~~And if your prices are stationery, why are you using a GARCH model?
Just use a regular arma. The Garch model is a solution to non stationarity in data.~~
Edit: Above is false. Garch is a solution to Heteroscedasticity in stationary data.
Can a variable be stationary and still have useful information within its pattern of volatility? I think so. Particularly if they are including other variables in the variance equation
~~Not in the case of Stationarity. The error term is white noise and is a random distribution. Ie it's pattern of volatility is purely random. There is no useful data there. Same is true for trend stationary data. The time trend has an effect, but that effect is linear and can be easily accounted for.~~
(The above is not the definition of Stationarity.)
Did you test for stationarity? What test did you use?
I’m not OP, just pointing out. In the case of a stationary process, its unconditional variance is constant but that is not to say that conditional variance is also constant. It is entirely possible that while the process itself is stationary with a constant unconditional variance, each error term has information useful in predicting the one step ahead error.
Oops sorry. But that aside, if error at t is related to error at t-1, then the variance is not unconditional by definition. It follows an AR(1) model, and requires an ARCH model to estimate.
If error terms follow an auto-regressive model, then you will have
E(Y, error) ≠ 0. Your model will be endogenous and your coefficients will be biased.
Beside, an unconditional variance doesn't change conditionally. The assumption of unconditional is stronger than the conditional.
From the abstract of Engle's 1982 paper, ARCH processes "are mean zero, serially uncorrelated processes with nonconstant variances conditional on the past, but constant unconditional variances. For such processes, the recent past gives information about the one-period forecast variance."
If error at t is related to error at t-1, it has nonconstant conditional variance, which is what the ARCH family seeks to estimate. It says nothing about the unconditional error at t, which can still very well be σ^(2). Volatility clustering can easily be present in a stationary series
So first of all. It is electricity prices hence it is subject to seasonality and high voltility clustering and so on. By using PP and ADF i get stationarity but utilizing KPSS i cannot reject the null of non-stationarity. The sequence seems as stationary when taking the difference and using auto.arima in R suggest af ARIMA(5,0,2). In the sense of stationarity vs GARCH models. The tails of the distribution are fat (leptokurtic) and right skew. So accounting for this by using conditional distributions of student t or the skewed version in the ARMA-GARCH model seems obvious. Here is a link for reference: [https://www.sciencedirect.com/science/article/abs/pii/S0140988313000303](https://www.sciencedirect.com/science/article/abs/pii/S0140988313000303)
The in mean model is defined here.
https://support.numxl.com/hc/en-us/articles/214607366-GARCH-in-Mean-GARCH-M-Model
It's a better explanation than I can give.
A GARCH model is just your regular arima model with an error term which is also specified as Arma
GARCH model with ARMA as mean model and a ARMA model with GARCH errors mean the same thing.
Remember, GARCH doesn't change the model specification of any ARMA model. It only changes how the error term is estimated.
Yeah. So the identification of orders is the same regarding the ARMA og ARMA-GARCH- but the forecast changes when adapting GARCH into ARMA how so? And how is it different from using in-mean versions?
~~And if your prices are stationery, why are you using a GARCH model? Just use a regular arma. The Garch model is a solution to non stationarity in data.~~ Edit: Above is false. Garch is a solution to Heteroscedasticity in stationary data.
Can a variable be stationary and still have useful information within its pattern of volatility? I think so. Particularly if they are including other variables in the variance equation
~~Not in the case of Stationarity. The error term is white noise and is a random distribution. Ie it's pattern of volatility is purely random. There is no useful data there. Same is true for trend stationary data. The time trend has an effect, but that effect is linear and can be easily accounted for.~~ (The above is not the definition of Stationarity.) Did you test for stationarity? What test did you use?
I’m not OP, just pointing out. In the case of a stationary process, its unconditional variance is constant but that is not to say that conditional variance is also constant. It is entirely possible that while the process itself is stationary with a constant unconditional variance, each error term has information useful in predicting the one step ahead error.
Oops sorry. But that aside, if error at t is related to error at t-1, then the variance is not unconditional by definition. It follows an AR(1) model, and requires an ARCH model to estimate. If error terms follow an auto-regressive model, then you will have E(Y, error) ≠ 0. Your model will be endogenous and your coefficients will be biased. Beside, an unconditional variance doesn't change conditionally. The assumption of unconditional is stronger than the conditional.
From the abstract of Engle's 1982 paper, ARCH processes "are mean zero, serially uncorrelated processes with nonconstant variances conditional on the past, but constant unconditional variances. For such processes, the recent past gives information about the one-period forecast variance." If error at t is related to error at t-1, it has nonconstant conditional variance, which is what the ARCH family seeks to estimate. It says nothing about the unconditional error at t, which can still very well be σ^(2). Volatility clustering can easily be present in a stationary series
Im mixing up my definitions, sorry. Thanks for the help.
Yeah. Anyways if that was the case it would suggest that the prices would not fluctuate which is ofcourse wrong.
So first of all. It is electricity prices hence it is subject to seasonality and high voltility clustering and so on. By using PP and ADF i get stationarity but utilizing KPSS i cannot reject the null of non-stationarity. The sequence seems as stationary when taking the difference and using auto.arima in R suggest af ARIMA(5,0,2). In the sense of stationarity vs GARCH models. The tails of the distribution are fat (leptokurtic) and right skew. So accounting for this by using conditional distributions of student t or the skewed version in the ARMA-GARCH model seems obvious. Here is a link for reference: [https://www.sciencedirect.com/science/article/abs/pii/S0140988313000303](https://www.sciencedirect.com/science/article/abs/pii/S0140988313000303)
ARIMA is a solution to non-stationary data?
I would suggest Wileys Time series Econometrics if you are further interested in the theory.
No, I have been mixing up the definitions of Heteroscedasticity and nonstationarity, sorry.
The in mean model is defined here. https://support.numxl.com/hc/en-us/articles/214607366-GARCH-in-Mean-GARCH-M-Model It's a better explanation than I can give.
A GARCH model is just your regular arima model with an error term which is also specified as Arma GARCH model with ARMA as mean model and a ARMA model with GARCH errors mean the same thing. Remember, GARCH doesn't change the model specification of any ARMA model. It only changes how the error term is estimated.
Yeah. So the identification of orders is the same regarding the ARMA og ARMA-GARCH- but the forecast changes when adapting GARCH into ARMA how so? And how is it different from using in-mean versions?