Solved – Forecasting Intermittent Demand with zeroes in times series

crostons-methodforecastingintermittent time seriesrtime series

I am trying to forecast intermittent demand (slow movers and extreme slow movers).

Here's the type of data I am working with

weekly data so I cannot really group it
has zeroes in time series
not sure if seasonal (at least not visibly)

Based on some research, I think I can use Croston's method for this type of data, but I want to know what the general approach is for handling this type of lumpy data with zeroes in it.

Burning questions for now would be-

How to handle zeroes in data
What models are generally used for Intermittent data
How to model seasonality if it's present

I am using R for my analysis.

https://drive.google.com/file/d/1_yfz1q9d0tih5WRmfzRWpedkeQvF3ctB/view?usp=sharing

Best Answer

I found the article by professor Hyndman for forecasting intermittent data very helpful. Although its main focus is on the error measurements, it suggests four simple models for forecasting intermittent data:

The historical mean
The naïve or random walk method
Simple exponential smoothing
As you suggested, and the most common for intermittent data as far as I know; Croston’s method for intermittent demands (Boylan, 2005)

Related Solutions

Solved – Error in optim – Auto.arima R

The following works in the sense that it returns a valid model:

library(forecast)
sku1 <- read.csv("Sample.csv")
actual_val = ts(sku1$Sal , frequency = 52)
dummy_val = seasonaldummy(actual_val) 
model_value <- auto.arima(actual_val , xreg = dummy_val )

Perhaps your problem is that you haven't defined xreg_val.

However, it isn't a sensible model as you use 51 degrees of freedom for seasonality but have only two years of daily data. I suggest you use Fourier terms instead:

seas <- fourier(actual_val, K=10)
model_value <- auto.arima(actual_val , xreg = seas , lambda=0) 
plot(forecast(model_value, xreg=fourierf(actual_val, h=52, K=10), lambda=0))

Solved – What will be frequency for daily observation in time series and how to deal with 0 values

ARIMA models are not very well suited for forecasting daily store sales.

You have multiple seasonalities. The intra-weekly seasonality is usually strongest, so you could in principle work with frequency=7 and hope for the best. However, there often is also yearly seasonality (frequency=365), or biweekly/monthly seasonality (frequency=14 or frequency=365/12 - not sure whether this even works) driven by paychecks. Standard ARIMA implementation can't deal with more than one seasonality. And long seasonal cycles are problematic for ARIMA.
You have store closures with zero sales on Sundays, which you very sensibly set to NA. However, ARIMA can't deal with NAs. You could in principle pretend to have a six-day week, remove all NAs and use frequency=6 - unless you have additional store closure days apart from Sundays (e.g., Christmas). ARIMA will run into problems here.
You will often have additional effects, like Black Friday, Christmas, Chinese New Year and so forth. You could in principle model these using a regression with ARIMA errors, using Boolean or ramp-up dummies.

Your best bet might be to run a regression with day-of-week dummies and harmonics or hump functions to model yearly seasonality, as well as ramp-ups or similar to model any special holiday effects, possibly try ARIMA errors using auto.arima - but fit the seasonality using the dummies, not the ARIMA part.

You may want to look through some of our earlier questions on daily time series.

Best Answer

Related Solutions

Solved – Error in optim – Auto.arima R

Solved – What will be frequency for daily observation in time series and how to deal with 0 values

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