Sample Essay

Three generalised autoregressive conditional heteroscedasticity (GARCH) processes will be used in order to derive conditional variances and to find its sign and significance in conditional mean model. Testing for the asymmetric relationship between industrial production and output growth will allow observation of the spillover volatility between these indicators. This is very important because the nature of output directly depends on the industrial production. In doing this, positive/negative/no relationship might be obtained. (Speight 1999).

For this two econometrics packages might be applied: PCGIVE and EVIEW.

If the variance of a time series depends on the past, series is conditionally heteroscedastic. If autoregression can capture this dependence, autoregressive conditional heteroskedasticity (ARCH) model might be used. Meanwhile for the series  generalized ARCH models (GARCH) are more appropriate (Heij aet al, 2004).

yt represents GDP in period t. It follows an autoregressive (AR) process with ‘risk premium’ described in terms of volatility and it will be denoted in three different ways: g(ht) = ht, g(ht) = √ht and g(ht) = ln(ht): the conditional variance, the conditional standard deviation, and the natural log of the conditional variability.

=  +  +  + … +  + δ +   → AR (L)

ht →  GARCH (1.1) → ht = a + b + c

All three parameters are non-negative.

εt = e√ht

is a sequence of independent, identically distributed random variables with mean zero and variance 1, ht – the conditional variance of output growth.

For the variance equation Fountas, Karanasos and Mendoza (2004) approach will be used. Therefore, GARCH models will be applied: Bollerslev’s model, Taylor/Schwert’s model and Nelson’s EGARCH model.

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