Time Series: Box-Jenkins Method
Aug 26, 2017 · 2 min read
Named after statisticians George Box and Gwilym Jenkins
The method uses an iterative three-stage modeling approach:
- Model Identification
- Model Estimation
- Model Diagnostics
- Model Identification
- Make sure the variables are stationary
- Identify seasonality
- Detecting stationarity: look at run sequence plot and autocorrelation plot, non-stationarity is often indicated by an autocorrelation plot with slow decay


- Detecting seasonality: look at autocorrelation plot, seasonal subseries plot, or a spectral plot

- Spectral plot: Graphical technique for examining cyclic structure in the frequency domain. Trends should be removed from time series before applying the spectral plot. Spectral plots are often used to find the start value for the frequency in the sinusoidal model.


- Differencing to achieve stationarity: Differencing approach to achieve stationarity. However, fitting a curve and subtracting the fitted values from the original data can also be used
- Seasonal differencing: For monthly data, common method is to apply a AR(p = 12) term or MA(q = 12) term. One could remove seasonality before applying a model
- Identify p and q with autocorrelation plots

2. Model Estimation
- Maximum Likelihood Estimation (preferred technique)
- Non-linear Least Squares
3. Model Diagnostics
- Residuals should be white noise
- Residuals distribution should have a mean of 0
- If not, autocorrelation plot of the residuals and repeat above steps
- Also look at Box-Ljung statistics