What does significant autocorrelation at lag k in a time series imply?

Explanation: Significant autocorrelation at lag kk k means that the value at a given time tt t is correlated with its value at time t−kt-k t − k . This predictable relationship is crucial in identifying patterns that can improve forecasting accuracy. High autocorrelation suggests that past values influence future values, forming the basis for autoregressive modeling. For instance, in stock market analysis, if prices at t−1t-1 t − 1 strongly correlate with tt t , autoregressive models like ARIMA are effective for prediction. Option A: Stationarity involves constant statistical properties over time, not autocorrelation. Option C: Seasonal decomposition deals with cyclical patterns, not autocorrelation. Option D: Random residuals indicate a well-fitted model, unrelated to autocorrelation. Option E: Significant autocorrelation indicates linear dependency, not independence.