Trend Moving Average Input
Enter one observation per line. Use either label,value or just value. Even centered windows are double-centered automatically.
Example Data Table
| Period | Observed Value |
|---|---|
| Jan | 120 |
| Feb | 128 |
| Mar | 133 |
| Apr | 145 |
| May | 149 |
| Jun | 158 |
| Jul | 164 |
| Aug | 170 |
| Sep | 176 |
| Oct | 184 |
| Nov | 191 |
| Dec | 198 |
This sample shows a gradually increasing series, which is useful for comparing raw values, smoothed values, and the extracted trend line.
Formula Used
1) Trailing Moving Average
MAt = (Yt + Yt-1 + ... + Yt-w+1) / w
2) Centered Moving Average
For odd windows, the average is placed at the center period. For even windows, two adjacent moving averages are averaged again to center the series.
3) Linear Trend on the Smoothed Series
T(t) = a + bt
b = [nΣ(xy) - ΣxΣy] / [nΣ(x²) - (Σx)²]
a = ȳ - b x̄
4) Forecast
Forecast at future step h: Ft+h = a + b(t + h)
How to Use This Calculator
- Paste your time series into the data box, one line per observation.
- Use label,value format if you want custom period names.
- Choose a window size based on how strongly you want smoothing applied.
- Select trailing or centered averaging depending on your analysis goal.
- Set forecast periods to extend the fitted trend into future periods.
- Press the calculate button to display results above the form.
- Review the table, trend equation, residuals, and interactive chart.
- Use the CSV and PDF buttons to export your analysis report.
Frequently Asked Questions
1) What does a trend moving average show?
It smooths short-term fluctuations so you can inspect the broader direction of a time series. After smoothing, the calculator fits a linear trend to summarize overall movement and generate simple forward projections.
2) What is the difference between trailing and centered averages?
A trailing average places the smoothed value at the end of each window, which is common for monitoring. A centered average places smoothing in the middle, which better aligns the trend visually for historical analysis.
3) Why are odd window sizes often preferred for centered averages?
Odd windows have a natural middle period, so the smoothed value aligns neatly at one point. Even windows need double-centering, which the calculator handles automatically, but odd windows are easier to interpret.
4) Can this calculator forecast future values?
Yes. It projects the fitted linear trend forward for the number of future periods you specify. These values are trend-based projections, so they are best used for direction rather than exact long-range prediction.
5) What input format should I use?
You can enter either a single numeric value per line or a label with a value separated by a comma, tab, or semicolon. Examples include Jan,120 or simply 120.
6) How do I choose a good window size?
Smaller windows respond faster to local changes, while larger windows smooth more aggressively. Pick a size that matches the rhythm of your data, such as weekly, monthly, or seasonal behavior.
7) Why are some moving-average cells blank?
Blank cells appear where there are not enough neighboring observations to compute the selected moving average. This is expected at the beginning of trailing averages and at both ends of centered averages.
8) Can I use irregular time labels?
Yes. You may label rows with months, weeks, codes, or other period names. However, the regression still treats the sequence as evenly spaced steps, so uneven real-world intervals should be interpreted carefully.