(e.g. predicting daily market demand for the next 7 days)<\/p>\n\n\n\n
Before the multi-step-ahead forecasting<\/em>, let’s take a brief look at the concept of one-step-ahead forecasting<\/em><\/strong> first. In the simplest case of univariate data, it can be represented as:<\/p>\n\n\n\n $$ \\hat{y}_{t+1} = f(y_{t-k:t}, \\textbf{x}_{t-k:t}, \\textbf{s}) $$<\/p>\n\n\n\n Here, \\( y_{t-k:t} = \\{ y_{t-k}, … ,y_t \\} \\) and \\( \\textbf{x}_{t-k:t} = \\{ \\textbf{x}_{t-k}, … , \\textbf{x}_t \\} \\) are observations of the target and exogenous inputs respectively, over a look-back window \\( k \\), \\( s \\) is static metadata of the entity (e.g. user profile), and \\( f(.) \\) is the model.<\/p>\n\n\n\n Namely, the objective of the model is to predict \\( y_{t+1} \\).<\/p>\n\n\n\n Actually, multi-horizon forecasting<\/em> is nothing more than a slight modification of one-step-ahead prediction<\/em>, as below:<\/p>\n\n\n\n $$ \\hat{y}_{t+\\tau} = f(y_{t-k:t}, \\textbf{x}_{t-k:t}, \\textbf{u}_{t-k:t+\\tau}, \\textbf{s}, \\tau) $$<\/p>\n\n\n\n Generally, there are two types of methods for multi-horizon forecasting: iterative methods<\/strong><\/em> vs. direct methods<\/em><\/strong>.<\/p>\n\n\n\n <\/p>\n\n\n\n
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Iterative Methods<\/em><\/strong> vs. Direct Methods<\/em><\/strong><\/h1>\n\n\n\n
![\"\"](\"http:\/\/logicalday.site\/wp-content\/uploads\/2025\/02\/image-9.png\")
<\/figure>\n\n\n\n1. Iterative Methods<\/h3>\n\n\n\n
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Advantages<\/summary>\n
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Disadvantages<\/summary>\n
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2. Direct Methods<\/h3>\n\n\n\n
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