Exponential smoothing or exponential moving average (EMA) is a rule of thumb technique for smoothing time series data using the exponential window function. Whereas in the simple moving average the past observations are weighted equally, exponential functions are used to assign exponentially decreasing weights over time. It is an easily learned and easily applied procedure for making some determination based on prior assumptions by the user, such as seasonality. Exponential smoothing is often used for analysis of time-series data.

Exponential smoothing is one of many window functions commonly applied to smooth data in signal processing, acting as low-pass filters to remove high-frequency noise. This method is preceded by Poisson's use of recursive exponential window functions in convolutions from the 19th century, as well as Kolmogorov and Zurbenko's use of recursive moving averages from their studies of turbulence in the 1940s.

The raw data sequence is often represented by ${\textstyle \{x_{t}\}}$ beginning at time ${\textstyle t=0}$, and the output of the exponential smoothing algorithm is commonly written as ${\textstyle \{s_{t}\}}$, which may be regarded as a best estimate of what the next value of ${\textstyle x}$ will be. When the sequence of observations begins at time ${\textstyle t=0}$, the simplest form of exponential smoothing is given by the following formulas:

where ${\textstyle \alpha }$ is the smoothing factor, and ${\textstyle 0<\alpha <1}$. If ${\textstyle s_{t-1}}$ is substituted into ${\textstyle s_{t}}$ continuously so that the formula of ${\textstyle s_{t}}$ is fully expressed in terms of ${\textstyle \{x_{t}\}}$, then exponentially decaying weighting factors on each raw data ${\textstyle x_{t}}$ is revealed, showing how exponential smoothing is named.

The simple exponential smoothing is not able to predict what would be observed at ${\textstyle t+m}$ based on the raw data up to ${\textstyle t}$, while the double exponential smoothing and triple exponential smoothing can be used for the prediction due to the presence of ${\displaystyle b_{t}}$ as the sequence of best estimates of the linear trend.

The use of the exponential window function is first attributed to Poisson as an extension of a numerical analysis technique from the 17th century, and later adopted by the signal processing community in the 1940s. Here, exponential smoothing is the application of the exponential, or Poisson, window function. Exponential smoothing was suggested in the statistical literature without citation to previous work by Robert Goodell Brown in 1956, and expanded by Charles C. Holt in 1957. The formulation below, which is the one commonly used, is attributed to Brown and is known as "Brown’s simple exponential smoothing". All the methods of Holt, Winters, and Brown may be seen as a simple application of recursive filtering, first found in the 1940s to convert finite impulse response (FIR) filters to infinite impulse response filters.

The simplest form of exponential smoothing is given by the formula:

where ${\displaystyle \alpha }$ is the smoothing factor, with ${\displaystyle 0\leq \alpha \leq 1}$. In other words, the smoothed statistic ${\displaystyle s_{t}}$ is a simple weighted average of the current observation ${\displaystyle x_{t}}$ and the previous smoothed statistic ${\displaystyle s_{t-1}}$. Simple exponential smoothing is easily applied, and it produces a smoothed statistic as soon as two observations are available. The term smoothing factor applied to ${\displaystyle \alpha }$ here is something of a misnomer, as larger values of ${\displaystyle \alpha }$ actually reduce the level of smoothing, and in the limiting case with ${\displaystyle \alpha }$ = 1 the smoothing output series is just the current observation. Values of ${\displaystyle \alpha }$ close to 1 have less of a smoothing effect and give greater weight to recent changes in the data, while values of ${\displaystyle \alpha }$ closer to 0 have a greater smoothing effect and are less responsive to recent changes. In the limiting case with ${\displaystyle \alpha }$ = 0, the output series is just flat or a constant as the observation ${\textstyle x_{0}}$ at the beginning of the smoothening process ${\textstyle t=0}$.