I am trying to forecast prices with exponential moving average method. The equation for EMA = [(Closing * k) + (EMA(y) * (1-k)] where: Closing is closing price of today, k is the weighted multiplier, EMA(y) is the previous EMA, and 1 - k is 1 - weighted multipler. This gives the EMA for today. I would like to know how can I modify this equation to forecast the EMA of the next day without knowing the closing price of the next day?


You can forecast your time series $(X_t)$ as follows $$F_{t+1} = k X_t + (1-k)F_t,$$ where $F_t$ is your forecast for today and $X_t$ the observed value for today (today's log-return). Note that the above equation is equivalent to $$F_{t+1}-F_t = k(X_t-F_t)$$ and hence, the change in the forecast value is proportional to the current forecasting error.

Due to low autocorrelation in return series however, I doubt how succesfulsuch forecasts are. By the way, this version of an EWMA does not incorporate seasonal patterns or (linear) trends but may be adjusted.

Note that the formula you quoted is used as exponential smoothing in order to reduce the ''roughness'' of an observed time series. In technical analysis, one frequently applies SMA, WMA or EMA in order to identify trends.

I typically see an EMWA used in time series analysis to forecast volatility (squared returns have a significant autocorrelation). Here, the EMWA formula (which is a special case of an IGARCH(1,1) model) for forecasting the conditional variancce reads as follows $$ \hat{s}_t^2 = (1-\lambda)X_{t-1}^2 + \lambda \hat{s}^2_{t-1},$$ where $\lambda=0.94$ and $(X_t)$ are the log-returns of your asset. Then, you can estimate tomorrow's volatility using today's log-return and variance estimate.


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