Gaodun slides quantitative

http://finance.gaodun.cn Brief Introduction Quantitative Methods T S E S S Level 2017 Instructor: Feng S S P M S E S S S S C S S E S S S F R S S A F I F S S S S Q I D A I P M W Brief Introduction Brief Introduction C Ø S Q • R • R M C M R A • R T • R E V R R S I A P Ø http://finance.gaodun.cn Brief Introduction Brief Introduction Ø Ø • R A D F M D • ISBN J E R D E P W Ø Ø • Correlation Analysis T Ø C Ø F Ø D http://finance.gaodun.cn Correlation Analysis Correlation Analysis S S ØA Ø A S K A C UK US X Y Ø R S J C üC XY üC XY  X XY Correlation Analysis Correlation Analysis S S Ø A C X Y XY X Ø R XY Y XY X Y Y C XY C http://finance.gaodun.cn Correlation Analysis Correlation Analysis S C S Correlation Analysis S Ø S Ø S Ø S Ø S Ø S Ø S Ø S C Correlation Analysis R L H Ø T üH ü H t= r n -2 -r üT üD H http://finance.gaodun.cn Correlation Analysis Correlation Analysis E A A Ø H X YT X Y T Ø X Y Ø T W X Y H Ø S Ø S X Y Correlation Analysis Correlation Analysis L L Ø O Ø S C http://finance.gaodun.cn Correlation Analysis L Summary C Ø I Ø C Ø N • C • H • L Ø E • Simple Linear Regression Simple Linear Regression T D Y Ø T Ø A Ø D Ø C I Ø T Ø I Ø A X http://finance.gaodun.cn Simple Linear Regression Simple Linear Regression L S Ø U Ø Y X Y Y X Simple Linear Regression X Simple Linear Regression T A Ø T Y Ø O OLS ˆ X Ø T ˆ X Ø T SSE E üS Ø T SSE E Ø T E Ø T Ø E Yˆ ˆ ˆ X http://finance.gaodun.cn Simple Linear Regression Simple Linear Regression T P ˆ ØE üC ˆ Ø T C ov XY  2X üI Y • T Y X ˆ ØE üC ˆ Y X X Simple Linear Regression Simple Linear Regression C Ø T ˆ  (t  s ) Y c f or S Ø H üT sf H H H ˆ - ( t  s )  Y  Yˆ  ( t  s ) Y c f c f Ø T c ˆ Xp Yˆ Y ˆ X üI P Yˆ ˆ X Ø D Ø R ˆ ˆ H http://finance.gaodun.cn Simple Linear Regression Summary C Ø I Ø T bˆ  ( t c  s bˆ ) or bˆ - ( t c  s bˆ )  b  bˆ  ( t c  s bˆ ) Ø C • U • P c s bˆ Ø C • I Ø E üI H • underlying consumption • predicted value of dependent variable Simple Linear Regression A ANOVA Analysis (1) ANOVA Ø A T Ø D ANOVA Ø C SEE R F üT Ø D • T SST RSS S R SSE http://finance.gaodun.cn Simple Linear Regression Simple Linear Regression A A C C Ø T Ø A SST SST  Y Y Ø R RSS R SS  Yˆ Y Simple Linear Regression Simple Linear Regression A A C Ø S SSE SSE • A  Y i Yˆ C Ø ANOVA S R S SS RSS E T ü MSR ü MSE SSE SST M S S MS MSR SSR MSE SSE http://finance.gaodun.cn Summary of Assumption Violations Multicollinearity T V Ø T R² F C H P Ø T N E T T I T I T II T II C •R •B BP P ×R •R •D DW W × χ • Ø E M F R Summary Ø I Other Issues in Regression Analysis Ø C • D T Ø F Ø E • effects of heteroskedasticity and serial correlation, Ø D Ø D http://finance.gaodun.cn Dummy Variable ( ) Dummy Variable D E Ø Q Ø Y X X X Y üD EPS Y Q Q Q Q Ø I X X EPS EPS EPS EPS Dummy Variable Model Misspecification ( I D Ø I Ø T Ø R X ) http://finance.gaodun.cn Model Misspecification Model Misspecification C E Ø M üI Ø R üV üP Ø I üL üI üI Ø O Model Misspecification Qualitative Dependent Variable ( A Q Ø T Ø T Ø T Ø T Ø T Ø D üP üD ) http://finance.gaodun.cn Summary Ø I Trend Models Ø C • D T • M Ø C • Q Ø E Ø D • Ø E Trend Models Trend Models L L Ø W Ø W ˆ ˆ ˆ L yt t http://finance.gaodun.cn Trend Models L Trend Models V L Ø I Ø I L Ø T üU D W Summary Ø I Ø C Autoregressive Models (AR) • L T • L Ø D AR Ø E • Ø C AR Ø E http://finance.gaodun.cn Autoregressive Model (AR) Autoregressive Model C A Ø A Ø U AR OLS ü AR F x t = b + b x t-1 + Ø A üC üC Autoregressive Model Autoregressive Model C D Ø A xˆ t+ = bˆ + bˆ x t xˆ t+ = bˆ + bˆ x t+ t • W üC Ø A t ü AR x t = b + b x t-1 + b x t-2 + + b p x t-p + AR Ø S E AR ü AR Ø S üA üT C t , t-k http://finance.gaodun.cn Autoregressive Model Autoregressive Model D C Ø S S T ü t= Ø T t 1/ , t-k Ø T T • T • D T üI üT üT Autoregressive Model Autoregressive Model S M C Ø C AR üT üQ üM Ø F üQ üM Ø A AR xˆ t  bˆ0  bˆ1 x t 1  b2 x t - xˆ t  bˆ0  bˆ1 x t 1  b2 x t -12 Ø M x üC ü t  b0 - b1 AR AR http://finance.gaodun.cn Summary Ø I Random Walk Ø C • C AR T • A Ø D • M Ø D Ø E • mean-reverting level Ø D Random Walk Random Walk R R Ø A Ø A x t  x t -1   t üA üT AR x t  b  x t -1   t üI http://finance.gaodun.cn Random Walk R Random Walk V C Ø A U Ø T üA üA xt  Ø T üT b0  - b1 • B AR AR Random Walk Random Walk U D C üT • I AR F Ø S AR Ø S üO Ø S üH H üC üI H http://finance.gaodun.cn Random Walk Summary F Ø I Ø A Ø C • R • T üS • F Ø E üD • O unit roots walk üT stationary random (first differencing) Model Evaluation C Model Evaluation Ø I T Ø O Ø C Ø E Ø D ARCH Ø R RMSE RMSE http://finance.gaodun.cn Model Evaluation Model Evaluation I A Ø F Ø R C H Ø ARCH üW Ø T • AR ARCH AR M Model Evaluation Model Evaluation ARCH P Ø V ARCH Ø I ˆt2  a  a1ˆt2-1  u t 2 ü ˆ t   aˆ  aˆ ˆ t üI ARCH üI ARCH ARCH ARCH ARCH http://finance.gaodun.cn Model Evaluation Model Evaluation S S C N D Y L F E DW N U Y C N Y U AR Y A S Y G AR T N S Regression With Two Time Series Regression With Two Time Series R R C üI Ø W • I Ø D üI üO F • I üC N ARCH http://finance.gaodun.cn Summary Ø I Simulation Ø C • I T • ARCH Ø D • R Ø E Ø D • Ø C Simulation Simulation S D Ø D Ø H Ø D Ø C Ø C Ø S Ø R http://finance.gaodun.cn Simulation Simulation T A Ø W Ø B Ø I üP üB Simulation Simulation C I Ø B Ø G Ø E Ø R Ø M Ø N Ø C http://finance.gaodun.cn Simulation Summary C Ø I Ø H Ø C • S üS üT • D üC üQ • A • C Ø E • ...http://finance .gaodun. cn Brief Introduction Brief Introduction Ø Ø • R A D F M D • ISBN J E R D E P W Ø Ø • Correlation Analysis T Ø C Ø F Ø D http://finance .gaodun. cn Correlation Analysis... http://finance .gaodun. cn Correlation Analysis Correlation Analysis S C S Correlation Analysis S Ø S Ø S Ø S Ø S Ø S Ø S Ø S C Correlation Analysis R L H Ø T üH ü H t= r n -2 -r üT üD H http://finance .gaodun. cn... http://finance .gaodun. cn Correlation Analysis L Summary C Ø I Ø C Ø N • C • H • L Ø E • Simple Linear Regression Simple Linear Regression T D Y Ø T Ø A Ø D Ø C I Ø T Ø I Ø A X http://finance .gaodun. cn