Time-series: ARIMA versus holt-winters

Barclaeys

Hi,
Can someone explain me in simple words (I hope) the difference between the ARIMA and Holt-Winters model? How are these conceptually different and how will it change the outcome of the forecast?
Many thanks!!
Bart

David_A

Hi Bart,

in short the basic differences are, that ARIMA combines an auto-regressive part (that's the AR in the name) that means each point is influenced by it's previously values and a moving average part (the MA part of the name) which is basically a linear combination of several points. Both parts are integrated together (the I) to fit a best model for the series.

In contrast Holt-Winters splits the series into several part (a linear forecast, a trend component and a repeating seasonal component) and combines the results back together afterwards.

Those two different approaches can be seen in the outcome and shape of the forecast.

An ARIMA forecast might look quite "boring" because often it's a straight line that does not show any deviating patterns. But for the underlying mathematical model that's the best fit.

In contrast, Holt-Winters, especially if there is a strong seasonal pattern (seasonal depends on the data, but are often things like daily, weekly  or monthly patterns), build forecasts that look more akin to the original data. Which is always nice when trying to interpret or sell your model, but that might be also a bit deceptive.

So in general ARIMA is always a good starting point, but as soon as there is the assumption of some repeating pattern in the data (because you have some knowledge of the real-world process behind it), Holt-Winters might give you better results.

I hope this helps a bit.

Best,
David

David_A

Hi Bart,

in short the basic differences are, that ARIMA combines an auto-regressive part (that's the AR in the name) that means each point is influenced by it's previously values and a moving average part (the MA part of the name) which is basically a linear combination of several points. Both parts are integrated together (the I) to fit a best model for the series.

In contrast Holt-Winters splits the series into several part (a linear forecast, a trend component and a repeating seasonal component) and combines the results back together afterwards.

Those two different approaches can be seen in the outcome and shape of the forecast.

An ARIMA forecast might look quite "boring" because often it's a straight line that does not show any deviating patterns. But for the underlying mathematical model that's the best fit.

In contrast, Holt-Winters, especially if there is a strong seasonal pattern (seasonal depends on the data, but are often things like daily, weekly  or monthly patterns), build forecasts that look more akin to the original data. Which is always nice when trying to interpret or sell your model, but that might be also a bit deceptive.

So in general ARIMA is always a good starting point, but as soon as there is the assumption of some repeating pattern in the data (because you have some knowledge of the real-world process behind it), Holt-Winters might give you better results.

I hope this helps a bit.

Best,
David

Barclaeys

Thanks David, clear and understandable. Much appreciated.