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I got 95 weeks of sales data (i.e., 95 data points) for a retail business, whose plot looks like this:

Sales by Week

Sales are evidently seasonal. Also see plot for Year 1 against Year 2 Sales by Week of Year

Weekly sales by Year

I also got events defined for 8 of the 52 weeks in a year (e.g X-mas, Thanksgiving). Considering there is no other additional data on break-up of sales by Day of Week, stores, products or any other potential regressor, what would be your suggested approach to forecast weekly sales for Year 3?

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If you are looking to fit an ARIMA model, first you will have to make sure that the series is stationary. Also check if the variance is stable. If not, I would suggest a ln transformation.

Now important to note, since you have seasonality in your data, your will most like have to take a seasonal difference as well. I would suggest starting with a periodogram, using it to identify the period. From there you can use the ACF and PACF to identify your seasonal part and after that your non-seasonal part of the model. This will give you a SARIMA model. Remember to check that the residuals are white noise before you choose a model.

Forecasting a full year ahead with only two years of data, can prove to be somewhat difficult or rather, it could be inaccurate. Each new forecasted value should be a different week as you stated that each observation is a different week.

Hope this answers your question more or less! You are welcome to ask, give suggestions or make corrections to this.

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  • $\begingroup$ Thanks Neil. I am still researching on the approach. The primary challenge is data availability being limited to less than two full seasonal cycles. I will consider your input & update my response once I've worked on them. $\endgroup$
    – Nibbles
    Commented May 12, 2020 at 11:42
  • $\begingroup$ I accept your answer as my eventual solution was a SARIMA model with a seasonal differencing order of 1. Additionally, I included an explanatory variable which indicated annual events such as Thanksgiving, Also, I did manage to procure 3 years of data further from the past that indicated trend. To account for this, I chose linear de-trending over differencing as the trend was deterministic. $\endgroup$
    – Nibbles
    Commented Aug 10, 2020 at 9:47

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