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In the study of time series analysis, autoregressive (AR) models and moving average (MA) models are two fundamental approaches used to capture and explain the behavior of data observed over time. Both models are linear stochastic processes, yet they differ significantly in their formulation, underlying assumptions, and interpretation. Understanding the differences between these models is essential in statistical quality control and forecasting, as choosing the right model directly affects the accuracy of predictions and the quality of decision-making. The autoregressive model is based on the principle that the present value of a time series is a linear function of its past values and a random error term. In mathematical terms, an ____ _________ ______ ___ _____ _____ ___ __________ _______ ____.
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