Analysis Results
Results update after the calculator processes your time-series data.
Interpretation
Multiple Lag Analysis
Compare selected lags, correlation strength, and recurring time-series structure.
Lagged Pair Data
The table shows current values, lagged values, differences, and diagnostic flags.
| Observation | Date | Current value | Lagged observation | Lagged date | Lagged value | Difference | Absolute difference | Valid | Outlier |
|---|---|---|---|---|---|---|---|---|---|
| No data available. | |||||||||
Export and Utility Tools
Statistical Details
| Run the calculator to view detailed statistics. |
Formula Used
Lag plot pairs: (x[t − k], x[t]) Pearson correlation: r = Σ((x − x̄)(y − ȳ)) / √(Σ(x − x̄)² × Σ(y − ȳ)²) Autocorrelation at lag k: rₖ = Σ((xₜ − x̄)(xₜ₋ₖ − x̄)) / Σ(xₜ − x̄)² Linear regression: y = b₀ + b₁x
How to Use
- Enter values manually or upload a CSV file.
- Select the value column and optional date column.
- Choose a lag and optional lag comparison range.
- Apply transformations, smoothing, differencing, or outlier controls.
- Adjust chart labels, markers, ranges, and reference lines.
- Generate the analysis and review the plots and statistics.
- Export charts, tables, processed data, or a PDF report.
Example Data
| Month | Value | Possible meaning |
|---|---|---|
| January | 12 | Starting observation |
| February | 15 | Moderate increase |
| March | 18 | Continued movement |
| April | 13 | Seasonal decline |
| May | 16 | Recurring recovery |
Understanding Lag Plots
A lag plot compares each value with an earlier value. Tight diagonal patterns usually indicate positive dependence. Scattered points often suggest weak serial structure.
Downward patterns can reveal negative dependence between observations. Curves may indicate nonlinear time-series behaviour. Repeating structures can suggest seasonal cycles.
Lag plots support forecasting, feature engineering, and residual checking. They also help reveal anomalies and variance changes. Visual results should accompany formal statistical tests.
Machine-Learning Applications
- Time-series forecasting
- Autoregressive feature engineering
- Seasonality detection
- Anomaly detection
- Sensor-data analysis
- Financial-data diagnostics
- Demand forecasting
- Predictive maintenance
- Residual diagnostics
- Model validation
Frequently Asked Questions
What is a lag plot?
It plots current values against earlier observations. The selected lag controls the time separation.
What does a diagonal pattern mean?
An upward diagonal often indicates positive autocorrelation. A downward diagonal suggests negative autocorrelation.
Which lag should I choose?
Start with lag one. Then test known seasonal periods and correlation peaks.
Can the calculator detect seasonality?
It compares many lags and highlights strong recurring correlations. Formal seasonal modelling may still be necessary.
How are missing values handled?
You can remove, forward-fill, backward-fill, or impute them. Choose a method suitable for your data.
What is the difference between a lag plot and ACF?
A lag plot shows point geometry. An ACF chart summarises correlation across many lags.
Can I analyse CSV files?
Yes. Upload a CSV and select the value and date columns.
Why is my lag plot empty?
The lag may exceed the available series length. Invalid transformations can also remove observations.
Can I export the results?
Yes. Export data, charts, summaries, tables, and PDF reports.