Programme MSc in Finance

Site HEC Lausanne

Semester Fall 2014

Module Leader Diane Pierret

Teaching Assistant Daria Kalyaeva

Assessment Type: Empirical Assignment

Assessment Title: A Dynamic Model for Switzerland GDP

Written by: Group Y (Ariane Kesrewani & Alan Lucero)

Additional attachments: Zip Folder containing Matlab code, data and figures.

Submission Date: December 15 at 00.05

1. Descriptive Statistics

a. Time series plots of GDP level and GDP growth i. Definition of weak stationarity. GDP level and growth stationarity.

A stochastic process

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The intercept is significant at a 1%. This can be understood as whenever p and q are equal to zero, the intercept can be read as the sample mean; however in this case where p and q are bigger than zero it will still be close to the sample mean but usually not identical as it is not the maximum likelihood estimate whenever p and q are bigger than zero. The AR(1) coefficient is significant at 10% with estimate of 0.31523, interpreted as a correlation of the current period GDP with the previous period as shown in equation 1.1. Moreover, shocks to highly correlated data will propagate and take more time to neutralize. Looking at figure 1.a we see that after the Q4 2008 shock, the GDP level takes several quarters to recover the trend it previously had. The MA (1) coefficient is not significant at 10% as well as the MA (2) coefficient. As a result of this insignificance of estimates, we can infer that for this particular model, the random shocks at each point can be interpreted as mutually independent and come from the same distribution. The main difference between MA and AR models is that in MA models a shock affects the values of X only for the current period and q periods in the future; while in the AR models a shock affects infinitely the values of X since affects Xt , which affects Xt+1, which affects Xt+2 ,

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The model successfully captures the dependence structure in the data and the residuals should look independent.

c. Final ARMA Model for Detrended GDP

Based on the above we decided to improve the model by removing the offsetting lag in AR, and adding up to 3 lags in MA after running numerous ARMA models with increasing lags. ARMA (1, 3) turned out to be one of the best models with the estimation: (Eq 3.3)

The results are:

ARMAout1 =

Estimate RobustSE tStat Intercept 2.6727e-06 1.6505e-06 1.6194 AR1 0.88141 0.052112 16.914 MA1 0.49069 0.13282 3.6944 MA2 0.36961 0.12305 3.0038 MA3 0.19385 0.10959 1.7688 logL 509.29 NaN NaN AIC -10.254 NaN NaN BIC -10.147 NaN NaN

Portman7 =

Qstat CriticalValue pValue Ljung-Box 7.9704 31.41 0.99206

The intercept is significant at a 10% but with an estimate close to zero. AR (1) coefficient is highly significant at a 1% as well as MA (1) and MA (2). MA (3) is significant at