Calculator
Example Data Table
| Time | Observed Value | Comment |
|---|---|---|
| 2026-01 | 120 | Observed baseline value |
| 2026-02 | Missing | Gap for monthly demand |
| 2026-03 | 136 | Observed rebound value |
| 2026-04 | 141 | Observed growth continues |
| 2026-05 | Missing | Second missing point |
| 2026-06 | 155 | Observed seasonal lift |
Paste similar time,value rows into the calculator. Leave missing values blank, or use markers such as NA or null.
Formula Used
Linear interpolation
x(t) = x(a) + (x(b) - x(a)) × (t - a) / (b - a). This estimates a missing point between two known values.
Forward and backward fill
x(t) = x(t-1) for forward fill, and x(t) = x(t+1) for backward fill. These methods copy the nearest observed neighbor.
Centered moving average
x(t) = average(x(t-k) ... x(t+k)). The selected window controls how many nearby values contribute to each estimate.
Seasonal mean
x(t) = average(x(t-s), x(t+s), x(t+2s) ...). The season length s matches repeating cycles such as months or quarters.
Exponential smoothing
S(t) = α × x(t) + (1 - α) × S(t-1). Missing values are replaced by the latest smoothed level.
How to Use This Calculator
- Paste time,value rows into the data box.
- Leave missing values blank, or mark them clearly.
- Select the imputation method that fits your series behavior.
- Adjust the moving window, season length, and alpha when needed.
- Press Impute Series to generate the cleaned series.
- Review summary metrics, completed values, and status labels.
- Export the results to CSV or PDF for documentation.
Frequently Asked Questions
1) What does this calculator do?
It fills missing numeric observations in a time series. You can compare several practical methods, inspect cleaned outputs, and export the finished series.
2) Which method is best for smooth trends?
Linear interpolation usually works well when nearby values change steadily. It estimates intermediate points from the nearest known values before and after the gap.
3) When should I use forward fill?
Forward fill is useful when the latest known state should continue until a new observation appears. Inventory levels and status-based process data often use this approach.
4) What is season length?
Season length is the number of periods in one repeating cycle. Monthly data with yearly repetition uses 12, while quarterly data often uses 4.
5) What does alpha control?
Alpha controls how quickly exponential smoothing reacts to recent changes. Larger values emphasize newer observations, while smaller values produce steadier estimates.
6) Can I paste dates instead of numeric periods?
Yes. The first column is treated as a time label, so dates, months, or custom identifiers all work as long as the value column is numeric or missing.
7) Does the tool replace observed values?
No. Observed rows stay unchanged. Only missing entries are filled, and each output row is marked as Observed or Imputed for clarity.
8) Why export the cleaned series?
Exporting helps you reuse the completed series in reports, forecasting models, dashboards, or audit files without manually copying the imputed values.