advertisement

Financial Econometric Models IV

100 %
0 %
advertisement
Information about Financial Econometric Models IV
Finance

Published on February 27, 2014

Author: vinzjeannnin

Source: slideshare.net

Description

Fourth Session, MSc 5th Year
advertisement

Q1 2012 ESGF 5IFM Q1 2012 Vincent JEANNIN – ESGF 5IFM vinzjeannin@hotmail.com Financial Econometric Models 1

Interim Exam Sum Up Reminder of Last Session Generic case AR, MA, ARMA & ARIMA Heteroscedasticity: Introduction ESGF 5IFM Q1 2012 • • • • vinzjeannin@hotmail.com Summary of the session (Est. 3h) 2

ESGF 4IFM Q1 2012 1 vinzjeannin@hotmail.com Interim Exam Sum-Up 3

When E is minimal? When partial derivatives i.r.w. a and b are 0 Attention, logarithms are not additive! vinzjeannin@hotmail.com Minimising residuals ESGF 5IFM Q1 2012 Two parameters to estimate: • Intercept α • Gradient β 4

Change the variable Z=ln(X) vinzjeannin@hotmail.com ESGF 5IFM Q1 2012 Solution? 5

vinzjeannin@hotmail.com ESGF 4IFM Q1 2012 Leads easily to the intercept 6

7 vinzjeannin@hotmail.com ESGF 5IFM Q1 2012

vinzjeannin@hotmail.com ESGF 5IFM Q1 2012 We have and Finally… 8

Z=ln(X) vinzjeannin@hotmail.com ESGF 5IFM Q1 2012 Don’t forget… 9

Accept or reject the regression? vinzjeannin@hotmail.com Hedging is linear… ESGF 5IFM Q1 2012 No forecast possible (one particular stock against the market) Check correlation and R Squared 10 Check the normality of residuals

11 vinzjeannin@hotmail.com ESGF 5IFM Q1 2012

Ultimate decider is the normality test on the residuals vinzjeannin@hotmail.com ESGF 5IFM Q1 2012 For every dataset of the Quarter 12

Trend Fit Seasonality Forecast Residual vinzjeannin@hotmail.com Identify ESGF 5IFM Q1 2012 2 13

Lag 0, Auto Correlation is 1 Lag 1 ESGF 5IFM Q1 2012 vinzjeannin@hotmail.com ACF = Auto Correlation in the series Lag 2 14 Regression of the series against the same series retarded

15 vinzjeannin@hotmail.com ESGF 4IFM Q1 2012

Marginal Auto Correlation ESGF 4IFM Q1 2012 vinzjeannin@hotmail.com PACF = Partial Auto Correlation in the series Conditional Auto Correlation knowing the Auto Correlation at a lower order 16

vinzjeannin@hotmail.com ESGF 5IFM Q1 2012 3 17

18 vinzjeannin@hotmail.com ESGF 5IFM Q1 2012

19 vinzjeannin@hotmail.com ESGF 5IFM Q1 2012

20 AR(1) vinzjeannin@hotmail.com ESGF 5IFM Q1 2012

Exploitation Identify Auto Correlation Analysis Fit Estimate the parameters Forecast vinzjeannin@hotmail.com Reminders of the 3 steps ESGF 4IFM Q1 2012 Reminder of the last session 21

Trend Seasonality Residual ESGF 4IFM Q1 2012 vinzjeannin@hotmail.com Reminders of the 3 components 22

There is a correlation between current data and previous data Parameters of the model White noise vinzjeannin@hotmail.com Main principle ESGF 4IFM Q1 2012 AR AR(n) If the parameters are identified, the prediction will be easy 23

24 vinzjeannin@hotmail.com ESGF 4IFM Q1 2012

25 vinzjeannin@hotmail.com ESGF 4IFM Q1 2012

26 vinzjeannin@hotmail.com ESGF 4IFM Q1 2012

PACF cancelling after order 1 ESGF 4IFM Q1 2012 vinzjeannin@hotmail.com ACF decreasing 27

Typically an Autoregressive Process vinzjeannin@hotmail.com PACF cancel after order 1 ESGF 4IFM Q1 2012 Decreasing ACF AR(1) 28

vinzjeannin@hotmail.com Modl<-ar(diff(DATA$Val),order.max=20) plot(Modl$aic) ESGF 4IFM Q1 2012 Let’s try to fit an AR(1) model 29 The likelihood for the order 1 is significant

> ar(diff(DATA$Val),order.max=20) Coefficients: 1 2 0.5925 -0.1669 sigma^2 estimated as 0.8514 vinzjeannin@hotmail.com Order selected 3 3 0.1385 ESGF 4IFM Q1 2012 Call: ar(x = diff(DATA$Val), order.max = 20) We know the first term of our series 30

Box-Pierce test data: Modl$resid X-squared = 7e-04, df = 1, p-value = 0.9789 vinzjeannin@hotmail.com Box.test(Modl$resid) ESGF 4IFM Q1 2012 Need to test the residuals H0 accepted, residuals are independently distributed (white noise) The differentiated series is a AR(1) 31

Stationary series with auto correlation of errors Parameters of the model White noise vinzjeannin@hotmail.com Main principle ESGF 4IFM Q1 2012 MA MA(n) More difficult to estimate than a AR(n) 32

33 vinzjeannin@hotmail.com ESGF 4IFM Q1 2012

PACF decays to 0 vinzjeannin@hotmail.com ACF cancels after order 1 ESGF 4IFM Q1 2012 acf(Data,20) pacf(Data,20) 34 ACF & PACF suggest MA(1)

> arima(Data, order = c(0, 0, 1),include.mean = FALSE) sigma^2 estimated as 0.937: log likelihood = -138.76, > Box.test(Rslt$residuals) Box-Pierce test data: Rslt$residuals X-squared = 0, df = 1, p-value = 0.9967 It works, MA(1), 0 mean, parameter -0.4621 aic = 281.52 vinzjeannin@hotmail.com Coefficients: ma1 -0.4621 s.e. 0.0903 ESGF 4IFM Q1 2012 Call: arima(x = Data, order = c(0, 0, 1), include.mean = FALSE) 35

The series is a function of past values plus current and past values of the noise ARMA(p,q) Combines AR(p) & MA(q) vinzjeannin@hotmail.com Main principle ESGF 4IFM Q1 2012 ARMA 36

37 vinzjeannin@hotmail.com ESGF 4IFM Q1 2012

ESGF 4IFM Q1 2012 vinzjeannin@hotmail.com Both ACF and PACF decreases exponentially after order 1 38

vinzjeannin@hotmail.com ESGF 5IFM Q1 2012 Generic case AR, MA, ARMA & ARIMA 39

ARIMA(p,d,q), AutoRegressive Integrated Moving Average vinzjeannin@hotmail.com Non stationary… But can be removed with a differentiation of d ESGF 5IFM Q1 2012 Combines AR(p) & MA(q) 40

Typical ARIMA vinzjeannin@hotmail.com ESGF 5IFM Q1 2012 Non stationary 41

Identification easier vinzjeannin@hotmail.com ESGF 5IFM Q1 2012 Differentiation (d order) MA(2) 42

Original series is ARIMA(p,d,q) vinzjeannin@hotmail.com If the d differentiation is an ARMA(p,q) ESGF 5IFM Q1 2012 Integration of the initial differentiation 43

When there is hetoroscedasticity, not applicable Conditional heteroscedasticity is the answer It assumes the current variance of residuals to be a function of the actual sizes of the previous time periods' residuals vinzjeannin@hotmail.com AR, MA, ARMA, ARIMA imply stationary series ESGF 5IFM Q1 2012 Heteroscedasticity: Introduction 44

GARCH(p,q) ARMA (p,q) with heteroscedasticity ESGF 5IFM Q1 2012 AR (q) with heteroscedasticity vinzjeannin@hotmail.com ARCH(q) 45

vinzjeannin@hotmail.com Variance is very rarely stable ESGF 5IFM Q1 2012 Useful for financial series 46

Add a comment

Related presentations

Les changements sur le marché du distressed aux Etats-Unis et en Europe

Main Sections of the Report 1) Nifty Technical View 2) 4 Large Cap Trade Ide...

This presentation consits the yearly results of Kinepolis Group

Related pages

Financial Econometric Modelling - mysmu.edu

Financial Econometric Modelling Stan Hurn, Vance Martin, Peter Phillips and Jun Yu Current Working Document: November 2015
Read more

Econometrics - Wikipedia

Basic econometric models: linear regression The ... Journal of Financial Econometrics; Econometric Society; The Econometrics Journal; Econometric Links;
Read more

Econometric Forecasting Models - gwu.edu

Time series models 6. Econometric forecasting models. ... technological, financial, international competitiveness, ... (iv) Forecast origin uncertainty
Read more

Financial Markets And Empirical Regularities An ...

Financial Markets And Empirical Regularities An Introduction to Financial ... Asset Pricing Models IV. ... Econometric Methods to Financial Markets
Read more

Financial Econometrics | Teaching | Econometrics | Chair ...

The focus will be on the analysis of financial data as well as on applications of econometric methods to ... C. and Zakoian J.M. (2011): GARCH models: ...
Read more

Forecasting and Econometric Models: The Concise ...

Forecasting and Econometric Models. by Saul H. Hymans. About the Author: Search CEE. Home | CEE | 2nd edition | Forecasting and Econometric Models;
Read more

Econometrics – Hansen - University of Wisconsin–Madison

ECONOMETRICS Bruce E. Hansen °c 2000, ... CONTENTS iv 7 ... models and the application of econometric methods to these models using economic data.
Read more

Introduction to the Financial Macro-econometric Model

Introduction to the Financial Macro-econometric Model Atsushi Ishikawa* atsushi.ishikawa@boj.or.jp Koichiro Kamada* kouichirou.kamada@boj.or.jp
Read more