Regression · Free
Time-series linear model
OLS on trend plus Fourier seasonal terms, and optional regressors.
What it assumes
Linear trend plus Fourier seasonal terms; optional regressors.
When to use
Calendar seasonality with (or without) a covariate.
When to avoid
Strong nonlinearity or too few points for the design matrix.
Knobs
OLS on [1, t, sin/cos harmonics, X].
How it works
The time-series linear model is ordinary least squares on a design matrix: intercept, time index, sine/cosine harmonics for the seasonal period, and optional extra columns you selected in Excel. It is transparent and good for calendar seasonality with (or without) a covariate. Strong nonlinearity or too few rows for the columns will fail the fit.
Sample forecast question
Twelve monthly gas-use figures show a winter peak and a mild rise. What is the time-series linear model forecast for the next four months?
Step-by-step on these numbers
| Period | Actual | Fitted |
|---|---|---|
| Jan | 22 | 22.02 |
| Feb | 24 | 23.91 |
| Mar | 28 | 28.17 |
| Apr | 36 | 35.84 |
| May | 48 | 48.05 |
| Jun | 62 | 62.04 |
| Jul | 70 | 69.99 |
| Aug | 66 | 65.87 |
| Sep | 52 | 52.27 |
| Oct | 38 | 37.72 |
| Nov | 28 | 28.17 |
| Dec | 24 | 23.95 |
| Period | Forecast | 95% interval |
|---|---|---|
| Jan | 23.30 | 22.99 – 23.61 |
| Feb | 25.19 | 24.75 – 25.62 |
| Mar | 29.46 | 28.93 – 29.99 |
| Apr | 37.12 | 36.51 – 37.73 |
Parameters the engine found
intercept= 40.913trend= 0.107b0= 40.913b1= 0.107b2= -0.845b3= -23.107b4= 1.340b5= 4.773b6= -0.227b7= -0.560k= 8m= 12
The question
Twelve monthly gas-use figures show a winter peak and a mild rise. What is the time-series linear model forecast for the next four months? Sample months: Jan=22, Feb=24, Mar=28, Apr=36, May=48, Jun=62, Jul=70, Aug=66, Sep=52, Oct=38, Nov=28, Dec=24 (therms).
Design matrix
OLS on [1, t, sin/cos harmonics for m = 12]. No extra regressor on this page (future X would be 0 if omitted). 8 coefficients.
Fit
Intercept = 40.913, trend (per period) = 0.107. Other Fourier coefficients are in the parameter table. Fitted values in the table are Xβ on the sample.
Forecast
Plug t = n, n+1, … into the same columns. Jan: 23.30; Feb: 25.19; Mar: 29.46; Apr: 37.12.
Interval
Residual σ = 0.156. For h = 1 the 95% band is [22.99, 23.61] around 23.30. The engine labels this a residual-Gaussian heuristic (σ√h), not a simulation interval.
Graph of this sample
The chart plots the canned table on this page (actuals, in-sample fitted, forecast, 95% interval). Not your Excel series. Free analysis never uploads raw data.
Educational only. Not investment, weather, or operational advice. In the add-in, rank is rolling-origin MASE — “best supported among candidates on this series.”