Contents
What is an ARCH 0 model?
An ARCH model is used to predict the variance at future time steps. [ARCH] 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.
Which is the formula of conditional variance?
The conditional variance is similar to the conditional expectation. Var(X |Y = y) is the variance of X, when Y is fixed at the value Y = y. Var(X |Y ) is a random variable, giving the variance of X when Y is fixed at a value to be selected randomly.
What is Arch model used for?
Autoregressive conditional heteroskedasticity (ARCH) is a statistical model used to analyze volatility in time series in order to forecast future volatility. In the financial world, ARCH modeling is used to estimate risk by providing a model of volatility that more closely resembles real markets.
What are ARCH effects?
The ARCH effect is concerned with a relationship within the heteroskedasticity, often termed serial correlation of the heteroskedasticity. It often becomes apparent when there is bunching in the variance or volatility of a particular variable, producing a pattern which is determined by some factor.
When to use an arch model in statistics?
ARCH models are used to describe a changing, possibly volatile variance. Although an ARCH model could possibly be used to describe a gradually increasing variance over time, most often it is used in situations in which there may be short periods of increased variation.
What is the relationship between arch and YT series?
An ARCH (m) process is one for which the variance at time t is conditional on observations at the previous m times, and the relationship is Var ( y t | y t − 1, …, y t − m) = σ t 2 = α 0 + α 1 y t − 1 2 + ⋯ + α m y t − m 2. With certain constraints imposed on the coefficients, the yt series squared will theoretically be AR (m).
Which is a useful property of the ARCH model?
Two potentially useful properties of the useful theoretical property of the ARCH (1) model as written in equation line (2) above are the following: y t 2 has the AR (1) model y t 2 = α 0 + α 1 y t − 1 2 + error. y t is white noise when 0 ≤ α 1 ≤ 1.
What does this say for the variance of the unconditional?
I am not sure if this cleans up nicely, but what does this say for the variance? it seems like the unconditional is just going to blow up infinitely (given I could have made a mistake in the derivation of this question).