Choosing right value of m in SARIMA models

Question

If I'm trying to avoid Auto-Arima function, is their any handy table/reference list which I can refer to for knowing what value of m to choose for working with SARIMA(p, d, q)(P, D, Q)m model?

Or, is these collation of values from different sources right?

• Daily data m=7,
• Weekly data m=53,
• Monthly data m=12,
• Quarterly data m=4

Answer 1

Automatic ARIMA fitting methods require the seasonal order as an input, they don't choose or fit $m$, so I'm not quite sure why you think avoiding auto.arima has anything to do with the choice of $m$.

The season length $m$ is the number of periods after which you expect a pattern to repeat. It does not necessarily have anything to do with your time granularity.

• Daily data can have $m=7$ (weekly seasonality), $m=14$ (biweekly seasonality, e.g., paycheck effects in locales where salaries are paid out every two weeks), $m\approx 30$ or $31$ (monthly seasonality), or $m\approx 365$ (yearly seasonality).
• Weekly data can have $m=2$ (biweekly seasonality), $m=4$ (four-weekly seasonality), or $m\approx 53$ (yearly seasonality).
• Monthly data can have $m=3$ (quarterly seasonality) or $m=12$ (yearly seasonality).
• Quarterly data can have $m=4$ (yearly seasonality).

In all these cases, many other values of $m$ are possible. If you want to model quarterly approval ratings of US presidents, you may want to use $m=16$ (four years in office, four quarters each). Your choice of $m$ should be governed by your use case.

Note that ARIMA has a hard time dealing with multiple-seasonalities.