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Lag and Lead Correlation

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When there exists a cause and effect relationship between two time series, it is usually observed that there is a time lag between the changes in the values of the independent variable (also called the subject series) and the dependent variable (also called the relative series). Such phenomenon is usually observed in most of the economic and business time series.

For example, the monthly advertisement expenditure of a firm on its product and the sales of the product have a fairly good degree of positive correlation. However, the effect of the advertisement expenditure will be felt on the increased sales of the product only after a certain period of time, which maybe 3 or 4 months or even more. This tendency on the part of the effect (change in the dependent variable or relative) to occur sometimes after the occurrence of the cause (change in independent variable or subject) is known as ‘lag’. If it is known that ‘lag’ exists between two time series, it is imperative to make adjustments for it, before computing the correlation coefficient between the two series otherwise fallacious conclusions will be drawn.


In order to make allowance for the ‘lag’, it is necessary to determine the ‘time-lag’ i.e., to estimate the time period which lapses before the change in the dependent variable is affected after a change in the independent variable. The ‘period of lag’ can be estimated by plotting the two series on a graph paper and noting the time distance between the peaks/troughs of two curves. If the peak (trough) in dependent variable (sales) comes after k-months of the peak (trough) in the independent variable (advertisement expenditure), then there is k-month time-lag between the two variables. Here we say that ‘advertisement expenditure curve’ will lead by k-months and the ‘sales curve’ would lag by k-months.

Reference: Business Statistics – S.C Gupta, Indra Gupta

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