# How can I forecast the Exponential Moving Average of the next day?

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.
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.