In other words, as we go back further in history, the weight becomes smaller. Since alpha is between 0 and 1, the weight becomes smaller as k becomes larger. The equation can be rearranged to show that the EWMA t is the weighted average of all the preceding observations, where the weight of the observation r t–k is given by: The process continues until we reach the base term EWMA 0. It can be further expanded by going back another period: The above equation can be rewritten in terms of older weights, as shown below: The EWMA’s recursive property leads to the exponentially decaying weights as shown below: The EWMA is a recursive function, which means that the current observation is calculated using the previous observation. r = Value of the series in the current period.The EWMA’s simple mathematical formulation described below: The higher the value of alpha, the more closely the EWMA tracks the original time series. The parameter decides how important the current observation is in the calculation of the EWMA. The only decision a user of the EWMA must make is the parameter alpha. The weights fall exponentially as the data point gets older – hence the name exponentially weighted. The moving average is designed as such that older observations are given lower weights. The EWMA is widely used in finance, the main applications being technical analysis and volatility modeling. The Exponentially Weighted Moving Average (EWMA) is a quantitative or statistical measure used to model or describe a time series. Updated OctoWhat is the Exponentially Weighted Moving Average (EWMA)?
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