and the staff in the Project for their long, kind encouragement and timely assistance And I wish to express my warmest thanks to my family and my friends for their encouragement and constructive suggestions throughout my course Without their spiritual and support, the thesis would have been made impossible Hanoi, November2011 Dinh Van Tuan ên uy Ch đề c ự th p tậ p iệ gh tn Tố ABBREVIATION HSX Hochiminh Stock Exchange HNX Hanoi Stock Exchange LSTR Logistic Smooth Transition Regression STR Smooth Transition Regression GBM Geometric Brownian Motion MR Mean Reversion Model AR Autoregressive Process ARIMA Autoregressive integrated moving average ADF Augmented Dickey-Fuller VAR Vector auto regression GSO General Statistics Office ên uy Ch đề c ự th p tậ p iệ gh tn Tố LIST OF TABLES Table 1: Capitalization level, proportion, and growth rate of the stock market 20 Table 2: The growth rate of the number of stock companies and asset management companies.22 Table 3: Business performance of Blue Chips 27 Table 4: Testing linear or non-linear of data series for suggesting model 33 Table 5: Augmented Dickey-Fuller (ADF) Unit Root Test results 37 Table 6: Estimation results of LSTR1 model .40 ên uy Ch đề c ự th p tậ p iệ gh tn Tố LIST OF FIGURES Figure 1: Size of listing on Vietnam’s Stock Trading Center 21 Figure 2: VN-Index in 2010 .24 Figure 3: Upcom-Index and tranding value in Upcom market 26 Figure 4: Performances of Blue chips on the stock market up to 31 October, 2011 .30 Figure 5: Defining initial values of γ and c by using the method of GRID SEARCH .35 Figure 7: ADF Test for residual of error terms with one lag .40 Figure 8: The graph of STR model 42 Figure 9: VN-Index, HN-Index, and five blue chips forecast 45 ên uy Ch đề c ự th p tậ p iệ gh tn Tố CHAPTER 1: INTRODUCTION 1.1 Problem Statement Vietnam’s stock market has operated for nearly ten years and played an important role on Vietnam’s economy Nowadays, most of financial organizations and investors have paid more their attentions to predict stock market, notably by analyzing random-walk behavior of stock time series, in order to take benefits from investing in the stock market However, there are lacking in qualitative studies in forecasting Vietnam’s stock market The main reason is that Vietnamese forecasters are lacking in professional knowledge and qualitative analysis skills Moreover, forecasting stock market has been becoming more difficulty due to the data of the economy, enterprises, and the market are not enough long time series and less confidence Nowadays, many scientists and researchers have paid more attention to develop an adaptive analysis method for non-linear time series A number of time series forecasting models have been developed and applied in analysing and forecasting the stock market and stock price moves such as Smoothing Exponential Regression, Threshold Regression, Artificial Neural Network, and Smooth Transition Regression (STAR), Logistic Smooth Transition Regression (LSTR), etc In fact, there are only some typical studies in Ch analyzing Vietnam’s stock market such as Hoang Dinh Tuan (2008) and most of current ên uy studies used ARIMA model to forecast stock index in short-term Therefore, this study is going to predict stock index, particularly VN-index, HN- đề Index and some of stock index with large capitalization, by applying non-linear model ự th (Logistic Smooth Transition Regression – LSTR) in order to provide useful information for investors and financial organizations The result of this study hopefully contributes an c p Vietnam tậ effective method in analyzing and forecasting the stock market and stock prices in p iệ gh tn Tố 1.2 Research Objectives The objective of this study is predicting the stock market and stock price moves, particularly VN-index and HN-Index and blue-chip stock price of stock with large capitalization, by applying non-linear model (Logistic Smooth Transition Regression – LSTR) in order to provide useful information for investors as well as financial organizations Suggesting recommendations and policy implications for developing Vietnam’s stock market in the near future is also an objective of this study 1.3 Research questions  Question 1: Whether non-linear model will be used to predict VN-Index and HNIndex?  Question 2: How does blue-chip stock price of HSX (Hochiminh Stock Exchange) and HNX (Hanoi Stock Exchange) look like by using non-linear model? 1.4 Literature review Analyzing and forecasting Vietnam’s stock market always attracts more concern of financial organizations and investors in the world, especially in term of stock market Ch prices Bachelier (1900) shows that stock market prices were changed consecutively with ên uy an augmentation: S(t+Δ)-S(t)=Δ1/2 at time t In 1923, Alber Einstein given Brown W(t) moving process as studying kinematic elements and then the stock market price is a đề component of Brown W(t) According to L.Savege, stock market prices were never ự th negative Brownian Motion Model was given in order to describe kinematics regarding to c the market price of different kinds of stocks (P.Samuelson, 1965), for instance: S(t) = tậ exp(at+bW(t)) As of the end of 1960s and the beginning of 1970s, Robert C Merton p Tố continued to develop financial theory based on Samuelson’s model p iệ gh tn Fischer Black and Myron Scholes (1973) declared their important study which is an application of Brownian Motion Model in generating stock valuation formulas suitable for options and other derivative securities Then, these formulas are known as Black-Scholes’s formula that is used by many investors and business to identify price evaluation options in various markets all over the world Studying works of Merton and Scholes were awarded the Nobel Prize in 1997 People often use Geometric Brownian Motion Model in financial mathematics to evaluate prices suitable for financial options Although, this model is relatively simple, it has still not reflected kinds of stock prices exactly Nowadays, analyzing and forecasting stock market prices in developed countries are often based on two major methods including (1) Trend Analysis and (2) Artificial Neuron Network However, these methods have not had high accurate level because of large standard error In empirical studies, there are some quantitative analyses for stock markets such as United State, United Kingdom, Canada, New Zealand, Ireland, and Japan stock markets est For example, Nektarios Aslanidis at all (2002) shows that a variety of financial and macroeconomic series, namely GDP, interest rates, inflation, money supply and US stock prices are assumed to influence UK stock returns In order to examine for a potential non- Ch linear relationship between UK index returns and both financial and macroeconomic ên uy variables, David G McMillan (2002) used smooth-transition threshold models The result of his study states that investor behavior does differ between large and small return Using đề cross-sectional power gained from industry-sorted portfolios, Gropp (2004) addressed that ự th there is a significantly positive speed of reversion with a half-life of approximately four years and a half to eight years to revert to long-term equilibrium c p tậ Moreover, time series forecasting has received increasing attention in many studies in recent years Most of recent studies use the STAR model to analysis and forecast stock Tố p iệ gh tn price indexes in the world Rodrigo Aranda and Patricio Jaramillo (2008) estimate Smooth [23] Sarantis N (2001), “Nonlinearities, cyclical behavior and predictability in stock markets: international evidence”, International Journal of Forecasting 17, 459-482 [24] Terasvirta T and H.M Anderson (1992), “Characterizing nonlinearities in business cycles using smooth transition autoregressive models”, Journal of Applied Econometrics 7, S119-S136 [25] Terasvirta, Timo (1994), “Specification, estimation and evaluation of smooth transition autoregressive models”, Journal of the American Statistical Association 89, 208-218 [26] Tong H (1990), Non-Linear Time Series, A Dynamical System Approach, Oxford University Press, Oxford In Vietnamese [27] Hoang Dinh Tuan (2008), “Using some random process of analyzing stock price moves on Vietnam’s stock market”, paper of the workshop: the issues of financial economics and applied mathematics, National Economic University [28] Nguyen Khac Minh (2009), “Smooth Transition and GDP growth in Vietnamese Ch industrial sector”, Journal of Economics & Development ên uy [29] Nguyen Viet Hung (2010), “Short term prediction of VN INDEX and HNX-INDEX”, Journal of Economics & Development, N0 152, pp 36-42 đề c ự th p tậ p iệ gh tn Tố 50 APPENDIX I STR Estimation Results VN-Index variables in AR part: restriction theta=0: restriction phi=0: restriction phi=-theta: transition variable: sample range: transition function: number of iterations: CONST trend(t) str_resids(t-1) str_resids(t-1) trend(t) [3, 706], T = 704 LSTR1 variable start Estimate SD t-stat p-value - linear part -CONST trend(t) str_resids(t-1) nonlinear part -CONST trend(t) Gamma C1 5.74781 -0.03734 0.96211 5.75850 0.0096 597.3638 -0.02929 0.0018 -16.3076 0.96132 0.0102 94.3639 0.63501 0.62309 0.03685 0.02880 7.33518 7.54421 27.24138 35.34717 ên uy Ch AIC: SC: HQ: R2: adjusted R2: variance of transition variable: SD of transition variable: variance of residuals: SD of residuals: 0.0108 0.0018 0.0902 2.0821 0.0000 0.0000 0.0000 57.8146 16.0476 83.6655 16.9769 0.0000 0.0000 0.0000 0.0000 -8.1920e+00 -8.1467e+00 -8.1745e+00 9.9224e-01 0.9923 41360.0000 đề 203.3716 0.0003 0.0166 ự th HN-Index c variables in AR part: p p iệ gh tn Tố restriction theta=0: restriction phi=0: CONST restriction phi=-theta: transition variable: HNX_trend(t) sample range: [3, 386], T = 384 tậ CONST HNX_trend(t) str_resids(t1) 51 transition function: number of iterations: LSTR1 17 variable start - linear part -HNX_trend(t 0.13597 ) str_resids(t-1) 23.25871 nonlinear part -CONST 3.65529 HNX_trend(t -0.13167 ) str_resids(t-1) -22.43561 Gamma C1 10.00000 49.37931 estimate SD 0.54385 0.0717 7.5813 0.0000 15.95064 2.0522 7.7724 0.0000 4.02354 -0.54087 0.0041 972.2327 0.0000 0.0717 -7.5401 0.0000 15.00868 6.92011 36.74764 2.0578 -7.2935 0.0000 0.2759 25.0803 5.3743 -6.8377 0.0000 0.0000 AIC: SC: HQ: R2: adjusted R2: variance of transition variable: SD of transition variable: variance of residuals: SD of residuals: Ch p-value -7.5366e+00 -7.4645e+00 -7.5080e+00 9.9448e-01 0.9945 12320.0000 110.9955 0.0005 0.0229 AGF CONST AGF_Trend(t) str_resids(t-1) ên uy variables in AR part: restriction theta=0: restriction phi=0: restriction phi=-theta: transition variable: sample range: transition function: number of iterations: t-stat đề c ự th AGF_Trend(t) [3, 336], T = 334 LSTR1 estimate SD t-stat 3.28000 -0.02275 0.47072 0.0134 244.3579 0.0000 0.0015 -14.7903 0.0000 0.1098 4.2865 0.0000 p-value p tậ p iệ gh tn Tố variable start - linear part -CONST 3.26166 AGF_Trend(t) -0.01892 str_resids(t-1) 0.42364 nonlinear part 52 CONST AGF_Trend(t) str_resids(t-1) Gamma C1 0.26586 0.01822 0.52029 7.33518 48.06897 0.26217 0.02199 0.47036 6.54484 44.05409 0.0143 0.0015 0.1143 0.1999 1.4600 18.2955 14.3873 4.1162 32.7448 30.1737 0.0000 0.0000 0.0000 0.0000 0.0000 ên uy Ch đề c ự th p tậ p iệ gh tn Tố 53 AIC: SC: HQ: R2: adjusted R2: variance of transition variable: SD of transition variable: variance of residuals: SD of residuals: -7.2738e+00 -7.1825e+00 -7.2374e+00 9.7913e-01 0.9792 9324.1667 96.5617 0.0007 0.0260 BMC variables in AR part: restriction theta=0: restriction phi=0: restriction phi=-theta: transition variable: sample range: transition function: number of iterations: CONST BMC_trend(t) str_resids(t-1) str_resids(t-1) BMC_trend(t) [3, 506], T = 504 LSTR1 estimate SD 4.06188 -0.00121 0.95238 0.0053 763.2601 0.0000 0.0001 -15.2747 0.0000 0.0136 69.7742 0.0000 -1.28970 0.00217 5.42040 221.5940 0.0159 0.0001 0.1656 1.1069 ên uy Ch variable start - linear part -CONST 4.08092 BMC_trend(t) -0.00157 str_resids(t-1) 0.95250 nonlinear part -CONST -1.31311 BMC_trend(t) 0.00255 Gamma 5.96602 C1 227.93103 t-stat p-value -81.1180 28.7178 32.7368 200.1980 0.0000 0.0000 0.0000 0.0000 đề ự th -7.0533e+00 -6.9947e+00 -7.0303e+00 9.9396e-01 0.9940 21210.0000 c p iệ gh tn Tố 145.6365 p tậ AIC: SC: HQ: R2: adjusted R2: variance of transition variable: SD of transition variable: 54 variance of residuals: SD of residuals: 0.0009 0.0292 FPT variables in AR part: restriction theta=0: restriction phi=0: restriction phi=-theta: transition variable: sample range: transition function: number of iterations: CONST FPT_trend(t) str_resids(t-1) str_resids(t-1) FPT_trend(t) [3, 463], T = 461 LSTR1 variable start - linear part -CONST 4.05179 FPT_trend(t) 0.00130 str_resids(t-1) 0.87429 nonlinear part -CONST -0.43944 FPT_trend(t) -0.00053 Gamma 4.85242 C1 272.24138 SD 4.04913 0.00133 0.87490 0.0030 1336.9162 0.0000 0.0000 42.9584 0.0000 0.0223 39.1528 0.0000 -0.34523 -0.00078 5.07363 267.08499 0.0266 0.0001 0.1614 1.1509 ên uy Ch t-stat p-value -12.9987 -12.7104 31.4332 232.0655 0.0000 0.0000 0.0000 0.0000 -7.8659e+00 -7.8031e+00 -7.8411e+00 9.8000e-01 0.9800 17748.5000 đề 133.2235 0.0004 0.0194 ự th AIC: SC: HQ: R2: adjusted R2: variance of transition variable: SD of transition variable: variance of residuals: SD of residuals: estimate c PVD tậ CONST PVD_trend(t) str_resids(t-1) restriction theta=0: restriction phi=0: restriction phi=-theta: str_resids(t-1) p variables in AR part: p iệ gh tn Tố 55 transition variable: sample range: transition function: number of iterations: variable - linear part -CONST PVD_trend(t) str_resids(t-1) nonlinear part -CONST PVD_trend(t) Gamma C1 PVD_trend(t) [3, 400], T = 398 LSTR1 start estimate SD t-stat p-value 4.03507 -0.00318 0.88923 4.03920 -0.00326 0.88953 0.0044 0.0001 0.0234 919.9152 -35.8396 37.9652 0.0000 0.0000 0.0000 0.55234 0.00064 4.85242 166.68966 0.52879 0.00079 4.91804 164.54306 0.0135 0.0001 0.1517 0.9976 39.2338 9.2443 32.4183 164.9453 0.0000 0.0000 0.0000 0.0000 AIC: SC: HQ: R2: adjusted R2: variance of transition variable: SD of transition variable: variance of residuals: SD of residuals: -7.7716e+00 -7.7015e+00 -7.7438e+00 9.7053e-01 0.9706 13233.5000 115.0370 0.0004 0.0204 SSI CONST TREND(t) str_resids(t-1) str_resids(t-1) TREND(t) [3, 433], T = 431 LSTR1 ên uy Ch variables in AR part: restriction theta=0: restriction phi=0: restriction phi=-theta: transition variable: sample range: transition function: number of iterations: estimate SD 3.73305 -0.00237 0.95621 0.0032 1167.5230 0.0000 0.0000 -107.3580 0.0000 0.0119 80.5657 0.0000 -3.10019 0.00802 6.10053 359.12680 0.1141 0.0003 0.4226 2.6530 đề c ự th p-value -27.1820 28.6032 14.4360 135.3687 0.0000 0.0000 0.0000 0.0000 p iệ gh tn Tố -7.3790e+00 -7.3130e+00 -7.3529e+00 9.9328e-01 p AIC: SC: HQ: R2: t-stat tậ variable start - linear part -CONST 3.72445 TREND(t) -0.00228 str_resids(t-1) 0.87259 nonlinear part -CONST -1.75402 TREND(t) 0.00460 Gamma 10.00000 C1 316.68966 56 adjusted R2: 0.9933 variance of transition 15516.0000 variable: SD of transition variable: 124.5632 variance of residuals: 0.0006 SD of residuals: 0.0248 II ADF Test for reidual of data series VN-Index ADF Test for series: u_resids sample range: [1961 Q2, 2136 Q2], T = 701 lagged differences: no intercept, no time trend asymptotic critical values reference: Davidson, R and MacKinnon, J (1993), "Estimation and Inference in Econometrics" p 708, table 20.1, Oxford University Press, London 1% 5% 10% -2.56 -1.94 -1.62 value of test statistic: -14.9965 regression results: variable coefficient t-statistic x(-1) -0.8389 -14.9965 dx(-1) 0.0938 1.9932 dx(-2) 0.0238 0.6291 RSS 0.1785 sample range: ên uy Ch OPTIMAL ENDOGENOUS LAGS FROM INFORMATION CRITERIA [1963 Q2, 2136 Q2], T = 693 đề optimal number of lags (searched up to 10 lags of differences): Akaike Info Criterion: Final Prediction Error: Hannan-Quinn Criterion: Schwarz Criterion: p p iệ gh tn Tố 13.1505 0.3582 13.3328 0.3453 tậ Portmanteau: p-Value (Chi^2): Ljung & Box: p-Value (Chi^2): c ự th PORTMANTEAU TEST with 12 lags 57 ên uy Ch đề c ự th p tậ p iệ gh tn Tố 58 HN-Index ADF Test for series: str_resids sample range: [1961 Q2, 2056 Q2], T = 381 lagged differences: intercept, time trend asymptotic critical values reference: Davidson, R and MacKinnon, J (1993), "Estimation and Inference in Econometrics" p 708, table 20.1, Oxford University Press, London 1% 5% 10% -3.96 -3.41 -3.13 value of test statistic: -7.5356 regression results: variable coefficient t-statistic x(-1) -0.4830 -7.5356 dx(-1) -0.2923 -4.7918 dx(-2) -0.1829 -3.6783 constant -0.0003 -0.3343 trend 0.0000 0.5795 RSS 0.1419 OPTIMAL ENDOGENOUS LAGS FROM INFORMATION CRITERIA sample range: [1963 Q2, 2056 Q2], T = 373 ên uy Ch optimal number of lags (searched up to 10 lags of differences): Akaike Info Criterion: Final Prediction Error: Hannan-Quinn Criterion: Schwarz Criterion: c 17.4597 0.1331 17.9926 0.1159 ự th Portmanteau: p-Value (Chi^2): Ljung & Box: p-Value (Chi^2): đề PORTMANTEAU TEST with 12 lags p tậ p iệ gh tn Tố 59 AGF ADF Test for series: str_resids sample range: [1961 Q2, 2043 Q4], T = 331 lagged differences: intercept, time trend asymptotic critical values reference: Davidson, R and MacKinnon, J (1993), "Estimation and Inference in Econometrics" p 708, table 20.1, Oxford University Press, London 1% 5% 10% -3.96 -3.41 -3.13 value of test statistic: -11.3531 regression results: variable coefficient t-statistic x(-1) -1.0166 -11.3531 dx(-1) 0.1477 2.0425 dx(-2) 0.0591 1.0761 constant -0.0001 -0.1055 trend 0.0000 0.1914 RSS 0.2112 OPTIMAL ENDOGENOUS LAGS FROM INFORMATION CRITERIA sample range: [1963 Q2, 2043 Q4], T = 323 ên uy Ch optimal number of lags (searched up to 10 lags of differences): Akaike Info Criterion: Final Prediction Error: Hannan-Quinn Criterion: Schwarz Criterion: đề PORTMANTEAU TEST with 12 lags c p tậ 16.8228 0.1564 17.3452 0.1371 ự th Portmanteau: p-Value (Chi^2): Ljung & Box: p-Value (Chi^2): p iệ gh tn Tố BMC 60 ADF Test for series: str_resids sample range: [1961 Q2, 2086 Q2], T = 501 lagged differences: intercept, time trend asymptotic critical values reference: Davidson, R and MacKinnon, J (1993), "Estimation and Inference in Econometrics" p 708, table 20.1, Oxford University Press, London 1% 5% 10% -3.96 -3.41 -3.13 value of test statistic: -11.1740 regression results: variable coefficient t-statistic x(-1) -0.7437 -11.1740 dx(-1) -0.0591 -1.0271 dx(-2) -0.0445 -0.9926 constant -0.0000 -0.0109 trend 0.0000 0.0259 RSS 0.4038 OPTIMAL ENDOGENOUS LAGS FROM INFORMATION CRITERIA sample range: [1963 Q2, 2086 Q2], T = 493 optimal number of lags (searched up to 10 lags of differences): Akaike Info Criterion: Final Prediction Error: Hannan-Quinn Criterion: Schwarz Criterion: Ch PORTMANTEAU TEST with 12 lags ên uy 8.2828 0.7627 8.4350 0.7503 đề Portmanteau: p-Value (Chi^2): Ljung & Box: p-Value (Chi^2): c ự th p tậ p iệ gh tn Tố 61 FPT ADF Test for series: str_resids sample range: [1961 Q2, 2075 Q3], T = 458 lagged differences: intercept, time trend asymptotic critical values reference: Davidson, R and MacKinnon, J (1993), "Estimation and Inference in Econometrics" p 708, table 20.1, Oxford University Press, London 1% 5% 10% -3.96 -3.41 -3.13 value of test statistic: -12.1304 regression results: variable coefficient t-statistic x(-1) -0.9223 -12.1304 dx(-1) -0.0263 -0.4109 dx(-2) 0.0370 0.7919 constant -0.0002 -0.2039 trend 0.0000 0.3560 RSS 0.1673 OPTIMAL ENDOGENOUS LAGS FROM INFORMATION CRITERIA sample range: [1963 Q2, 2075 Q3], T = 450 Ch optimal number of lags (searched up to 10 lags of differences): Akaike Info Criterion: Final Prediction Error: Hannan-Quinn Criterion: Schwarz Criterion: ên uy PORTMANTEAU TEST with 12 lags 6.4791 0.8900 6.6231 0.8815 đề Portmanteau: p-Value (Chi^2): Ljung & Box: p-Value (Chi^2): c ự th p tậ p iệ gh tn Tố 62 PVD ADF Test for series: str_resids sample range: [1961 Q2, 2059 Q4], T = 395 lagged differences: no intercept, no time trend asymptotic critical values reference: Davidson, R and MacKinnon, J (1993), "Estimation and Inference in Econometrics" p 708, table 20.1, Oxford University Press, London 1% 5% 10% -2.56 -1.94 -1.62 value of test statistic: -11.6700 regression results: variable coefficient t-statistic x(-1) -0.9661 -11.6700 dx(-1) 0.0758 1.1196 dx(-2) 0.0169 0.3332 RSS 0.1589 OPTIMAL ENDOGENOUS LAGS FROM INFORMATION CRITERIA sample range: [1963 Q2, 2059 Q4], T = 387 optimal number of lags (searched up to 10 lags of differences): Akaike Info Criterion: Final Prediction Error: Hannan-Quinn Criterion: Schwarz Criterion: Ch PORTMANTEAU TEST with 12 lags 12.7482 0.3876 13.0099 0.3683 ên uy Portmanteau: p-Value (Chi^2): Ljung & Box: p-Value (Chi^2): đề c ự th p tậ p iệ gh tn Tố 63 SSI ADF Test for series: str_resids sample range: [1961 Q2, 2068 Q1], T = 428 lagged differences: no intercept, no time trend asymptotic critical values reference: Davidson, R and MacKinnon, J (1993), "Estimation and Inference in Econometrics" p 708, table 20.1, Oxford University Press, London 1% 5% 10% -2.56 -1.94 -1.62 value of test statistic: -10.8424 regression results: variable coefficient t-statistic x(-1) -0.8635 -10.8424 dx(-1) -0.0248 -0.3804 dx(-2) -0.0764 -1.5778 RSS 0.2369 OPTIMAL ENDOGENOUS LAGS FROM INFORMATION CRITERIA sample range: [1963 Q2, 2068 Q1], T = 420 optimal number of lags (searched up to 10 lags of differences): Akaike Info Criterion: Final Prediction Error: Hannan-Quinn Criterion: Schwarz Criterion: Ch PORTMANTEAU TEST with 12 lags 7.0971 0.8511 7.2809 0.8385 ên uy Portmanteau: p-Value (Chi^2): Ljung & Box: p-Value (Chi^2): đề c ự th p tậ p iệ gh tn Tố 64