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FRM Part I · FRM Exam Part I · Stationary Time Series

A risk analyst models monthly trading volume of a commodity exchange and observes a pronounced spike every December. Which feature of the sample autocorrelation function (ACF) would most clearly point to seasonality in this monthly series?

Significant autocorrelations at lags 12, 24 and 36 indicate annual seasonality in monthly data, because observations one full cycle apart are correlated. Short-lag cutoffs or a lone lag-1 pattern do not reflect a repeating yearly cycle.

  1. ASignificant autocorrelations at lags 12, 24 and 36 in addition to short lagsCorrect
  2. BAutocorrelations that are exactly zero at every lag beyond 1
  3. CA sharp cutoff after lag 3 with no further significant spikes
  4. DAutocorrelations that alternate in sign but only at lag 1

Explanation

Seasonality of period s produces correlation between observations s periods apart. With monthly data and a yearly cycle, s = 12, so ACF spikes recur at lags 12, 24, 36. A cutoff after lag 3 or zero autocorrelation beyond lag 1 indicates no yearly pattern.

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