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Answers for “为什么恢复求和在最后观测索引 l 处停止?”

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You recover the original series qkq_k by summing the predicted differences ZtZ_t and adding them to the last known actual value qlq_l (or q1q_1 depending on the starting index). The formula is qk=∑i=1k−lZk−i+qlq_k = \sum_{i=1}^{k-l} Z_{k-i} + q_l.

Conditions: You have forecasts for the differenced series ZtZ_t.; You know the last observed value of the original series qlq_l.; The relationship Zt=qt+1−qtZ_t = q_{t+1} - q_t holds.