# Covariance nonstationary vs. ARCH

How are they related?

they aren’t… Arch is used when an autoregressive model sufferers from hetroscadiscity (spelt wrong)… covariance stationary is when an AR model does not have: equal mean equal variance equity covariance with itself

mambovipi Wrote: ------------------------------------------------------- > they aren’t… Arch is used when an > autoregressive model sufferers from > hetroscadiscity (spelt wrong)… covariance > stationary is when an AR model does not have: > equal mean > equal variance > equity covariance with itself Dude…you have screwed this up completely. To the original poster, you really should do a forum search. This topic has been discussed. But…to answer the question anyway… They are absolutely related. Stationarity relates to have both constant and finite mean, variance, and covariance among successive observations. ARCH (standing for autoregressive conditional hetero) is used on a nonstationary model whose volatility is not constant, hence the use of the term heteroskedasticity. The point is that we have some process that may or may not be appropriately regressed on its own lagged values due to it being nonstationary, but sense its volatility is not constant, maybe we can model that. As often used in option valuation, ARCH or GARCH or some other form will be used to forecast short-term volatility as an input to the valuation model.

Thanks for clarifying things for us! Any link between unit root test and ARCH test? Non-constant variance= variance depends on independent variable?

Thanks for clarifying things for us! Any link between unit root test and ARCH test? Non-constant variance= variance depends on independent variable?

Thanks for clarifying things for us! Any link between unit root test and ARCH test? Non-constant variance= variance depends on independent variable? The C in ARCH comes from the fact that variance of period t is conditional on that of period t-1?

conditional means it depends on the value of the independent variable. that’s where C comes from.

Then, what is the difference between conditional H* and H*?

h* can be unconditional too. that doesnt cause any problems for us in the regression test, we dont care if its unconditional h* is present.

I guess I do not know what is unconditional h*…

h* means variance of residuals is not the same across all observations. unconditional is when the H* isnt related to the value of the independent variable (violates assumptions, but causes no problem!) conditional is when the H* is related to the value of the independent variable. (causes problem. must be fixed).

bobsters Wrote: ------------------------------------------------------- > h* means variance of residuals is not the same > across all observations. > > unconditional is when the H* isnt related to the > value of the independent variable (violates > assumptions, but causes no problem!) > > conditional is when the H* is related to the value > of the independent variable. (causes problem. must > be fixed). No. It has nothing to do with dependence on the independent variable. It has to do with dependence on prior volatility. An ARCH/GARCH model regresses volatility on past values of volatility…hence phenomenons such as volatility clustering. Periods of high vol are typically followed by periods of high vol, and vice-a-versa.

ah you;re right. i was thinking about multiple regression i think, not time series.

wyantjs Wrote: ------------------------------------------------------- > bobsters Wrote: > -------------------------------------------------- > ----- > > h* means variance of residuals is not the same > > across all observations. > > > > unconditional is when the H* isnt related to > the > > value of the independent variable (violates > > assumptions, but causes no problem!) > > > > conditional is when the H* is related to the > value > > of the independent variable. (causes problem. > must > > be fixed). > > > No. It has nothing to do with dependence on the > independent variable. It has to do with > dependence on prior volatility. An ARCH/GARCH > model regresses volatility on past values of > volatility…hence phenomenons such as volatility > clustering. Periods of high vol are typically > followed by periods of high vol, and vice-a-versa. I’m a bit confused. He defined the two terms correctly, but you’re saying he’s wrong? Also what is H*? Can’t deny that ARCH models are something I need to brush up on. Schweser: Unconditional heteroskedasticity occurs when the heteroskedasticity is not correlated with the independent variables. While this is a violation of the equal variance assumption, it causes no major problems in most cases. Conditional heteroskedasticity is heteroskedasticity that is correlated with the values of the independent variables. Conditional heteroskedasticity does create significant problems for statistical inference.

H* is because we’re too lazy to write heteroskedasticity. The unconditional/condition definitions are for the multiple regression section. But for ARCH models, which are in Time Series, the definition is different. There, it means the variance of one error term is dependent on the variance of the error term in the previous period.

Then in time series, unconditional H* = not dependent on previous period, right?

PLEASE SOMEONE CONFIRM THE DIFFERENCE BETWEEN COND. HS: - IN TREND MODEL - IN AR MODEL From the book, it says CH in Trend is where the variance of the residuals (error) are correlated with the level of the independent variable. And for AR Model, it says CH is where the variance of the residuals are dependent on the variance of residuals in prior periods… To me, the definition for CH in AR Model relates to Autocorrelation… ANYONE CAN HELP!! Thanks

Bump