Time Series Smoothing & Forecasting Calculator

Smooth out random noise in your time series data to identify underlying trends and generate next-period forecasts. Enter your chronological data to instantly calculate a Simple Moving Average (SMA) and Single Exponential Smoothing (SES).

How to use this calculator

1. Enter your data: Paste your sequential data (like monthly sales or daily temperatures) into the data box. The data must be in chronological order from oldest to newest.
2. Set the SMA Period ($k$): Choose how many data points to average together. A 3-period SMA averages the last 3 data points to predict the next one.
3. Set the Alpha Factor ($\alpha$): This controls the Exponential Smoothing. It must be a decimal between 0 and 1.
   • Closer to 1: Gives heavy weight to recent data (best if your data changes rapidly).
   • Closer to 0: Gives heavy weight to older data, creating a much smoother, flatter trend line.

Understanding Your Results

Time series forecasting relies on the idea that past patterns can predict future behavior. However, real-world data is often “noisy” and jagged.

• Simple Moving Average (SMA): An unweighted mean of the previous $k$ data points. It is great for smoothing out short-term fluctuations, but it “lags” behind sudden trend changes because it treats older data in the window with the exact same importance as yesterday’s data.
• Exponential Smoothing (SES): Unlike SMA, Exponential Smoothing applies decreasing, exponential weights to older data. It reacts to sudden trend changes much faster than a standard moving average while still filtering out random noise.
• Forecast (Period $t+1$): The calculator uses your historical data to predict the very next data point in your sequence.