An arch is a curved structure capable of spanning a space while supporting significant weight (e.g. a doorway in a stone wall). The arch appeared in Mesopotamia, Indus Valley civilization, Egypt, Assyria, Etruria, and later refined in Ancient Rome. The arch became an important technique in cathedral building and is still used today in some modern structures such as bridges.

"ARCH" redirects here. For the children's rights organization, see Action on Rights for Children.

In econometrics, an autoregressive conditional heteroskedasticity (ARCH, Engle (1982)) model considers the variance of the current error term to be a function of the variances of the previous time period's error terms. ARCH relates the error variance to the square of a previous period's error. It is employed commonly in modeling financial time series that exhibit time-varying volatility clustering, i.e. periods of swings followed by periods of relative calm.