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?

Have you tried just shifting the EMA 1-bar forward?

OR,

Given that the only unknown variable you seem to show is the "Closing", could you work out the average move (velocity) of closing prices are, and project forward?

EG, if the last 3 Closing prices are 100, 110, 118, the market has closed (118 - 100) = 18 points higher per past 3 days, which is a velocity of 6 per day. Could you project the Closing as 124 (118 + 6) and go from there?

Predictions imply the market wont spike, surge, stall, congest, etc. Past performance is no guarantee of (you know the rest)

Some people use trendlines.

Good luck with this.