SARIMA

SARIMA is the abbreviation for Seasonal Autoregressive Integrated Moving Average, a time series analysis in the fields of statistics and econometrics.

Without accounting for seasonality, we utilize three parameters:

p: Number of historical points considered for auto-regression (AR)
q: Number of historical points considered for moving averages (MA).
d: Number of times to apply differencing. Specifies that calculations should be made on the differences between consecutive points, rather than the raw points.

To make predictions, we maximize p and q historical points. This means that we use \$max(p,q)+d\$ historical points to make a prediction.

When considering seasonality, we add these additional parameters:

sp: Seasonally-adjusted number of historical points considered for auto-regression (AR)
sq: Seasonally-adjusted number of historical points considered for moving averages (MA).
sd: Seasonally-adjusted number of times to apply differencing.
sm: Number of discrete timestamps in a period.

In Kloudfuse, we implement the SARIMA algorithm as the agile option for anomaly detection.

In Dashboards

To use the sarima operator in a dashboard, apply the following function:

sarima( \
  ${promql}, \ (1)
  2, 1, 2, 0, 0, 0, 0, \
  ${bound}, \ (2)
  ${band} \ (3)
)

code

1	`${promql}`: PromQL query to evaluate
2	`${band}`: 4 = lower band, 5 = upper band, 6 = both upper and lower bands
3	`${bound}`: Number of standard deviations (stdv): 1, 2, or 3

Limitations

If the evaluated metrics do not exhibit true seasonality, SARIMA may create incorrect (invalid) alerts, or mask valid alerting conditions.

Next steps

For an in-depth discussion of the SARIMA functions, see these external resources:

Seasonal AutoRegressive Integrated Moving Average with eXogenous regressors model in StatsModels
Autoregressive integrated moving average in Wikipedia