Practical Examples using Eviews

Presented by 顏廣杰 2013/10/24

P.40-P.43

File: SandPhedge.xls

Estimation of an optimal hedge ratio   1.

1.

This section shows how to run a bivariate regression using Eviews.

We focus on the relationship between SPOT and FUTURES: Level regression (long run relationship) 𝑆 𝑡 𝛼 + 𝑡 Return regression (short run relationship)   𝑟 𝑆,𝑡 𝛼 + 𝐹,𝑡 The appropriate hedge ratio will be the slope estimate, and the independent variable is the futures return.

𝛽 , in a regression where the dependent variable is the spot returns Test whether  𝛽 = 1 or not, we can View  Coeff. Restrictions. Type C(2)=1.

Coeff. Tests

Input Data

Descriptive Statistics  

Genr

 type rfutures=100*dlog(futures)

rspot=100*dlog(spot)

Do not forget to Save the workfile.

Run Regression   If you want to save the summary statistics, you must name them by clicking Name and then choose a name, e.g. Descstats. We can now proceed to estimate the regression.



Name



returnreg

 In the same way, we also obtain levelreg

Test Coefficients of Regression  Suppose now that we wanted to test the null hypothesis that 𝐻 0 : 𝛽 = 1 rather than 𝐻 0 : 𝛽 = 0 .

P.77-P.80

File: capm.xls

Example for CAPM

Generate New Variables    

RSANDP=100*DLOG(SANDP) RFORD=100*DLOG(FORD) USTB3M=USTB3M/12 ERSANDP=RSANDP-USTB3M

CAPM test   To estimate the CAPM equation, click on Equation 𝑟 𝐹𝑜𝑟𝑑 − 𝑟 𝑓 𝑡 = 𝛼 + 𝛽 𝑟 Type in the equation window 𝑚 − 𝑟 𝑓 𝑡 + 𝑢 𝑡

ERFORD C ERSANDP

Or

100*DLOG(FORD)-USTB3M C 100*DLOG(SANDP) USTB3M

P.99-P.104

File: macro.xls

Period: 1986/03~2007/04

APT-style Model   In the spirit of APT, the following example will examine regressions that seek to determine whether the monthly returns on Microsoft stock an be explained by reference to unexpected changes in a set of macroeconomic and financial variables.

Press Genr or type in the Command window

Genr dspread = d(baa_aaa_spread) Genr dprod = d(industrial_production) Genr dcredit = d(consumer_credit) Genr rmsoft = 100*dlog(microsoft) Genr rsandp = 100*dlog(sandp) Genr dmoney = d(m1money_supply) Genr inflation = 100*dlog(cpi) Genr term = ustb10y – ustb3m

 Press Genr

Genr dinflation = d(inflation) Genr mustb3m = ustb3m/12 Genr rterm = d(term) Genr ermsoft = rmsoft – mustb3m Genr ersandp = rsandp – mustb3m

 Use Least Squares over the whole sample period.

𝑟 𝑚𝑠𝑜𝑓𝑡 − 𝑟 𝑓 = 𝛼 + 𝛽 1 𝑟 𝑚 − 𝑟 𝑓 + 𝜷 ′ ∗ 𝚫𝑴𝒂𝒄𝒓𝒐 + 𝝐 (ermsoft c ersandp dprod dcredit dinflation dmoney dspread rterm)

Stepwise regression

P.136-P.139

File: macro.wfl

Period: 1986/03~2007/04

Testing for heteroscedasticity  If the residuals of the regression have systematically changing variability over the sample, that is a sign of heteroscedasticity.

30 20 10 0 -10 -20 -30 -40 -50 -60 86 88 90 92 94 96 98 00 02 04 06 ERMSOFT Residuals  It is hard to see any clear pattern, so we need to run the formal statistical test. (White’s test)

 To test for heteroscedasticity using White’s test.

V V  X ambiguous!!

Using White’s modified standard error estimates in EViews The heteroscedasticity-consistent s.d. errors are smaller than OLS Durbin-Watson (DW) is a test for first order autocorrelation.

Detecting autocorrelation  𝑢 𝑡 Breusch-Godfrey test: = 𝜌 1 𝑢 𝑡−1 + 𝜌𝑢 𝑡−2 𝐻 0 : 𝜌 1 𝐻 1 : 𝜌 1 + ⋯ + 𝜌 = 𝜌 2 𝑟 𝑢 𝑡−𝑟 = ⋯ = 𝜌 ≠ 0 𝑜𝑟 ⋯ 𝑜𝑟 𝜌 𝑟 𝑟 + 𝑣 𝑡 , 𝑣 𝑡 ~𝑁(0, 𝜎 𝑣 2 = 0 ) ≠ 0

Testing for non-normality   The Bera-Jarque normality tests

View



Test Residual Tests



Histogram



Normality

Multicollinearity  

Quick/Group



Statistics/Correlations

In the dialog box that appears:

Ersandp dprod dcredit dinflation dmoney dspread rterm

RESET tests (p.177) 

View



Stability tests



Ramsey RESET test

It would be concluded that the linear model for the Microsoft returns is appropriate.

Stability tests (p.188) 

View



Stability Tests



Chow Breakpoint Test

P.234-P.238

File: UKHP.wfl

Period: 1991/03~2007/05

Constructing ARMA models in Eviews  1.

2.

We use the monthly UK house price series in the chapter one to build an ARMA model for the house price changes.

Autocorrelation Partial autocorrelation

Estimating the autocorrelation coefficients for up to 12 lags  Double click DHP 

View/Correlation



Lag 12



OK

Using information criteria to decide on model orders 

Quick



Estimate Equation

 This specify an ARMA(1,1). The output is given in the table below.

   One more example: “dhp c ar(1) ar(2) ar(3) ar(4) ar(5) ma(1) ma(2) ma(3) ma(4) ma(5)” Using AIC to decide which one model is good.

Smaller AIC imlies better model.

AIC

Forecasting using ARMA models in Eviews   Suppose that the AR(2) model selected for the house price percentage changes series were estimated using observations Feb. 1991-Dec. 2004, leaving 29 remaining observations to construct forecasts.

Quick



Equation Estimation





Forecast



dynamic/static

Simultaneous equations modelling using EViews   What is the relationship between inflation and stock returns?

In EViews, to do this we need to specify a list of instruments, which would be all of the variables from the reduced form equation. The reduced form equations: 

Quick



Estimation Equation

   The coefficients are all not significant.

The fitted relationship between the stock returns and inflation series is positive (albeit not significantly so).

The adjusted 𝑅 2 is negative.

P.308

File: currencies.wfl

Period: 1991/03~2007/05

Vector autoregressive models  The simplest case:  Open “currencies.wfl” 

Quick



Estimate VAR

    How to decide the length of lagged term?

View



Lag Structure



Lag Length Criteria



10

Conclusion: choose VAR(1).

Granger causality test  very little evidence of lead-lag interactions between the series.