Where does lag collide?

In Social Change with Respect to Culture and Original Nature (1922), William F. Ogburn named cultural lag: the interval during which the nonmaterial parts of a culture, such as its laws, customs, and institutions, adjust to a change in its material conditions, such as a new technology. The gap opens because material culture tends to change first and the dependent culture responds only after a delay, leaving a stretch of poor fit between the two. Here the referent is a period of social time measured across a whole society, and it is unrelated to the angular delay of a periodic output behind its input in engineering or a shifted past value of a data series in time-series statistics.[1]

Unit

One episode of maladjustment between a material change and the culture adapting to it

Recovery means

The gap closes once the dependent institutions and customs adjust to the new material conditions

Measured by

Assessed historically by dating a material change and its later adaptation and taking the interval between them

Yule's 1927 study On a method of investigating periodicities in disturbed series modeled a value of a series as depending on its own earlier, or lagged, values, where a lag of order k is simply the observation k periods before the current one. Almon's 1965 The distributed lag between capital appropriations and expenditures extended this to distributed lags, spreading the influence of a past input across several of its lagged terms. Here the referent is an index shift on a sequence of measurements, counted in periods such as days or quarters, and it is not the interval before a society adapts to a new technology or the phase delay of an oscillating output in engineering.[2][3]

Unit

One backward shift of a series by a whole number of time periods

Recovery means

Not applicable

Measured by

Computed by shifting the series in time, as in an autocorrelation at each lag or a predictor entered at lag k

Nyquist's 1932 Regeneration theory analyzed how a feedback system's steady output to an oscillating input trails that input, a delay expressed as phase lag: the angle, in degrees, by which the output waveform falls behind the driving waveform at a given frequency. Engineers add a lag compensator, a network that deliberately introduces this delay, to shape a system's frequency response and hold it stable. The word lagging, for one alternating quantity trailing another, was already routine in alternating-current theory before this work. Here the referent is an angle between two oscillations at a single frequency, and it is not the interval before a society adapts to new technology or a whole-period shift of a data series in statistics.[4]

Unit

An angle, in degrees or radians, between an output oscillation and its input at a given frequency

Recovery means

Not applicable

Measured by

Read from a Bode phase plot or a frequency-response measurement as the phase angle at each frequency