In econometrics, an autoregressive conditional heteroskedasticity (ARCH) model considers the variance of the current error term to be a function of the variances of the previous time period's error terms.

If an autoregressive moving average model is assumed for the error variance, the model is a generalized autoregressive conditional heteroskedasticity (GARCH) model.

Generally, when testing for heteroskedasticity in econometric models, the best test is the White test. However, when dealing with time series data, the best test is Engle's ARCH test.

References

• Tim Bollerslev. "Generalized Autorregressive Conditional Heteroskedasticity", Journal of Econometrics, 31:307-327, 1986.

• Robert F. Engle. "Autoregressive Conditional Heteroscedasticity with Estimates of Variance of United Kingdom Inflation", Econometrica 50:987-1008, 1982. (the paper which sparked the general interest in ARCH models)

• Robert F. Engle. "GARCH 101: The Use of ARCH/GARCH Models in Applied Econometrics", Journal of Economic Perspectives 15(4):157-168, 2001. (a short, readable introduction)