# Time Series: GARCH and ARMA

To model time series we look at GARCH models to estimate how volatility auto correlates over time and look at autoregressive patterns in the time series as well as exponentially declining moving average shocks that may change the measured variable. For instance the shocks of last period may be forgotten or the shocks of two or three periods ago may still be remembered but discounted. The key thing as with all modeling is to look to see if the error terms are well-behaved. If the measured variable in question is not well-behaved in its errors, then we have reason to suspect the model is incorrect and that everything is not what it appears to be. But to go beyond basic intuition, we have to consider whether the problematic behavior in error terms is conditional on a lurking variable. If error terms are very volatile initially and drop in volatility later then perhaps a lurking variable has turned on or off beyond the time series. For example, if someone asks you what does all this intellectual nonsense have to do with the price of oranges in Colombia, you answer that he is the connection as he is suggesting that one thing leads to another in the economy which does not follow in an efficient market because of anticipation effects yet he is the connection because if he wants to speculate on the prices of commodities internationally he has no business learning about the economy, all he needs is psychology as speculation is just about outsmarting the lawyer on the other end of the phone call. There is also the law which impacts how you function in every bit of society. Now I’m not saying psychology is not useful it just is often misused. If I want to answer that question properly: what does the price of oranges in Colombia have to do with intellectual work on the economy, I would argue in a land with rational actors, I am studying rational human behavior and can eventually imply a fair price for oranges in Colombia for which we can push prices to in some sort of microeconomic equilibrium. So I can answer that question fine. What he can’t answer though, is why he asked that question.

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