Abstract
Financial Time Series Forecasting is an important tool to support both individual and organizational decisions. Periodic phenomena are very popular in econometrics. Many models have been built aiding capture of these periodic trends as a way of enhancing forecasting of future events as well as guiding business and social activities. The nature of real-world systems is characterized by many uncertain fluctuations which makes prediction difficult. In situations when randomness is mixed with periodicity, prediction is even much harder. We therefore constructed an ANN Time Varying Garch model with both linear and non-linear attributes and specific for processes with fixed and random periodicity. To eliminate the need for time series linear component filtering, we incorporated the use of Artificial Neural Networks (ANN) and constructed Time Varying GARCH model on its disturbances. We developed the estimation procedure of the ANN time varying GARCH model parameters using non parametric techniques.
Highlights
Periodic phenomena such as business and temperature cycles appear in our daily life very often
To eliminate the need for time series linear component filtering, we incorporated the use of Artificial Neural Networks (ANN) and constructed Time Varying Generalised Autoregressive Conditional Heteroskedasticity (GARCH) model on its disturbances
We developed the estimation procedure of the ANN time varying GARCH model parameters using non parametric techniques
Summary
The introduction of periodic models into economics dates back to the late 1980s. the focus was on describing trending consumption and income data, and the use of periodic models for out-of-sample forecasting. The fixed periodic models assume that the coefficients of the underlying model are purely repetitive, that is, they vary with the fixed period s. The number of the coefficients is s times more than the standard coefficients in the standard stochastic model. A fixed periodic model permits a different standard stochastic model for each fixed period s. Random periodic models have all the coefficients vary with time t. All the coefficients are different from each other even if they are in the same random period τ. The major difference between fixed and random periodicity is that the same time points in different periods will have the same behaviour in fixed periodicity but there will be small fluctuations between different periods in random periodicity. The following are the graphical representation of fixed periodicity, random periodicity and a combination of fixed and random periodicity (Figures 1-3)
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