Non Linear Flashcards
Leptokurtis
Non linear- of Disturbance term which doesn’t follow normal
Non linear formula
Yt=g(ut_1, ut_2) +ut🔁squared( ut_1, ut_2)
Past error term + non linear variance term
Ramsey test
Non linear dependence
Adds higher order terms (think Gordon!)
Why volatility is important
Finance- measures riskiness of assets
Simple model= using variance of past prices to predict future prices
Arch and formula
Autoregressive heteroscedastic model
Variance t= a0+a1ut_1 squared
Arch q
Variance depends on q lags
Regress q lags, test for arch order q
Problems with arch
Deciding on q number of lags
Garch
Gets round arch problem of number of lags
Variance = a0 + a1ut_1 squared Bvariance
Garch (p,q)
Garch extended for more lags
Problem with garch
Doesn’t account for leverage effects- sample size
E garch
Cancels exponential
Has Ln in formula
Parameter stability test
Tests if parameters are constant for sample
Chow test- splits data into 2 time periods - restricted and unrestricted
Test using the f tables
Chow test formula
Test statistic=
RSS- (RSS1+RSS2)
/RSS1+RSS2 X T-2K/K
If test stat is >city value from F reject
Improving models
Test CLRM assumptions
Take actions- logs, add lags, dummy variables, bigger sample
Reparametise- take out insig variables
Re check assumptions
Use for forecasting
Chow test null hypothesis
If testing if one time period equal to another
H0: a1=A2 and b1=b2
