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date: 24 May 2018

Long Memory Models

This is an advance summary of a forthcoming article in the Oxford Research Encyclopedia of Economics and Finance. Please check back later for the full article.

Long memory models are statistical models that describe strong correlation or dependence across time series data. This kind of phenomenon is often referred to as “long memory” or “long-range dependence.” It refers to persisting correlation between distant observations in a time series. For scalar time series observed at equal intervals of time that are covariance stationary, so that the mean, variance, and autocovariances (between observations separated by a lag j) do not vary over time, it typically implies that the autocovariances decay so slowly, as j increases, as not to be absolutely summable. However, it can also refer to certain nonstationary time series, including ones with an autoregressive unit root, which exhibit even stronger correlation at long lags. Evidence of long memory has often been found in economic and financial time series, where the noted extension to possible nonstationarity can cover many macroeconomic time series, as well as in such fields as astronomy, agriculture, geophysics, and chemistry.

As long memory is now a technically well-developed topic, formal definitions are needed, and we defer these to the paper itself. But by way of partial motivation, long memory models can be thought of as complementary to the very well-known and widely applied stationary and invertible autoregressive and moving average (ARMA) models, whose autocovariances are not only summable but decay exponentially fast as a function of lag j. Such models are often referred to as “short memory” models because there is negligible correlation across distant time intervals. However, these models are often combined with the most basic long memory ones, since together they offer the ability to describe both short and long memory features in many time series.